diff --git a/404.html b/404.html index bd6da7a..fe98353 100755 --- a/404.html +++ b/404.html @@ -1 +1 @@ - WelSim Documentation

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\ No newline at end of file diff --git a/beamsection/beamsection_getstart/index.html b/beamsection/beamsection_getstart/index.html index 7548882..058bac2 100644 --- a/beamsection/beamsection_getstart/index.html +++ b/beamsection/beamsection_getstart/index.html @@ -1 +1 @@ - Getting Started - WelSim Documentation
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Getting Started

Using BeamSection is straightforward, this section shows you how to calculate the beam properties step by step.

Graphical Interface

An overview of the Graphical User Interface (GUI) with notation is shown in the figure below.

finite_element_analysis_curvefit_gui_notation

This section provides you basic actions in using CurveFitter. The actions include:

  • Exit: Quits the program.
  • Help: Runs your default web browser and visits official website welsim.com/curvefit.
  • About: Displays About dialog and shows software and hardware information.

Toolbox

This section lists all available curves for you to choose from. The default curve is the straight line (first-order polynomial). The curves are grouped by the characteristics as follows.

Basic Curves

Straight line, Natural logarithm, Exponential, Power, Gaussian

Polynomial Curves

2nd Order Polynomial, 3rd Order Polynomial, 4th Order Polynomial, 5th Order Polynomial

Nonlinear Curves

Symmetrical Sigmoidal, Asymmetrical Sigmoidal, Rectangular Hyperbola, Basic Exponential, Half-Life Exponential, Proportional Rate Growth or Decrease

Hyperelastic Material Model Curves

Arruda-Boyce, Gent, Mooney-Rivlin 2, 3, 5, and 9 Parameters, Neo-Hookean, Ogden 1st-3rd Orders, Polynomial 1st-3rd Orders, Yeoh 1st-3rd Orders

Electromagnetic Model Curves

Electrical Steel, Power Ferrite

Curve Description

This section contains details about the selected curve, such as the function or energy functional, parameters to fit, variable descriptions.

For the hyperelastic model curves, additional Hyperelastic Test Data checkboxes shows in this seciton. It allows users to set/edit the test data at different deformations.

Fitted Parameters

This section outputs the fitted parameters for users. You also can edit the constants in the line edit widget and review the curves in the Chart window.

Actions

There are three actions provided for users to analyze or fit the test data.

  • Check button: examines the input data in the tabular data window.
  • Solve button: solves the curve fitting based on the input tabular data. The check process is implemented before the solution. If the curve fitting succeeded, the fitted constants will be set in the Fitted Parameters section, the curves will be plotted in the Chart window as well.
  • Update Chart button: allows you to update the curves in the Chart window with the current constants.

Chart Windows

This section displays the test data dots and fitted curves in the same window, these dots and curves can be differentiated by legends and colors. Zoom in and out showing area are supported. You also can set the logarithmic axis for the curve display.

Workflow

This section demonstrates the procedures in applying curve fitting. The steps are followed:

  1. Select the designated curve type from the toolbox.
    finite_element_analysis_curvefit_select_curve

  2. Edit table data or import data from an external file.
    finite_element_analysis_curvefit_edit_table

  3. Review the test data in the Chart.
    finite_element_analysis_curvefit_review_testdata

  4. Check the input data (Optional). A pop-up message box indicates the status of the input data.
    finite_element_analysis_curvefit_check

  5. Solve the curves with the input tabular data. If it succeeded, the Constants line edits are filled with fitted parameters, and the Chart window displays the fitted curves along with the test data. These fitted parameters are the answers that we want.
    finite_element_analysis_curvefit_solve

  6. Adjust parameters to evaluate the similar curves (Optional). You can change the parameters and hit the Update Chart button to see the new curves with modified parameters.

Note

Your test data is critical for your fitted constants, please ensure that the test data cover the entire range of your curve expreience.

\ No newline at end of file + Getting Started - WelSim Documentation
Skip to content

Getting Started

Using BeamSection is straightforward, this section shows you how to calculate the beam properties step by step.

Graphical Interface

An overview of the Graphical User Interface (GUI) with notation is shown in the figure below.

finite_element_analysis_curvefit_gui_notation

This section provides you basic actions in using CurveFitter. The actions include:

  • Exit: Quits the program.
  • Help: Runs your default web browser and visits official website welsim.com/curvefit.
  • About: Displays About dialog and shows software and hardware information.

Toolbox

This section lists all available curves for you to choose from. The default curve is the straight line (first-order polynomial). The curves are grouped by the characteristics as follows.

Basic Curves

Straight line, Natural logarithm, Exponential, Power, Gaussian

Polynomial Curves

2nd Order Polynomial, 3rd Order Polynomial, 4th Order Polynomial, 5th Order Polynomial

Nonlinear Curves

Symmetrical Sigmoidal, Asymmetrical Sigmoidal, Rectangular Hyperbola, Basic Exponential, Half-Life Exponential, Proportional Rate Growth or Decrease

Hyperelastic Material Model Curves

Arruda-Boyce, Gent, Mooney-Rivlin 2, 3, 5, and 9 Parameters, Neo-Hookean, Ogden 1st-3rd Orders, Polynomial 1st-3rd Orders, Yeoh 1st-3rd Orders

Electromagnetic Model Curves

Electrical Steel, Power Ferrite

Curve Description

This section contains details about the selected curve, such as the function or energy functional, parameters to fit, variable descriptions.

For the hyperelastic model curves, additional Hyperelastic Test Data checkboxes shows in this seciton. It allows users to set/edit the test data at different deformations.

Fitted Parameters

This section outputs the fitted parameters for users. You also can edit the constants in the line edit widget and review the curves in the Chart window.

Actions

There are three actions provided for users to analyze or fit the test data.

  • Check button: examines the input data in the tabular data window.
  • Solve button: solves the curve fitting based on the input tabular data. The check process is implemented before the solution. If the curve fitting succeeded, the fitted constants will be set in the Fitted Parameters section, the curves will be plotted in the Chart window as well.
  • Update Chart button: allows you to update the curves in the Chart window with the current constants.

Chart Windows

This section displays the test data dots and fitted curves in the same window, these dots and curves can be differentiated by legends and colors. Zoom in and out showing area are supported. You also can set the logarithmic axis for the curve display.

Workflow

This section demonstrates the procedures in applying curve fitting. The steps are followed:

  1. Select the designated curve type from the toolbox.
    finite_element_analysis_curvefit_select_curve

  2. Edit table data or import data from an external file.
    finite_element_analysis_curvefit_edit_table

  3. Review the test data in the Chart.
    finite_element_analysis_curvefit_review_testdata

  4. Check the input data (Optional). A pop-up message box indicates the status of the input data.
    finite_element_analysis_curvefit_check

  5. Solve the curves with the input tabular data. If it succeeded, the Constants line edits are filled with fitted parameters, and the Chart window displays the fitted curves along with the test data. These fitted parameters are the answers that we want.
    finite_element_analysis_curvefit_solve

  6. Adjust parameters to evaluate the similar curves (Optional). You can change the parameters and hit the Update Chart button to see the new curves with modified parameters.

Note

Your test data is critical for your fitted constants, please ensure that the test data cover the entire range of your curve expreience.

\ No newline at end of file diff --git a/beamsection/beamsection_overview/index.html b/beamsection/beamsection_overview/index.html index 08be021..c0ec733 100644 --- a/beamsection/beamsection_overview/index.html +++ b/beamsection/beamsection_overview/index.html @@ -1,4 +1,4 @@ - Overview - WelSim Documentation
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Beam Cross-Section Overview

BeamSection is a free beam cross-section software program for engineers. This tool provides you comprehensive beam property calculations those are often used in engineering simulation and practice.

finite_element_analysis_curvefit_gui

WelSim/docs

Beam Cross-Section Overview

BeamSection is a free beam cross-section software program for engineers. This tool provides you comprehensive beam property calculations those are often used in engineering simulation and practice.

finite_element_analysis_curvefit_gui

Questions or Comments?

Feel free to send questions, comments, requests, bug reports, and success stories. Asking for a new feature usually results in adding the request to the TODO list or, if it already is in the list, in assigning higher priority to it.

\ No newline at end of file +![finite_element_analysis_curvefit_coreloss](../img/curvefitter/curve_fitter_coreloss.png "Core Loss curve fitting example in CurveFitter") -->

Questions or Comments?

Feel free to send questions, comments, requests, bug reports, and success stories. Asking for a new feature usually results in adding the request to the TODO list or, if it already is in the list, in assigning higher priority to it.

\ No newline at end of file diff --git a/curvefitter/curvefit_getstart/index.html b/curvefitter/curvefit_getstart/index.html index f894082..30d2b0f 100755 --- a/curvefitter/curvefit_getstart/index.html +++ b/curvefitter/curvefit_getstart/index.html @@ -1 +1 @@ - Getting Started - WelSim Documentation
Skip to content

Getting Started

Using CurveFitter is straightforward, this section shows you how to conduct the curve fitting step by step.

Graphical Interface

An overview of the Graphical User Interface (GUI) with notation is shown in the figure below.

finite_element_analysis_curvefit_gui_notation

This section provides you basic actions in using CurveFitter. The actions include:

  • Exit: Quits the program.
  • Help: Runs your default web browser and visits official website welsim.com/curvefit.
  • About: Displays About dialog and shows software and hardware information.

Toolbox

This section lists all available curves for you to choose from. The default curve is the straight line (first-order polynomial). The curves are grouped by the characteristics as follows.

Basic Curves

Straight line, Natural logarithm, Exponential, Power, Gaussian

Polynomial Curves

2nd Order Polynomial, 3rd Order Polynomial, 4th Order Polynomial, 5th Order Polynomial

Nonlinear Curves

Symmetrical Sigmoidal, Asymmetrical Sigmoidal, Rectangular Hyperbola, Basic Exponential, Half-Life Exponential, Proportional Rate Growth or Decrease

Hyperelastic Material Model Curves

Arruda-Boyce, Gent, Mooney-Rivlin 2, 3, 5, and 9 Parameters, Neo-Hookean, Ogden 1st-3rd Orders, Polynomial 1st-3rd Orders, Yeoh 1st-3rd Orders

Electromagnetic Model Curves

Electrical Steel, Power Ferrite

Curve Description

This section contains details about the selected curve, such as the function or energy functional, parameters to fit, variable descriptions.

For the hyperelastic model curves, additional Hyperelastic Test Data checkboxes shows in this seciton. It allows users to set/edit the test data at different deformations.

Fitted Parameters

This section outputs the fitted parameters for users. You also can edit the constants in the line edit widget and review the curves in the Chart window.

Actions

There are three actions provided for users to analyze or fit the test data.

  • Check button: examines the input data in the tabular data window.
  • Solve button: solves the curve fitting based on the input tabular data. The check process is implemented before the solution. If the curve fitting succeeded, the fitted constants will be set in the Fitted Parameters section, the curves will be plotted in the Chart window as well.
  • Update Chart button: allows you to update the curves in the Chart window with the current constants.

Tabular Data Windows

This section enables you to edit and review the table data. For most of curves, the tables have two columns. The frequency-dependent curves have a sub-table for each frequency row. You can input tabular values cell by cell, or import a plain text or Excel file to input massive data. The external file formats are depicted here.

You also can export the tabular data to an external file in plain text or Excel format.

Chart Windows

This section displays the test data dots and fitted curves in the same window, these dots and curves can be differentiated by legends and colors. Zoom in and out showing area are supported. You also can set the logarithmic axis for the curve display.

Workflow

This section demonstrates the procedures in applying curve fitting. The steps are followed:

  1. Select the designated curve type from the toolbox.
    finite_element_analysis_curvefit_select_curve

  2. Edit table data or import data from an external file.
    finite_element_analysis_curvefit_edit_table

  3. Review the test data in the Chart.
    finite_element_analysis_curvefit_review_testdata

  4. Check the input data (Optional). A pop-up message box indicates the status of the input data.
    finite_element_analysis_curvefit_check

  5. Solve the curves with the input tabular data. If it succeeded, the Constants line edits are filled with fitted parameters, and the Chart window displays the fitted curves along with the test data. These fitted parameters are the answers that we want.
    finite_element_analysis_curvefit_solve

  6. Adjust parameters to evaluate the similar curves (Optional). You can change the parameters and hit the Update Chart button to see the new curves with modified parameters.

Note

Your test data is critical for your fitted constants, please ensure that the test data cover the entire range of your curve expreience.

\ No newline at end of file + Getting Started - WelSim Documentation
Skip to content

Getting Started

Using CurveFitter is straightforward, this section shows you how to conduct the curve fitting step by step.

Graphical Interface

An overview of the Graphical User Interface (GUI) with notation is shown in the figure below.

finite_element_analysis_curvefit_gui_notation

This section provides you basic actions in using CurveFitter. The actions include:

  • Exit: Quits the program.
  • Help: Runs your default web browser and visits official website welsim.com/curvefit.
  • About: Displays About dialog and shows software and hardware information.

Toolbox

This section lists all available curves for you to choose from. The default curve is the straight line (first-order polynomial). The curves are grouped by the characteristics as follows.

Basic Curves

Straight line, Natural logarithm, Exponential, Power, Gaussian

Polynomial Curves

2nd Order Polynomial, 3rd Order Polynomial, 4th Order Polynomial, 5th Order Polynomial

Nonlinear Curves

Symmetrical Sigmoidal, Asymmetrical Sigmoidal, Rectangular Hyperbola, Basic Exponential, Half-Life Exponential, Proportional Rate Growth or Decrease

Hyperelastic Material Model Curves

Arruda-Boyce, Gent, Mooney-Rivlin 2, 3, 5, and 9 Parameters, Neo-Hookean, Ogden 1st-3rd Orders, Polynomial 1st-3rd Orders, Yeoh 1st-3rd Orders

Electromagnetic Model Curves

Electrical Steel, Power Ferrite

Curve Description

This section contains details about the selected curve, such as the function or energy functional, parameters to fit, variable descriptions.

For the hyperelastic model curves, additional Hyperelastic Test Data checkboxes shows in this seciton. It allows users to set/edit the test data at different deformations.

Fitted Parameters

This section outputs the fitted parameters for users. You also can edit the constants in the line edit widget and review the curves in the Chart window.

Actions

There are three actions provided for users to analyze or fit the test data.

  • Check button: examines the input data in the tabular data window.
  • Solve button: solves the curve fitting based on the input tabular data. The check process is implemented before the solution. If the curve fitting succeeded, the fitted constants will be set in the Fitted Parameters section, the curves will be plotted in the Chart window as well.
  • Update Chart button: allows you to update the curves in the Chart window with the current constants.

Tabular Data Windows

This section enables you to edit and review the table data. For most of curves, the tables have two columns. The frequency-dependent curves have a sub-table for each frequency row. You can input tabular values cell by cell, or import a plain text or Excel file to input massive data. The external file formats are depicted here.

You also can export the tabular data to an external file in plain text or Excel format.

Chart Windows

This section displays the test data dots and fitted curves in the same window, these dots and curves can be differentiated by legends and colors. Zoom in and out showing area are supported. You also can set the logarithmic axis for the curve display.

Workflow

This section demonstrates the procedures in applying curve fitting. The steps are followed:

  1. Select the designated curve type from the toolbox.
    finite_element_analysis_curvefit_select_curve

  2. Edit table data or import data from an external file.
    finite_element_analysis_curvefit_edit_table

  3. Review the test data in the Chart.
    finite_element_analysis_curvefit_review_testdata

  4. Check the input data (Optional). A pop-up message box indicates the status of the input data.
    finite_element_analysis_curvefit_check

  5. Solve the curves with the input tabular data. If it succeeded, the Constants line edits are filled with fitted parameters, and the Chart window displays the fitted curves along with the test data. These fitted parameters are the answers that we want.
    finite_element_analysis_curvefit_solve

  6. Adjust parameters to evaluate the similar curves (Optional). You can change the parameters and hit the Update Chart button to see the new curves with modified parameters.

Note

Your test data is critical for your fitted constants, please ensure that the test data cover the entire range of your curve expreience.

\ No newline at end of file diff --git a/curvefitter/curvefit_io/index.html b/curvefitter/curvefit_io/index.html index f7bedb3..f78c3e9 100755 --- a/curvefitter/curvefit_io/index.html +++ b/curvefitter/curvefit_io/index.html @@ -1 +1 @@ - I/O File Format - WelSim Documentation
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I/O File Format

The I/O file format is consistent to the Import/Export format in MatEditor module. For more details please refer to the Import/Export Tabular Data

\ No newline at end of file + I/O File Format - WelSim Documentation
Skip to content

I/O File Format

The I/O file format is consistent to the Import/Export format in MatEditor module. For more details please refer to the Import/Export Tabular Data

\ No newline at end of file diff --git a/curvefitter/curvefit_overview/index.html b/curvefitter/curvefit_overview/index.html index fb7c45e..873f572 100755 --- a/curvefitter/curvefit_overview/index.html +++ b/curvefitter/curvefit_overview/index.html @@ -1,4 +1,4 @@ - Overview - WelSim Documentation
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Curve Fitter Overview

CurveFitter is a free software program for nonlinear curve fitting of analytical functions to experimental data. It provides tools for linear, polynomial, exponential, power, Schulz-Flory, nonlinear, hyperelastic materials, magnetic core loss curve fitting along with validation, and goodness-of-fit tests. The easy-to-use graphical user interface enables you to start fitting projects with no learning curves. You can summarize and present your results with customized fitting reports. There are many time-saving options such as an import-export feature which allows you to quickly input/output massive tabular data from/to external files.

finite_element_analysis_curvefit_gui

Curve fitting is one of the most widely used analysis methods in science and technology. Curve fitting examines the relationship between one or more predictors (independent variables) and a response variable (dependent variable), with the goal of defining a "best fit" model of the relationship. It is reportedly used in crystallography, chromatography, photoluminescence and photoelectron spectroscopy, infrared, Raman spectroscopy, and finite element analysis.

Specification

The system requirements for running CurveFitter are given in the table below.

Specification Description
Operation system Microsoft Windows 10 to 11; 64-bit
Physical memory At least 4 GB
Import/Export file format Plain text, Excel

The supported functions/curves are listed in the table below.

Category Materials
Basic Straight line, Natural logarithm, Exponential, Power, Gaussian
Polynomial 2nd-5th Order Polynomial
Schulz-Flory 1nd-6th Order Schulz-Flory
Nonlinear Symmetrical Sigmoidal, Asymmetrical Sigmoidal, Rectangular Hyperbola, Basic Exponential, Half-Life Exponential, Proportional Rate Growth or Decrease
Hyperelastic material model Arruda-Boyce, Gent, Mooney-Rivlin 2 3 5 and 9 Parameters, Neo-Hookean, 1st-3rd Order Ogden, 1st-3rd Order Polynomial, 1st-3rd Order Yeoh
Electromagnetic Core loss Model Electrical Steel, Power Ferrite (Steinmetz)

Linear, Polynomial Regression

Linear and Polynomial regressions in CurveFitter make use of the least-square method to fit a linear model function or a polynomial model function to data, respectively.

finite_element_analysis_curvefit_polynomial

Nonlinear Curve Fitting

CurveFitter's nonlinear fit tool is powerful, flexible, and easy to use. This tool includes more than 10 built-in fitting functions, selected from a wide range of categories and disciplines.

finite_element_analysis_curvefit_nonlinear

WelSim/docs

Curve Fitter Overview

CurveFitter is a free software program for nonlinear curve fitting of analytical functions to experimental data. It provides tools for linear, polynomial, exponential, power, Schulz-Flory, nonlinear, hyperelastic materials, magnetic core loss curve fitting along with validation, and goodness-of-fit tests. The easy-to-use graphical user interface enables you to start fitting projects with no learning curves. You can summarize and present your results with customized fitting reports. There are many time-saving options such as an import-export feature which allows you to quickly input/output massive tabular data from/to external files.

finite_element_analysis_curvefit_gui

Curve fitting is one of the most widely used analysis methods in science and technology. Curve fitting examines the relationship between one or more predictors (independent variables) and a response variable (dependent variable), with the goal of defining a "best fit" model of the relationship. It is reportedly used in crystallography, chromatography, photoluminescence and photoelectron spectroscopy, infrared, Raman spectroscopy, and finite element analysis.

Specification

The system requirements for running CurveFitter are given in the table below.

Specification Description
Operation system Microsoft Windows 10 to 11; 64-bit
Physical memory At least 4 GB
Import/Export file format Plain text, Excel

The supported functions/curves are listed in the table below.

Category Materials
Basic Straight line, Natural logarithm, Exponential, Power, Gaussian
Polynomial 2nd-5th Order Polynomial
Schulz-Flory 1nd-6th Order Schulz-Flory
Nonlinear Symmetrical Sigmoidal, Asymmetrical Sigmoidal, Rectangular Hyperbola, Basic Exponential, Half-Life Exponential, Proportional Rate Growth or Decrease
Hyperelastic material model Arruda-Boyce, Gent, Mooney-Rivlin 2 3 5 and 9 Parameters, Neo-Hookean, 1st-3rd Order Ogden, 1st-3rd Order Polynomial, 1st-3rd Order Yeoh
Electromagnetic Core loss Model Electrical Steel, Power Ferrite (Steinmetz)

Linear, Polynomial Regression

Linear and Polynomial regressions in CurveFitter make use of the least-square method to fit a linear model function or a polynomial model function to data, respectively.

finite_element_analysis_curvefit_polynomial

Nonlinear Curve Fitting

CurveFitter's nonlinear fit tool is powerful, flexible, and easy to use. This tool includes more than 10 built-in fitting functions, selected from a wide range of categories and disciplines.

finite_element_analysis_curvefit_nonlinear

Hyperelastic Material Model Fitting

CurveFitter's hyperelastic model fitting tool allows you to obtain material constants from the uniaxial, biaxial, or shear test data. You can choose the available test data type by toggling the corresponding checkbox. The supported hyperelastic models are: Arruda-Boyce, Gent, Mooney-Rivlin, Neo-Hookean, Ogden, Polynomial, and Yeoh. The input test data is engineering strain and engineering stress.

finite_element_analysis_curvefit_hyperelastic

Magnetic Core Loss Model Fitting

Core Loss Model fitting tool enables you to fit the parameters in estimating energy loss analysis. The tabular data window contains both regular tables and sub-tables for you to input multiple frequency-based data. The chart supports the logarithmic axis to better review the frequency-based curves.

finite_element_analysis_curvefit_coreloss

Questions or Comments?

Feel free to send questions, comments, requests, bug reports, and success stories. Asking for a new feature usually results in adding the request to the TODO list or, if it already is in the list, in assigning higher priority to it.

\ No newline at end of file +![finite_element_analysis_curvefit_surface](../img/curvefitter/curve_fitter_surface.png "Surface fitting example") -->

Hyperelastic Material Model Fitting

CurveFitter's hyperelastic model fitting tool allows you to obtain material constants from the uniaxial, biaxial, or shear test data. You can choose the available test data type by toggling the corresponding checkbox. The supported hyperelastic models are: Arruda-Boyce, Gent, Mooney-Rivlin, Neo-Hookean, Ogden, Polynomial, and Yeoh. The input test data is engineering strain and engineering stress.

finite_element_analysis_curvefit_hyperelastic

Magnetic Core Loss Model Fitting

Core Loss Model fitting tool enables you to fit the parameters in estimating energy loss analysis. The tabular data window contains both regular tables and sub-tables for you to input multiple frequency-based data. The chart supports the logarithmic axis to better review the frequency-based curves.

finite_element_analysis_curvefit_coreloss

Questions or Comments?

Feel free to send questions, comments, requests, bug reports, and success stories. Asking for a new feature usually results in adding the request to the TODO list or, if it already is in the list, in assigning higher priority to it.

\ No newline at end of file diff --git a/curvefitter/curvefit_theory/index.html b/curvefitter/curvefit_theory/index.html index c2f9bd7..e4bc013 100755 --- a/curvefitter/curvefit_theory/index.html +++ b/curvefitter/curvefit_theory/index.html @@ -1 +1 @@ - Theory - WelSim Documentation
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Curve Fitting Theory

The section shows you the theoretical details of each curve or function.

Basic Curves

The group of Basic contains all commonly used curves.

Straight line

The function of this curve is given by

\[ y(x)=a+bx \]

where \(a\) and \(b\) are constants to fit, \(x\) and \(y\) are the test data pair. This function is also called 1st order polynomial.

Natural logarithm

The function of this curve is given by

\[ y(x)=a+b \cdot ln(x) \]

where \(a\) and \(b\) are constants to fit, \(x\) and \(y\) are the test data pair.

Note

Independent variable \(x\) must be larger than zero.

Exponential

The function of this curve is given by

\[ y(x)=ae^{bx} \]

where \(a\) and \(b\) are constants to fit, \(x\) and \(y\) are the test data pair.

Note

Dependent variable \(y\) must be larger than zero.

Power

The function of this curve is given by

\[ y(x)=ax^{b} \]

where \(a\) and \(b\) are constants to fit, \(x\) and \(y\) are the test data pair.

Note

Variables \(x\) and \(y\) must be larger than zero.

Gaussian

The function of this curve is given by

\[ y(x)=a \exp{(-\dfrac{(x-b)^2}{2c^2})} \]

where \(a\), \(b\), and \(c\) are constants to fit, \(x\) and \(y\) are the test data pair.

Note

Dependent variables \(y\) must be larger than zero.

Polynomial Curves

The group of Polynomial contains polynomial curves. The first-order polynomial is located in the Basic group as Straight Line.

2nd Order Polynomial

The function of this curve is given by

\[ y(x)=a+bx+cx^2 \]

where \(a\), \(b\), and \(c\) are constants to fit, \(x\) and \(y\) are the test data pair.

3rd Order Polynomial

The function of this curve is given by

\[ y(x)=a+bx+cx^2+dx^3 \]

where \(a\), \(b\), \(c\), and \(d\) are constants to fit, \(x\) and \(y\) are the test data pair.

4th Order Polynomial

The function of this curve is given by

\[ y(x)=a+bx+cx^2+dx^3+ex^4 \]

where \(a\), \(b\), \(c\), \(d\), and \(e\) are constants to fit, \(x\) and \(y\) are the test data pair.

5th Order Polynomial

The function of this curve is given by

\[ y(x)=a+bx+cx^2+dx^3+ex^4+ex^5 \]

where \(a\), \(b\), \(c\), \(d\), \(e\), and \(f\) are constants to fit, \(x\) and \(y\) are the test data pair.

Schulz-Flory functions

Schulz Flory distribution function to describe relative ratios of polymers after a polymerization process. The function of this curve is given by

\[ y(x) = \sum_{i=1}^{n} ln(10) \dfrac{a_i}{b_i^2} \exp{(4.6x-\dfrac{\exp{(2.3x)}}{b_i})} \]

where \(a_i\) and \(b_i\) are constants to fit, \(x\) and \(y\) are the test data pair. The parameter must satisfy the condition: \(0<a_i<1\).

Nonlinear Curves

The group of Nonlinear curves contains nonlinear curves that do not belong to the polynomial.

Symmetrical Sigmoidal

The function of this curve is given by

\[ y(x)=d + \dfrac{a-d}{1+(\dfrac{x}{c})^b} \]

where \(a\), \(b\), \(c\), and \(d\) are constants to fit, \(x\) and \(y\) are the test data pair.

Asymmetrical Sigmoidal

The function of this curve is given by

\[ y(x)=d + \dfrac{a-d}{ (1+(\dfrac{x}{c})^b)^m } \]

where \(a\), \(b\), \(c\), \(d\), and \(m\) are constants to fit, \(x\) and \(y\) are the test data pair.

Rectangular Hyperbola

The function of this curve is given by

\[ y(x)=\dfrac{V_{max}x}{ K_m + x} \]

where \(V_{max}\) and \(K_m\) are constants to fit, \(x\) and \(y\) are the test data pair.

Basic Exponential

The function of this curve is given by

\[ y(x)=a + be^{-cx} \]

where \(a\), \(b\), and \(c\) are constants to fit, \(x\) and \(y\) are the test data pair.

Half-Life Exponential

The function of this curve is given by

\[ y(x)=a + \dfrac{b}{2^{(\dfrac{x}{c})}} \]

where \(a\), \(b\), and \(c\) are constants to fit, \(x\) and \(y\) are the test data pair.

Proportional Rate Growth or Decrease

The function of this curve is given by

\[ y(x)=Y_0 + \dfrac{V_0}{K}(1-e^{-Kx}) \]

where \(Y_0\), \(V_0\), and \(K\) are constants to fit, \(x\) and \(y\) are the test data pair.

Log-Normal Particle Size Distribution

The function of this curve is given by

\[ \dfrac{dy(x)}{d\ln{x}}=\dfrac{C_t}{\sigma_g\sqrt{2}\pi} \exp{(-\dfrac{(\ln{x}-\ln{D_m})^2}{2\ln{\sigma_g}^2})} \]

where \(D_m\), \(\sigma_g\), and \(C_t\) are constants to fit, x and y are test data pair. In the computation, the Left-Hand-Side term (\(dy(x)/d\ln{x}\)) is calculated using finite difference scheme.

Note

Independent variables \(x\) must be larger than zero. The number of input x-y pairs must be large than 3.

Hyperelastic Material Model Curves

The group of hyperelastic material models contains the commonly used hyperelastic models in the finite element analysis. The test data pair is engineering strain and stress.

Arruda-Boyce

The form of the strain-energy potential for Arruda-Boyce model is

\[ \begin{array}{ccl} W & = & \mu[\dfrac{1}{2}(\bar{I}_{1}-3)+\dfrac{1}{20\lambda_{m}^{2}}(\bar{I_{1}^{2}}-9)+\dfrac{11}{1050\lambda_{m}^{4}}(\bar{I_{1}^{3}}-27)\\ & + & \dfrac{19}{7000\lambda_{m}^{6}}(\bar{I_{1}^{4}}-81) + \dfrac{519}{673750\lambda_{m}^{8}}(\bar{I_{1}^{5}}-243)] \end{array} \]

where \(\mu\) is the initial shear modulus of the material, \(\lambda_{m}\) is limiting network stretch.

Gent

The form of the strain-energy potential for the Gent model is:

\[ W=-\frac{\mu J_{m}}{2}\mathrm{ln}\left(1-\frac{\bar{I}_{1}-3}{J_{m}}\right) \]

where \(\mu\) is the initial shear modulus of the material, \(J_m\) is limiting value of \(\bar{I}_1-3\).

Mooney-Rivlin 2 3 5 and 9 Parameters

This model includes two-, three-, five-, and nine-terma Mooney-Rivlin models. The form of the strain-energy potential for a two-parameter Mooney-Rivlin model is

\[ W=C_{10}\left(\bar{I}_{1}-3\right)+C_{01}\left(\bar{I}_{2}-3\right) \]

where \(C_{10}\), \(C_{01}\), and \(D_{1}\) are the material constants.

The form of strain-energy potential for a three-parameter Mooney-Rivlin model is

\[ W=C_{10}\left(\bar{I}_{1}-3\right)+C_{01}\left(\bar{I}_{2}-3\right)+C_{11}\left(\bar{I}_{1}-3\right)\left(\bar{I}_{2}-3\right) \]

where \(C_{10}\), \(C_{01}\), and \(C_{11}\) are material constants.

The form of strain-energy potential for a five-parameter Mooney-Rivlin model is

\[ \begin{array}{ccl} W & = & C_{10}\left(\bar{I}_{1}-3\right)+C_{01}\left(\bar{I}_{2}-3\right)+C_{20}\left(\bar{I}_{1}-3\right)^{2}\\ & + & C_{11}\left(\bar{I}_{1}-3\right)\left(\bar{I}_{2}-3\right)+C_{02}\left(\bar{I}_{2}-3\right)^{2} \end{array} \]

where \(C_{10}\), \(C_{01}\), \(C_{20}\), \(C_{11}\), and \(C_{02}\) are material constants.

The form of strain-energy potential for a nine-parameter Mooney-Rivlin model is

\[ \begin{array}{ccl} W & = & C_{10}\left(\bar{I}_{1}-3\right)+C_{01}\left(\bar{I}_{2}-3\right)+C_{20}\left(\bar{I}_{1}-3\right)^{2}\\ & + & C_{11}\left(\bar{I}_{1}-3\right)\left(\bar{I}_{2}-3\right)+C_{02}\left(\bar{I}_{2}-3\right)^{2}+C_{30}\left(\bar{I}_{1}-3\right)^{3}\\ & + & C_{21}\left(\bar{I}_{1}-3\right)^{2}\left(\bar{I}_{2}-3\right)+C_{12}\left(\bar{I}_{1}-3\right)\left(\bar{I}_{2}-3\right)^{2}+C_{03}\left(\bar{I}_{2}-3\right)^{3} \end{array} \]

where \(C_{10}\), \(C_{01}\), \(C_{20}\), \(C_{11}\), \(C_{02}\), \(C_{30}\), \(C_{21}\), \(C_{12}\), and \(C_{03}\) are material constants.

Neo-Hookean

The Neo-Hookean model is a well-known hyperelastic model with an expanded linear rule (Hooke rule) having isotropy so that it can respond to finite deformation problems. The elastic potential is as follows.

\[ W=\frac{\mu}{2}(\bar{I}_{1}-3) \]

where \(\mu\) is initial shear modulus of materials.

Ogden

The strain-energy potential of the Ogden compressible foam model is based on the principal stretches of left Cauchy strain tensor, which has the form:

\[ W=\sum_{i=1}^{N}\frac{\mu_{i}}{\alpha_{i}}\left(\bar{\lambda}_{1}^{\alpha_{i}}+\bar{\lambda}_{2}^{\alpha_{i}}+\bar{\lambda}_{3}^{\alpha_{i}}-3\right)+\sum_{k=1}^{N}\frac{1}{D_{k}}\left(J-1\right)^{2k} \]

where N determines the order of the polynomial, \(\mu_i\), \(\alpha_i\) are material constants. The reduced principal strench is defined by:

\[ \bar{\lambda}_{p}=J^{-\frac{1}{3}}\lambda_p,\; J=(\lambda_{1}\lambda_{2}\lambda_{3})^{\frac{1}{2}} \]

When parameters N=1, \(\alpha_1\)=2, the Ogden model is converted to the neo-Hookean model. When parameters N=2, \(\alpha_1\)=2 and \(\alpha_2\)=-2, the Ogden model is converted to the 2-parameter Mooney-Rivlin model.

Polynomial

The polynomial form of strain-energy potential is:

\[ W=\sum_{i+j=1}^{N}c_{ij}\left(\bar{I}_{1}-3\right)^{i}\left(\bar{I_{2}}-3\right)^{j} \]

where \(N\) determines the order of the polynomial, \(c_{ij}\) are material constants.

The Polynomial model is converted to following models with specific parameters:

Parameters of Polynomial model Equivalent model
N=1, \(C_{01}\)=0 neo-Hookean
N=1 2-parameter Mooney-Rivlin
N=2 5-parameter Mooney-Rivlin
N=3 9-parameter Mooney-Rivlin

Yeoh

The Yeoh model is also called the reduced polynomial form. The strain-energy potential is

\[ W=\sum_{i=1}^{N}c_{i0}\left(\bar{I}_{1}-3\right)^{i} \]

where N denotes the order of the polynomial, \(C_{i0}\) are material constants. When N=1, Yeoh becomes neo-Hookean model.

Electromagnetic Model Curves

This group includes the commonly used fitting curves in the electromagnetic analysis.

Electrical Steel

The iron-core loss without DC flux bias is expressed as the following:

\[ p_v=P_h+P_c+P_e=K_{f} f (B_m)^2 + K_c (fB_m)^2 + K_e(fB_m)^{1.5} \]

where

  • \(B_m\) is the amplitude of the AC flux component,
  • \(f\) is the frequency,
  • \(K_h\) is the hysteresis core loss coefficient,
  • \(K_c\) is the eddy-current core loss coefficient, and
  • \(K_e\) is the excess core loss coefficient,

Power Ferrite

The iron-core loss is expressed as the Steinmetz approximation

\[ p_v=C_m f^x B_m^y \]

where \(p_v\) is the average power density, \(f\) is the excitation frequency, and \(B_m\) is the peak flux density, is commonly used to characterize core loss data for sinusoidal excitation, but can also be applied to square-wave data.

To linearize the equation for curve fitting, we used base-10 logarithms. The equation above can be rewritten to

\[ log(p_v)=c + x\cdot log(f) + y \cdot(B_m) \]

where \(c=log(C_m)\).

\ No newline at end of file + Theory - WelSim Documentation
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Curve Fitting Theory

The section shows you the theoretical details of each curve or function.

Basic Curves

The group of Basic contains all commonly used curves.

Straight line

The function of this curve is given by

\[ y(x)=a+bx \]

where \(a\) and \(b\) are constants to fit, \(x\) and \(y\) are the test data pair. This function is also called 1st order polynomial.

Natural logarithm

The function of this curve is given by

\[ y(x)=a+b \cdot ln(x) \]

where \(a\) and \(b\) are constants to fit, \(x\) and \(y\) are the test data pair.

Note

Independent variable \(x\) must be larger than zero.

Exponential

The function of this curve is given by

\[ y(x)=ae^{bx} \]

where \(a\) and \(b\) are constants to fit, \(x\) and \(y\) are the test data pair.

Note

Dependent variable \(y\) must be larger than zero.

Power

The function of this curve is given by

\[ y(x)=ax^{b} \]

where \(a\) and \(b\) are constants to fit, \(x\) and \(y\) are the test data pair.

Note

Variables \(x\) and \(y\) must be larger than zero.

Gaussian

The function of this curve is given by

\[ y(x)=a \exp{(-\dfrac{(x-b)^2}{2c^2})} \]

where \(a\), \(b\), and \(c\) are constants to fit, \(x\) and \(y\) are the test data pair.

Note

Dependent variables \(y\) must be larger than zero.

Polynomial Curves

The group of Polynomial contains polynomial curves. The first-order polynomial is located in the Basic group as Straight Line.

2nd Order Polynomial

The function of this curve is given by

\[ y(x)=a+bx+cx^2 \]

where \(a\), \(b\), and \(c\) are constants to fit, \(x\) and \(y\) are the test data pair.

3rd Order Polynomial

The function of this curve is given by

\[ y(x)=a+bx+cx^2+dx^3 \]

where \(a\), \(b\), \(c\), and \(d\) are constants to fit, \(x\) and \(y\) are the test data pair.

4th Order Polynomial

The function of this curve is given by

\[ y(x)=a+bx+cx^2+dx^3+ex^4 \]

where \(a\), \(b\), \(c\), \(d\), and \(e\) are constants to fit, \(x\) and \(y\) are the test data pair.

5th Order Polynomial

The function of this curve is given by

\[ y(x)=a+bx+cx^2+dx^3+ex^4+ex^5 \]

where \(a\), \(b\), \(c\), \(d\), \(e\), and \(f\) are constants to fit, \(x\) and \(y\) are the test data pair.

Schulz-Flory functions

Schulz Flory distribution function to describe relative ratios of polymers after a polymerization process. The function of this curve is given by

\[ y(x) = \sum_{i=1}^{n} ln(10) \dfrac{a_i}{b_i^2} \exp{(4.6x-\dfrac{\exp{(2.3x)}}{b_i})} \]

where \(a_i\) and \(b_i\) are constants to fit, \(x\) and \(y\) are the test data pair. The parameter must satisfy the condition: \(0<a_i<1\).

Nonlinear Curves

The group of Nonlinear curves contains nonlinear curves that do not belong to the polynomial.

Symmetrical Sigmoidal

The function of this curve is given by

\[ y(x)=d + \dfrac{a-d}{1+(\dfrac{x}{c})^b} \]

where \(a\), \(b\), \(c\), and \(d\) are constants to fit, \(x\) and \(y\) are the test data pair.

Asymmetrical Sigmoidal

The function of this curve is given by

\[ y(x)=d + \dfrac{a-d}{ (1+(\dfrac{x}{c})^b)^m } \]

where \(a\), \(b\), \(c\), \(d\), and \(m\) are constants to fit, \(x\) and \(y\) are the test data pair.

Rectangular Hyperbola

The function of this curve is given by

\[ y(x)=\dfrac{V_{max}x}{ K_m + x} \]

where \(V_{max}\) and \(K_m\) are constants to fit, \(x\) and \(y\) are the test data pair.

Basic Exponential

The function of this curve is given by

\[ y(x)=a + be^{-cx} \]

where \(a\), \(b\), and \(c\) are constants to fit, \(x\) and \(y\) are the test data pair.

Half-Life Exponential

The function of this curve is given by

\[ y(x)=a + \dfrac{b}{2^{(\dfrac{x}{c})}} \]

where \(a\), \(b\), and \(c\) are constants to fit, \(x\) and \(y\) are the test data pair.

Proportional Rate Growth or Decrease

The function of this curve is given by

\[ y(x)=Y_0 + \dfrac{V_0}{K}(1-e^{-Kx}) \]

where \(Y_0\), \(V_0\), and \(K\) are constants to fit, \(x\) and \(y\) are the test data pair.

Log-Normal Particle Size Distribution

The function of this curve is given by

\[ \dfrac{dy(x)}{d\ln{x}}=\dfrac{C_t}{\sigma_g\sqrt{2}\pi} \exp{(-\dfrac{(\ln{x}-\ln{D_m})^2}{2\ln{\sigma_g}^2})} \]

where \(D_m\), \(\sigma_g\), and \(C_t\) are constants to fit, x and y are test data pair. In the computation, the Left-Hand-Side term (\(dy(x)/d\ln{x}\)) is calculated using finite difference scheme.

Note

Independent variables \(x\) must be larger than zero. The number of input x-y pairs must be large than 3.

Hyperelastic Material Model Curves

The group of hyperelastic material models contains the commonly used hyperelastic models in the finite element analysis. The test data pair is engineering strain and stress.

Arruda-Boyce

The form of the strain-energy potential for Arruda-Boyce model is

\[ \begin{array}{ccl} W & = & \mu[\dfrac{1}{2}(\bar{I}_{1}-3)+\dfrac{1}{20\lambda_{m}^{2}}(\bar{I_{1}^{2}}-9)+\dfrac{11}{1050\lambda_{m}^{4}}(\bar{I_{1}^{3}}-27)\\ & + & \dfrac{19}{7000\lambda_{m}^{6}}(\bar{I_{1}^{4}}-81) + \dfrac{519}{673750\lambda_{m}^{8}}(\bar{I_{1}^{5}}-243)] \end{array} \]

where \(\mu\) is the initial shear modulus of the material, \(\lambda_{m}\) is limiting network stretch.

Gent

The form of the strain-energy potential for the Gent model is:

\[ W=-\frac{\mu J_{m}}{2}\mathrm{ln}\left(1-\frac{\bar{I}_{1}-3}{J_{m}}\right) \]

where \(\mu\) is the initial shear modulus of the material, \(J_m\) is limiting value of \(\bar{I}_1-3\).

Mooney-Rivlin 2 3 5 and 9 Parameters

This model includes two-, three-, five-, and nine-terma Mooney-Rivlin models. The form of the strain-energy potential for a two-parameter Mooney-Rivlin model is

\[ W=C_{10}\left(\bar{I}_{1}-3\right)+C_{01}\left(\bar{I}_{2}-3\right) \]

where \(C_{10}\), \(C_{01}\), and \(D_{1}\) are the material constants.

The form of strain-energy potential for a three-parameter Mooney-Rivlin model is

\[ W=C_{10}\left(\bar{I}_{1}-3\right)+C_{01}\left(\bar{I}_{2}-3\right)+C_{11}\left(\bar{I}_{1}-3\right)\left(\bar{I}_{2}-3\right) \]

where \(C_{10}\), \(C_{01}\), and \(C_{11}\) are material constants.

The form of strain-energy potential for a five-parameter Mooney-Rivlin model is

\[ \begin{array}{ccl} W & = & C_{10}\left(\bar{I}_{1}-3\right)+C_{01}\left(\bar{I}_{2}-3\right)+C_{20}\left(\bar{I}_{1}-3\right)^{2}\\ & + & C_{11}\left(\bar{I}_{1}-3\right)\left(\bar{I}_{2}-3\right)+C_{02}\left(\bar{I}_{2}-3\right)^{2} \end{array} \]

where \(C_{10}\), \(C_{01}\), \(C_{20}\), \(C_{11}\), and \(C_{02}\) are material constants.

The form of strain-energy potential for a nine-parameter Mooney-Rivlin model is

\[ \begin{array}{ccl} W & = & C_{10}\left(\bar{I}_{1}-3\right)+C_{01}\left(\bar{I}_{2}-3\right)+C_{20}\left(\bar{I}_{1}-3\right)^{2}\\ & + & C_{11}\left(\bar{I}_{1}-3\right)\left(\bar{I}_{2}-3\right)+C_{02}\left(\bar{I}_{2}-3\right)^{2}+C_{30}\left(\bar{I}_{1}-3\right)^{3}\\ & + & C_{21}\left(\bar{I}_{1}-3\right)^{2}\left(\bar{I}_{2}-3\right)+C_{12}\left(\bar{I}_{1}-3\right)\left(\bar{I}_{2}-3\right)^{2}+C_{03}\left(\bar{I}_{2}-3\right)^{3} \end{array} \]

where \(C_{10}\), \(C_{01}\), \(C_{20}\), \(C_{11}\), \(C_{02}\), \(C_{30}\), \(C_{21}\), \(C_{12}\), and \(C_{03}\) are material constants.

Neo-Hookean

The Neo-Hookean model is a well-known hyperelastic model with an expanded linear rule (Hooke rule) having isotropy so that it can respond to finite deformation problems. The elastic potential is as follows.

\[ W=\frac{\mu}{2}(\bar{I}_{1}-3) \]

where \(\mu\) is initial shear modulus of materials.

Ogden

The strain-energy potential of the Ogden compressible foam model is based on the principal stretches of left Cauchy strain tensor, which has the form:

\[ W=\sum_{i=1}^{N}\frac{\mu_{i}}{\alpha_{i}}\left(\bar{\lambda}_{1}^{\alpha_{i}}+\bar{\lambda}_{2}^{\alpha_{i}}+\bar{\lambda}_{3}^{\alpha_{i}}-3\right)+\sum_{k=1}^{N}\frac{1}{D_{k}}\left(J-1\right)^{2k} \]

where N determines the order of the polynomial, \(\mu_i\), \(\alpha_i\) are material constants. The reduced principal strench is defined by:

\[ \bar{\lambda}_{p}=J^{-\frac{1}{3}}\lambda_p,\; J=(\lambda_{1}\lambda_{2}\lambda_{3})^{\frac{1}{2}} \]

When parameters N=1, \(\alpha_1\)=2, the Ogden model is converted to the neo-Hookean model. When parameters N=2, \(\alpha_1\)=2 and \(\alpha_2\)=-2, the Ogden model is converted to the 2-parameter Mooney-Rivlin model.

Polynomial

The polynomial form of strain-energy potential is:

\[ W=\sum_{i+j=1}^{N}c_{ij}\left(\bar{I}_{1}-3\right)^{i}\left(\bar{I_{2}}-3\right)^{j} \]

where \(N\) determines the order of the polynomial, \(c_{ij}\) are material constants.

The Polynomial model is converted to following models with specific parameters:

Parameters of Polynomial model Equivalent model
N=1, \(C_{01}\)=0 neo-Hookean
N=1 2-parameter Mooney-Rivlin
N=2 5-parameter Mooney-Rivlin
N=3 9-parameter Mooney-Rivlin

Yeoh

The Yeoh model is also called the reduced polynomial form. The strain-energy potential is

\[ W=\sum_{i=1}^{N}c_{i0}\left(\bar{I}_{1}-3\right)^{i} \]

where N denotes the order of the polynomial, \(C_{i0}\) are material constants. When N=1, Yeoh becomes neo-Hookean model.

Electromagnetic Model Curves

This group includes the commonly used fitting curves in the electromagnetic analysis.

Electrical Steel

The iron-core loss without DC flux bias is expressed as the following:

\[ p_v=P_h+P_c+P_e=K_{f} f (B_m)^2 + K_c (fB_m)^2 + K_e(fB_m)^{1.5} \]

where

  • \(B_m\) is the amplitude of the AC flux component,
  • \(f\) is the frequency,
  • \(K_h\) is the hysteresis core loss coefficient,
  • \(K_c\) is the eddy-current core loss coefficient, and
  • \(K_e\) is the excess core loss coefficient,

Power Ferrite

The iron-core loss is expressed as the Steinmetz approximation

\[ p_v=C_m f^x B_m^y \]

where \(p_v\) is the average power density, \(f\) is the excitation frequency, and \(B_m\) is the peak flux density, is commonly used to characterize core loss data for sinusoidal excitation, but can also be applied to square-wave data.

To linearize the equation for curve fitting, we used base-10 logarithms. The equation above can be rewritten to

\[ log(p_v)=c + x\cdot log(f) + y \cdot(B_m) \]

where \(c=log(C_m)\).

\ No newline at end of file diff --git a/features/index.html b/features/index.html index 866c3e9..b3cadf7 100755 --- a/features/index.html +++ b/features/index.html @@ -1 +1 @@ - Features - WelSim Documentation
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Features

As a general-purpose engineering simulation software program, WELSIM contains tons of features those allow you to conduct various simulation studies.

Specification

Specification Description
Operaton system Microsoft Windows 10/11, 64-bit;
Linux: Ubuntu 22.04 LTS and higher versions, 64-bit;
3D rendering driver: OpenGL 3.2 or higher
Physical memory At least 4 GB, and 32 GB and higher is recommended
Geometry modules Imported geometry formats: STEP, IGES, STL, GDS
Built-in geometry generation: Box, Cylinder, Sphere, Plane, Line, Circle, Vertex
Boolean operations: Union, Intersection, Cut
Supported automatic mesh Tet10, Tet4, Tri6, Tri3
  • Project data: file with suffix "wsdb" and the associated folder (same file name).
  • Export mesh formats: UNV, MFEM, SU2, VTK.
  • Export result formats: VTK, Tecplot, Plain Text.
  • Export solver scripts: FrontISTR, OpenRadioss, MFEM, SU2, Palace, etc.

Structural

Structural analysis Description
Types Static, transient, and modal
Materials Isotropic elastic, hyper-elastic, plastic, visco-elastic, and creep
Deformation types Small, and finite
Contact types bonded, frictionless, and frictional; small and finite sliding
Boundary conditions constraints, displacement, force, pressure, velocity, acceleration
Body conditions body force, acceleration, standard earth gravity, rotational velocity
Results deformations, stresses, strains, velocity, acceleration
Probe results reaction force (total, x, y, z)
  • Nonlinear materials.
  • Contact analysis.
  • Multi-body analysis.
  • Multi-step quasi-static analysis.
  • Implicit dynamics.

Explicit Structural Dynamics (using OpenRadioss)

Structural analysis Description
Materials Isotropic elasto-plastic (Johnson-Cook, Zerillii-Armstrong, Gray, Cowper-Symonds, Yoshida-Uemori, Hensel-Spittel, voce), Isotropic linear elastic (Hooke's law, Johnson-Cook), hyper-elastic (Ogden, Neo-Hookean, Mooney–Rivlin), visco-elastic (Boltamann, Generalized Maxwell-Kelvin), creep, explosive (JWL), Rock (Drucker-Prager), Hill orthotropic
Equation of state Compaction, Gruneisen, ideal gas, linear, LSZK, Murnaghan, NASG, Noble, Polynomial, Puff, Sesame, Tillotson
Failure models Alter, Biquad, Chang, Cockcroft, EMC, Energy, Fabric, forming limit diagram, Gurson, Hashin, Johnson, Ladeveze, Mullins effect with Ogden and Roxburgh criteria, NXT, orthotropic biquad, Puck, Spalling, Wierzbicki
Element type Solid, shell
Contact types bonded, frictionless, and frictional; small and finite sliding
Boundary conditions constraints, displacement, force, pressure, velocity, acceleration, etc.
Body conditions rigid body, body force, acceleration, standard earth gravity, rotational velocity, etc.
Results deformations, stresses, strains, velocity, acceleration, etc

Thermal

Thermal analysis Description
Types Static, and transient
Materials linear and nonlinear
Initial conditions Initial temperature
Boundary conditions temperature, convection, radiation, heat flux, heat flow, perfectly insulated
Body conditions Internal heat generation
Results temperature
  • Multi-body analysis.
  • Temperature-dependent nonlinear material.
  • Implicit transient analysis.
  • Orthotropic thermal conductivity material.
  • Heat flux results.

Computational Fluid Dynamics (through SU2)

Fluid analysis Description
Types Steady-state, and transient
Governing equation Euler, Navier-Stokes, RANS
Boundary conditions wall, inlet, outlet, pressure, velocity, temperature, convection, heat flux
Results velocity, pressure, mass density, pressure coefficient, mach number, energy
  • incompressible fluids.
  • compressible fluids.

Electromangetic

Electromagnetic analysis Description
Types Electrostatic, magnetostatic, eigenmode, driven, full-wave transient
Materials linear
Boundary conditions ground, voltage, symmetry, zero charge, surface charge density, electric displacement, insulting, magnetic vector potential, magnetic flux density
Results voltage, electric field, electric displacement, magnetic vector potential, magnetic flux density, magnetic field, energy density
  • Vector result display.
  • Parallel computing.
  • Multi-body analysis.
  • Nonlinear materials.

Need new features?

Feel free to send questions, comments, requests, bug reports, and success stories. Asking for a new feature usually results in adding the request to the TODO list or, if it already is in the list, in assigning higher priority to it.

\ No newline at end of file + Features - WelSim Documentation
Skip to content

Features

As a general-purpose engineering simulation software program, WELSIM contains tons of features those allow you to conduct various simulation studies.

Specification

Specification Description
Operaton system Microsoft Windows 10/11, 64-bit;
Linux: Ubuntu 22.04 LTS and higher versions, 64-bit;
3D rendering driver: OpenGL 3.2 or higher
Physical memory At least 4 GB, and 32 GB and higher is recommended
Geometry modules Imported geometry formats: STEP, IGES, STL, GDS
Built-in geometry generation: Box, Cylinder, Sphere, Plane, Line, Circle, Vertex
Boolean operations: Union, Intersection, Cut
Supported automatic mesh Tet10, Tet4, Tri6, Tri3
  • Project data: file with suffix "wsdb" and the associated folder (same file name).
  • Export mesh formats: UNV, MFEM, SU2, VTK.
  • Export result formats: VTK, Tecplot, Plain Text.
  • Export solver scripts: FrontISTR, OpenRadioss, MFEM, SU2, Palace, etc.

Structural

Structural analysis Description
Types Static, transient, and modal
Materials Isotropic elastic, hyper-elastic, plastic, visco-elastic, and creep
Deformation types Small, and finite
Contact types bonded, frictionless, and frictional; small and finite sliding
Boundary conditions constraints, displacement, force, pressure, velocity, acceleration
Body conditions body force, acceleration, standard earth gravity, rotational velocity
Results deformations, stresses, strains, velocity, acceleration
Probe results reaction force (total, x, y, z)
  • Nonlinear materials.
  • Contact analysis.
  • Multi-body analysis.
  • Multi-step quasi-static analysis.
  • Implicit dynamics.

Explicit Structural Dynamics (using OpenRadioss)

Structural analysis Description
Materials Isotropic elasto-plastic (Johnson-Cook, Zerillii-Armstrong, Gray, Cowper-Symonds, Yoshida-Uemori, Hensel-Spittel, voce), Isotropic linear elastic (Hooke's law, Johnson-Cook), hyper-elastic (Ogden, Neo-Hookean, Mooney–Rivlin), visco-elastic (Boltamann, Generalized Maxwell-Kelvin), creep, explosive (JWL), Rock (Drucker-Prager), Hill orthotropic
Equation of state Compaction, Gruneisen, ideal gas, linear, LSZK, Murnaghan, NASG, Noble, Polynomial, Puff, Sesame, Tillotson
Failure models Alter, Biquad, Chang, Cockcroft, EMC, Energy, Fabric, forming limit diagram, Gurson, Hashin, Johnson, Ladeveze, Mullins effect with Ogden and Roxburgh criteria, NXT, orthotropic biquad, Puck, Spalling, Wierzbicki
Element type Solid, shell
Contact types bonded, frictionless, and frictional; small and finite sliding
Boundary conditions constraints, displacement, force, pressure, velocity, acceleration, etc.
Body conditions rigid body, body force, acceleration, standard earth gravity, rotational velocity, etc.
Results deformations, stresses, strains, velocity, acceleration, etc

Thermal

Thermal analysis Description
Types Static, and transient
Materials linear and nonlinear
Initial conditions Initial temperature
Boundary conditions temperature, convection, radiation, heat flux, heat flow, perfectly insulated
Body conditions Internal heat generation
Results temperature
  • Multi-body analysis.
  • Temperature-dependent nonlinear material.
  • Implicit transient analysis.
  • Orthotropic thermal conductivity material.
  • Heat flux results.

Computational Fluid Dynamics (through SU2)

Fluid analysis Description
Types Steady-state, and transient
Governing equation Euler, Navier-Stokes, RANS
Boundary conditions wall, inlet, outlet, pressure, velocity, temperature, convection, heat flux
Results velocity, pressure, mass density, pressure coefficient, mach number, energy
  • incompressible fluids.
  • compressible fluids.

Electromangetic

Electromagnetic analysis Description
Types Electrostatic, magnetostatic, eigenmode, driven, full-wave transient
Materials linear
Boundary conditions ground, voltage, symmetry, zero charge, surface charge density, electric displacement, insulting, magnetic vector potential, magnetic flux density
Results voltage, electric field, electric displacement, magnetic vector potential, magnetic flux density, magnetic field, energy density
  • Vector result display.
  • Parallel computing.
  • Multi-body analysis.
  • Nonlinear materials.

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Glossary

A

  • ACCELERATION： The second time derivative of the displacement (the first time derivative of the velocity).
  • ADAPTIVE FINITE ELEMENT METHOD/ADAPTIVE MESHING： An adaptive finite element solver iteratively performs finite element analysis, determines the areas of the mesh where the solution is not sufficiently accurate and refines the mesh in those areas until the solution obtains the prescribed degree of accuracy. Adaptive Meshing involves automatically improving the mesh where necessary to meet specified convergence criteria.
  • ASPECT RATIO: The ratio of the longest to shortest side lengths on an element.
  • ASSEMBLY: Geometric:Two or more parts mated together. FEA: The process of assembling the element matrices together to form the global matrix. Typically element stiffness matrices are assembled to form the complete stiffness matrix of the structure.
  • AUTOMATIC MESH GENERATION: The process of generating a mesh of elements over the volume that is being analyzed. There are two forms of automatic mesh generation: Free Meshing -Where the mesh has no structure to it. Free meshing generally uses triangular and tetrahedral elements. Mapped Meshing -Where large regions, if not all, of the volume is covered with regular meshes. This can use any form of element. Free meshing can be used to fill any shape. Mapped meshing can only be used on some shapes without elements being excessively distorted.
  • AXISYMMETRY: If a shape can be defined by rotating a cross- section about a line (e.g. a cone) then it is said to be axisymmetric. This can be used to simplify the analysis of the system. Such models are sometimes called two and a half dimensional since a 2D cross- section represents a 3D body.

B

  • BARLOW POINTS： The set of Gauss integration points that give the best estimates of the stress for an element. For triangles and tetrahedra these are the full Gauss integration points. For quadrilateral and brick elements they are the reduced Gauss points.
  • BASIS SPACE： When an element is being constructed it is derived from a simple regular shape in non-dimensional coordinates. The coordinates used to define the simple shape form the basis space. In its basis space a general quadrilateral is a 2×2 square and a general triangle is an isosceles triangle with unit side lengths.
  • BEAM ELEMENT: A line element that has both translational and rotational degrees of freedom. It represents both membrane and bending actions.
  • BENDING: Bending behavior is where the strains vary linearly from the centerline of a beam or center surface of a plate or shell.There is zero strain on the centerline for pure bending. Plane sections are assumed to remain plane. If the stresses are constant normal to the centerline then this is called membrane behavior.
  • BENDING STRESS: A compressive and/or tensile stress resulting from the application of a nonaxial force to a structural member.
  • BODY FORCE VECTOR: Mechanical loadings within the interior of the volume, typically inertia loadings in a stiffness analysis.
  • BOUNDARY CONDITIONS: The boundary conditions of a function are values of the function at the edge of the range of some of its variables. Knowledge of some of the boundary conditions is needed to solve an engineering problem or to find an unknown function.
  • BOUNDARY ELEMENT/INTEGRAL: A method of solving differential equations by taking exact solutions to the field equations loaded by a point source and then finding the strengths of sources distributed around the boundary of the body required to satisfy the boundary conditions on the body.
  • BUBBLE FUNCTIONS: Element shape functions that are zero along the edges of the element. They are non-zero within the interior of the element.
  • BUCKLING (SNAP THROUGH): The situation where the elastic stiffness of the structure is cancelled by the effects of compressive stress within the structure. If the effect of this causes the structure to suddenly displace a large amount in a direction normal to the load direction then it is classical bifurcation buckling. If there is a sudden large movement in the direction of the loading it is snap through buckling.

C

  • CAE: computer aided engineering.
  • CENTRAL DIFFERENCE METHOD: A method for numerically integrating second order dynamic equations of motion. It is widely used as a technique for solving non-linear dynamic problems.
  • CHARACTERISTIC VALUE: Same as the eigenvalue.
  • CHARACTERISTIC VECTOR: Same as the eigenvector.
  • CHOLESKY FACTORISATION (SKYLINE): A method of solving a set of simultaneous equations that is especially well suited to the finite element method. It is sometimes called a skyline solution. Choose to optimize the profile o f the matrix if a renumbering scheme is used.
  • COEFFICIENT OF VISCOUS DAMPING: The system parameter relating force to velocity.
  • COMPATIBILITY OF STRAINS: Compatibility of strain is satisfied if strains that are continuous before loading are continuous after.
  • COMPLETE DISPLACEMENT FIELD: When the functions interpolating the field variable (typically the displacements) form a complete nth order polynomial in all directions.
  • COMPLEX EIGENVALUES: The eigenvectors of a damped system. For proportionally damped systems they are the same as the undamped eigenvectors. For non-proportionally damped systems with damping in all modes less th an critical they are complex numbers and occur as complex conjugate pairs.
  • COMPLEX EIGENVECTORS: The eigenvalues of any damped system. If the damping is less than critical they will occur as complex conjugate pairs even for proportionally damped systems. The real part of the complex eigenvalue is a measure of the damping in the mode and should always be negative. The imaginary part is a measure of the resonant frequency.
  • COMPOSITE MATERIAL: A material that is made up of discrete components, typically a carbon-epoxy composite material or a glass-fiber material. Layered material and foam materials are also forms of composite materials.
  • COMPUTATIONAL FLUID DYNAMICS (CFD): A computer-based numerical study of turbulent fluid flow using approximate methods such as the finite element method, the fine difference method, the boundary element method, the finite volume methods, and so on.
  • CONDITION NUMBER: The ratio of the highest eigenvalue to the lowest eigenvalue of a matrix. The exponent of this number gives a measure of the number of digits required in the computation to maintain numerical accuracy. The higher the condition number the more chance of numerical error and the slower the rate of convergence for iterative solutions.
  • CONDITIONAL/UNCONDITIONAL STABILITY: Any scheme for numerically integrating dynamic equations of motion in a step-by- step form is conditionally stable if there is a maximum time step value that can be used. It is unconditionally stable (but not necessarily accurate) if any length of time step can be used.
  • CONJUGATE GRADIENT METHOD: A method for solving simultaneous equations iteratively. It is closely related to the Lanczos method for finding the first few eigenvalues and eigenvectors of a set of equations.
  • CONSISTENT DISPLACEMENTS AND FORCES: The displacements and forces act at the same point and in the same direction so that the sum of their products give a work quantity. If consistent displacements and forces are used the resulting stiffness and mass matrices are symmetric.
  • CONSTANT STRAIN CONSTANTSTRESS: For structural analysis an element must be able to reproduce a state of constant stress and strain under a suitable loading to ensure that it will converge to the correct solution. This is tested for using the patch test.
  • CONSTITUTIVE RELATIONSHIPS: The equations defining the material behavior for an infinitesimal volume of material. For structures these are the stress -strain laws and include Hookes law for elasticity and the Prandle-Reuss equations for plasticity.
  • CONSTRAINT EQUATIONS (MULTI POINT CONSTRAINTS): If one group of variables can be defined in terms of another group then the relationship between the two are constraint equations. Typically the displacements on the face of an element can be constrained to remain plane but the plane itself can move.
  • CONSTRAINTS: Known values of, or relationships between, the displacements in the coordinate system.
  • CONTACT PROBLEMS: A contact problem occurs when two bodies that are originally apart can come together, or two bodies that are originally connected can separate.
  • CONTINUOUS MASS MODELS: The system mass is distributed between the degrees of freedom. The mass matrix is not diagonal.
  • CONTOUR PLOTTING: A graphical representation of the variation of a field variable over a surface, such as stress, displacement, or temperature. A contour line is a line of constant value for the variable. A contour band is an area of a single color for values of the variable within two limit values.
  • CONVERGENCE REQUIREMENTS: For a structural finite element to converge as the mesh is refined it must be able to represent a state of constant stress and strain free rigid body movements exactly. There are equivalent requirements for other problem types.
  • CRANK-NICHOLSON SCHEME: A method for numerically integrating first order dynamic equations of motion. It is widely used as a technique for solving thermal transient problems.
  • CRITICAL ENERGY RELEASE: This is a material property defining the minimum energy that a propagating crack must release in order for it to propagate. Three critical energies, or modes of crack propagation, have been identified. Mode 1 is the two surfaces of the crack moving apart. Mode 2 is where the two surfaces slide from front to back. Mode 3 is where the to surfaces slide sideways.
  • CRITICALLY DAMPED SYSTEM CRITICAL DAMPING: The dividing line between under damped and over damped systems where the equation of motion has a damping value that is equal to the critical damping.
  • CYCLIC SYMMETRY: A generalization of axisymmetry. The structure is composed of a series of identical sectors that are arranged circumferentially to form a ring. A turbine disc with blades attached is atypical example.

D

  • DAMPED EIGENVALUES: Same as complex eigenvalues.
  • DAMPED EIGENVECTORS: Same as complex eigenvectors.
  • DAMPED NATURAL FREQUENCY: The frequency at which the damped system vibrates naturally when only an initial disturbance is applied.
  • DAMPING: Any mechanism that dissipates energy in a vibrating system.
  • DAMPING FACTOR (DECAY FACTOR): The damping factor is the ratio of the actual damping to the critical damping. It is often specified as a percentage. If the damping factor is less than one then the system can undergo free vibrations. The free vibrations will decay to zero with time. If the damping factor is greater than one then the decay is exponential and no vibrations occur. For most structures the damping factor is very small.
  • DEGENERATE ELEMENTS: Elements that are defined as one shape in the basis space but they are a simpler shape in the real space. A quadrilateral can degenerate into a triangle. A brick element can degenerate into a wedge, a pyramid or a tetrahedron. Degenerate elements should be avoided in practice.
  • DEGREES OF FREEDOM: The number of equations of equilibrium for the system. In dynamics, the number of displacement quantities which must be considered in order to represent the effects of all of the significant inertia forces. Degrees of freedom define the ability of a given node to move in any direction in space. There are six types of DOF for any given node: 3 possible translations (one each in the X,Y and Z directions) and 3 possible rotations (one rotation about each of the X,Y, and X axes). DOF are defined and restricted by the elements and constraints associated with each node.
  • DET(J) DET J: The Jacobian matrix is used to relate derivatives in the basis space to the real space. The determinant of the Jacobian – det(j) -is a measure of the distortion of the element when mapping from the basis to the real space.
  • DEVIATORIC STRESS STRESS DEVIATORS: A measure of stress where the hydrostatic stress has been subtracted from the actual stress. Material failures that are flow failures (plasticity and creep) fail independently of the hydrostatic stress. The failure is a function of the deviatoric stress.
  • DIAGONAL GENERALIZED MATRIX: The eigenvectors of a system can be used to define a coordinate transformation such that, in these generalized coordinates the coefficient matrices (typically mass and stiffness) are diagonal.
  • DIE-AWAY LENGTH: If there is a stress concentration in a structure the high stress will reduce rapidly with distance from the peak value. The distance over which it drops to some small value is called the die-away length. A fine mesh is required over this die-away length for accurate stress results.
  • DIRECT INTEGRATION: The name for various techniques for numerically integrating equations of motion. These are either implicit or explicit methods and include central difference, Crank-Nicholson, Runge-Kutta, Newmark beta and Wilson theta.
  • DISCRETE PARAMETER MODELS (DISCRETISED APPROACH): The model is defined in terms of an ordinary differential equation and the system has a finite number of degrees of freedom.
  • DISCRETIZATION: The process of dividing geometry into smaller pieces (finite elements) to prepare for analysis, i.e. Meshing.
  • DISPLACEMENT METHOD (DISPLACEMENT SOLUTION) :A form of discrete parameter model where the displacements of the system are the basic unknowns.
  • DISPLACEMENT: The distance, translational and rotational, that a node travels from its initial position to its post-analysis position. The total displacement is represented by components in each of the 3 translational directions and the 3 rotational directions.
  • DISPLACEMENT PLOTS: Plots showing the deformed shape of the structure. For linear small deflection problems the displacements are usually multiplied by a magnifying factor before plotting the deformed shape.
  • DISPLACEMENT VECTOR: The nodal displacements written as a column vector.

  • DOMAIN: In mathematics, a domain is the set of independent variables for which a function is defined. In finite element analysis, a domain is a continuous system (region) over which the laws of physics govern. In structural engineering, a domain could be a beam or a complete building frame. In mechanical engineering, a domain could be a piece of machine parts or a thermal field.

  • DRUCKER-PRAGER EQUIVALENT STRESSES: An equivalent stress measure for friction materials (typically sand). The effect of hydrostatic stress is included in the equivalent stress.

  • DYNAMIC ANALYSIS: An analysis that includes the effect of the variables changing with time as well as space.

  • DYNAMIC FLEXIBILITY MATRIX: The factor relating the steady state displacement response of a system to a sinusoidal force input. It is the same as the recep tance.

  • DYNAMIC MODELLING: A modeling process where consideration as to time effects in addition to spatial effects are included. A dynamic model can be the same as a static model or it can differ significantly depending upon the nature of the problem.
  • DYNAMIC RESPONSE: The time dependent response of a dynamic system in terms of its displacement, velocity or acceleration at any given point of the system.
  • DYNAMIC STIFFNESS MATRIX: If the structure is vibrating steadily at a frequency w then the dynamic stiffness is (K+iwC w2M) It is the inverse of the dynamic flexibility matrix.
  • DYNAMIC STRESSES：Stresses that vary with time and space.
  • DYNAMIC SUBSTRUCTURING： Special forms of substructuring used within a dynamic analysis. Dynamic substructuring is always approximate and causes some loss of accuracy in the dynamic solution.

E

  • EIGENVALUE PROBLEM： Problems that require calculation of eigenvalues and eigenvectors for their solution. Typically solving free vibration problems or finding buckling loads.
  • ELASTIC FOUNDATION： If a structure is sitting on a flexible foundation the supports are treated as a continuous elastic foundation. The elastic foundation can have a significant effect upon the structural response.
  • ELASTIC STIFFNESS： If the relationship between loads and displacements is linear then the problem is elastic. For a multi-degree of freedom system the forces and displacements are related by the elastic stiffness matrix.
  • ELECTRIC FIELDS： Electro-magnetic and electro-static problems form electric field problems.

  • ELEMENT： An element is a portion of the problem domain, and is typically some simple shape like a triangle or quadrilateral in 2D, or tetrahedron or hex solid in 3D.

  • ELEMENT ASSEMBLY： Individual element matrices have to be assembled into the complete stiffness matrix. This is basically a process of summing the element matrices. This summation has to be of the correct form. For the stiffness method the summation is based upon the fact that element displacements at common nodes must be the same.

  • ELEMENT STRAINS/STRESSES： Stresses and strains within elements are usually defined at the Gauss points (ideally at the Barlow points) and the node points. The most accurate estimates are at the reduced Gauss points (more specifically the Barlow points). Stresses and strains are usually calculated here and extrapolated to the node points.
  • ENERGY METHODS HAMILTONS PRINCIPLE： Methods for defining equations of equilibrium and compatibility through consideration of possible variations of the energies of the system. The general form is Hamiltons principle and sub-sets of this are the principle of virtual work including the principle of virtual displacements (PVD) and the principle of virtual forces (PVF).
  • ENGINEERING/MATHEMATICAL NORMALIZATION： Each eigenvector (mode shape or normal mode) can be multiplied by an arbitrary constant and still satisfy the eigenvalue equation. Various methods of scaling the eigenvector are used Engineering normalization -The vector is scaled so that the largest absolute value of any term in the eigenvector is unity. This is useful for inspecting printed tables of eigenvectors. Mathematical normalization -The vector is scaled so that the diagonal modal mass matrix is the unit matrix. The diagonal modal stiffness matrix is the system eigenvalues. This is useful for response calculations.
  • EQUILIBRIUM EQUATIONS：Internal forces and external forces must balance. At the infinitesimal level the stresses and the body forces must balance. The equations of equilibrium define these force balance conditions.
  • EQUILIBRIUM FINITE ELEMENTS： Most of the current finite elements used for structural analysis are defined by assuming displacement variations over the element. An alternative approach assumes the stress variation over the element. This leads to equilibrium finite elements.
  • EQUIVALENT MATERIAL PROPERTIES： Equivalent material properties are defined where real material properties are smeared over the volume of the element. Typically, for composite materials the discrete fiber and matrix material properties are smeared to give average equivalent material properties.
  • EQUIVALENT STRESS： A three dimensional solid has six stress components. If material properties have been found experimentally by a uniaxial stress test then the real stress system is related to this by combining the six stress components to a single equivalent stress. There are various forms of equivalent stress for different situations. Common ones are Tresca, Von-Mises, Mohr-Coulomb and Drucker-Prager.
  • EULERIAN/LAGRANGIAN METHOD： For non-linear large deflection problems the equations can be defined in various ways. If the material is flowing though a fixed grid the equations are defined in Eulerian coordinates. Here the volume of the element is constant but the mass in the element can change. If the grid moves with the body then the equations are defined in Lagrangian coordinates. Here the mass in the element is fixed but the volume changes.
  • EXACT SOLUTIONS： Solutions that satisfy the differential equations and the associated boundary conditions exactly. There are very few such solutions and they are for relatively simple geometries and loadings.
  • EXPLICIT/IMPLICIT METHOD： These are methods for integrating equations of motion. Explicit methods can deal with highly non-linear systems but need small steps. Implicit methods can deal with mildly nonlinear problems but with large steps.
  • EXTRAPOLATION INTERPOLATION： The process of estimating a value of a variable from a tabulated set of values. For interpolation values inside the table are estimated. For extrapolation values outside the table are estimated. Interpolation is generally accurate and extrapolation is only accurate for values slightly outside the table. It becomes very inaccurate for other cases.

F

  • FACETED GEOMETRY： If a curved line or surface is modeled by straight lines or flat surfaces then the modeling is said to produce a faceted geometry.
  • FAST FOURIER TRANSFORM： A method for calculating Fourier transforms that is computationally very efficient.
  • FIELD PROBLEMS： Problems that can be defined by a set of partial differential equations are field problems. Any such problem can be solved approximately by the finite element method.
  • FINITE DIFFERENCES： A numerical method for solving partial differential equations by expressing them in a difference form rather than an integral form. Finite difference methods are very similar to finite element methods and in some cases are identical.
  • FINITE ELEMENT MODELING (FEM)： The process of setting up a model for analysis, typically involving graphical generation of the model geometry, meshing it into finite elements, defining material properties, and applying loads and boundary conditions.
  • FINITE VOLUME METHODS： A technique related to the finite element method. The equations are integrated approximately using t he weighted residual method, but a different form of weighting function is used from that in the finite element method. For the finite element method the Galerkin form of the weighted residual method is used.
  • FIXED BOUNDARY CONDITIONS： All degrees of freedom are restrained for this condition. The nodes on the fixed boundary can not move: translation or rotation.
  • FLEXIBILITY MATRIX FORCE METHOD： The conventional form of the finite element treats the displacements as unknowns, which leads to a stiffness matrix form. Alternative methods treating the stresses (internal forces) as unknowns lead to force methods with an associated flexibility matrix. The inverse of the stiffness matrix is the flexibility matrix.
  • FORCED RESPONSE： The dynamic motion results from a time varying forcing function.
  • FORCING FUNCTIONS： The dynamic forces that are applied to the system.
  • FOURIER EXPANSIONS FOURIER SERIES： Functions that repeat themselves in a regular manner can be expanded in terms of a Fourier series.
  • FOURIER TRANSFORM： A method for finding the frequency content of a time varying signal. If the signal is periodic it gives the same result as the Fourier series.
  • FOURIER TRANSFORM PAIR：The Fourier transform and its inverse which, together, allow the complete system to be transformed freely in either direction between the time domain and the frequency domain.
  • FRAMEWORK ANALYSIS： If a structure is idealized as a series interconnected line elements then this forms a framework analysis model. If the connections between the line elements a re pins then it is a pin-jointed framework analysis. If the joints are rigid then the lines must be beam elements.
  • FREE VIBRATION： The dynamic motion which results from specified initial conditions. The forcing function is zero.
  • FREQUENCY DOMAIN： The structures forcing function and the consequent response is defined in terms of their frequency content. The inverse Fourier transform of the frequency domain gives the corresponding quantity in the time domain.
  • FRONTAL SOLUTION WAVEFRONT SOLUTION： A form of solving the finite element equations using Gauss elimination that is very efficient for the finite element form of equations.

G

  • GAP/CONTACT ELEMENT: These are special forms of non-linear element that have a very high stiffness in compression and a low stiffness in tension. They are used to model contact conditions between surfaces. Most of these elements also contain a model for sliding friction between the contacting surfaces. Some gap elements are just line springs between points and others are more general forms of quadrilateral or brick element elements. The line spring elements should only be used in meshes of first order finite elements.

  • GAUSS POINT EXTRAPOLATION GAUSS POINT STRESSES: Stresses calculated internally within the element at the Gauss integration points are called the Gauss point stresses. These stresses are usually more accurate at these points than the nodal points.

  • GAUSS POINTS GAUSS WEIGHTS: The Gauss points are the sample points used within the elements for the numerical integration of the matrices and loadings. They are also the points at which the stresses can be recovered. The Gauss weights are associated factors used in the numerical integration process. They represent the volume of influence of the Gauss points. The positions of the Gauss points, together with the associated Gauss weights, are available in tables for integrations of polynomials of various orders.

  • GAUSSIAN ELIMINATION: A form of solving a large set of simultaneous equations. Within most finite element systems a form of Gaussian elimination forms the basic solution process.
  • GAUSSIAN INTEGRATION GAUSSIAN QUADRATURE: A form of numerically integrating functions that is especially efficient for integrating polynomials. The functions are evaluated at the Gauss points, multiplied by the Gauss weights and summed to give the integral.
  • GENERALIZED COORDINATES: A set of linearly independent displacement coordinates which are consistent with the constraints and are just sufficient to describe any arbitrary configuration of the system. Generalized coordinates are usually patterns of displacements, typically the system eigenvectors.
  • GENERALIZED MASS: The mass associated with a generalized displacement.
  • GENERALIZED STIFFNESS: The stiffness associated with a generalized displacement.
  • GEOMETRIC PROPERTIES: Various shape dependent properties of real structures, such as thickness, cross sectional area, sectional moments of inertia, centroid location and others that are applied as properties of finite elements.
  • GEOMETRIC/STRESS STIFFNESS: The component of the stiffness matrix that arises from the rotation of the internal stresses in a large deflection problem. This stiffness is positive for tensile stresses and negative for compressive stresses. If the compressive stresses are sufficiently high then the structure will buckle when the geometric stiffness cancels the elastic stiffness.
  • GEOMETRICAL ERRORS: Errors in the geometrical representation of the model. These generally arise from the approximations inherent in the finite element approximation.

  • GLOBAL STIFFNESS MATRIX: The assembled stiffness matrix of the complete structure.

  • GROSS DEFORMATIONS: Deformations sufficiently high to make it necessary to include their effect in the solution process. The problem requires a large deflection non-linear analysis.

  • GOVERNING EQUATIONS: The governing equations for a system are the equations derived from the physics of the system. Many engineering systems can be described by governing equations, which determine the system's characteristics and behaviors.
  • GUARD VECTORS: The subspace iteration (simultaneous vector iteration) method uses extra guard vectors in addition to the number of vectors requested by the user. These guard the desired vectors from being contaminated by the higher mode vectors and speed up convergence.
  • GUI: GUI stands for graphical user interface, which provides a visual tool to build a finite element model for a domain with complex geometry and boundary conditions.

H

  • HARDENING STRUCTURE: A structure where the stiffness increases with load.
  • HARMONIC LOADING: A dynamic loading that is periodic and can be represented by a Fourier series.
  • HEAT CONDUCTION: The analysis of the steady state heat flow within solids and fluids. The equilibrium balance between internal and external heat flows.
  • HERMITIAN SHAPE FUNCTIONS: Shape functions that provide both variable and variable first derivative continuity (displacement and slope continuity in structural terms) across element boundaries.
  • HEXAHEDRON ELEMENTS: Type of 3D element which has six quadrilateral faces.
  • HIGH/LOW ASPECT RATIO: The ratio of the longest side length of a body to the shortest is termed its aspect ratio. Generally bodies with high aspect ratios (long and thin) are more ill conditioned for numerical solution than bodies with an aspect ratio of one.
  • HOOKES LAW: The material property equations relating stress to strain for linear elasticity. They involve the material properties of Young’s modulus and Poisson ratio.
  • HOURGLASS MODE: Zero energy modes of low order quadrilateral and brick elements that arise from using reduced integration. These modes can propagate through the complete body.
  • H-CONVERGENCE: Convergence towards a more accurate solution by subdividing the elements into a number of smaller elements. This approach is referred to as H-convergence because of improved discretization due to reduced element size.
  • H-METHOD: A finite element method which requires an increasing number of elements to improve the solution.
  • H/P-REFINEMENT: Making the mesh finer over parts or all of the body is termed h-refinement. Making the element order higher is termed p-refinement.
  • HYBRID ELEMENTS: Elements that use stress interpolation within their volume and displacement interpolation around their boundary.
  • HYDROSTATIC STRESS: The stress arising from a uniform pressure load on a cube of material. It is the average value of the direct stress components at any point in the body.
  • HYSTERETIC DAMPING: A damping model representing internal material loss damping. The energy loss per unit cycle is independent of frequency. It is only valid for harmonic response.

I

  • ILL-CONDITIONING ERRORS: Numerical (rounding) errors that arise when using ill-conditioned equations.
  • ILL-CONDITIONING ILL-CONDITIONED EQUATIONS: Equations that are sensitive to rounding errors in a numerical operation. The numerical operation must also be defined. Equations can be ill conditioned for solving simultaneous equations but not for finding eigenvalues.
  • IMPULSE RESPONSE FUNCTION: The response of the system to an applied impulse.
  • IMPULSE RESPONSE MATRIX: The matrix of all system responses to all possible impulses. It is always symmetric for linear systems. It is the inverse Fourier transform of the dynamic flexibility matrix.
  • INCREMENTAL SOLUTION: A solutions process that involves applying the loading in small increments and finding the equilibrium conditions at the end of each step. Such solutions are generally used for solving non-linear problems.
  • INELASTIC MATERIAL BEHAVIOR: A material behavior where residual stresses or strains can remain in the body after a loading cycle, typically plasticity and creep.
  • INERTANCE (ACCELERANCE): The ratio of the steady state acceleration response to the value of the forcing function for a sinusoidal excitation.
  • INERTIA FORCE: The force that is equal to the mass times the acceleration.
  • INITIAL BUCKLING: The load at which a structure first buckles.
  • INITIAL STRAINS: The components of the strains that are non-elastic. Typically thermal strain and plastic strain.
  • INTEGRATION BY PARTS: A method of integrating a function where high order derivative terms are partially integrated to reduce their order.
  • INTERPOLATION FUNCTIONS SHAPE FUNCTIONS: The polynomial functions used to define the form of interpolation within an element. When these are expressed as interpolations associated with each node they become the element shape functions.
  • ISOPARAMETRIC ELEMENT: Elements that use the same shape functions (interpolations) to define the geometry as were used to define the displacements. If these elements satisfy the convergence requirements of constant stress representation and strain free rigid body motions for one geometry then it will satisfy the conditions for any geometry.
  • ISOTROPIC MATERIAL: Materials where the material properties are independent of the co-ordinate system.

J

  • JACOBI METHOD: A method for finding eigenvalues and eigenvectors of a symmetric matrix.
  • JACOBIAN MATRIX: A square matrix relating derivatives of a variable in one coordinate system to the derivatives of the same variable in a second coordinate system. It arises when the chain rule for differentiation is written in matrix form.
  • J-INTEGRAL METHODS: A method for finding the stress intensity factor for fracture mechanics problems.
  • JOINTS: The interconnections between components. Joints can be difficult to model in finite element terms but they can significantly affect dynamic behavior.

K

  • KINEMATIC BOUNDARY CONDITIONS: The necessary displacement boundary conditions for a structural analysis. These are the essential boundary conditions in a finite element analysis.
  • KINEMATICALLY EQUIVALENT FORCES (LOADS): A method for finding equivalent nodal loads when the actual load is distributed over a surface of a volume. The element shape functions are used so that the virtual work done by the equivalent loads is equal to the virtual work done by the real loads over the same virtual displacements. This gives the most accurate load representation for the finite element model. These are the non-essential stress boundary conditions in a finite element analysis.
  • KINEMATICALLY EQUIVALENT MASS: If the mass and stiffness are defined by the same displacement assumptions then a kinematically equivalent mass matrix is produced. This is not a diagonal (lumped) mass matrix.
  • KINETIC ENERGY: The energy stored in the system arising from its velocity. In some cases it can also be a function of the structural displacements.

L

  • LAGRANGE INTERPOLATION LAGRANGE SHAPE FUNCTIONS： A method of interpolation over a volume by means of simple polynomials. This is the basis of most of the shape function definitions for elements.
  • LAGRANGE MULTIPLIER TECHNIQUE： A method for introducing constraints into an analysis where the effects of the constraint are represented in terms of the unknown Lagrange multiplying factors.
  • LANCZOS METHOD： A method for finding the first few eigenvalues and eigenvectors of a set of equations. It is very well suited to the form of equations generated by the finite element method. It is closely related to the method of conjugate gradients used for solving simultaneous equations iteratively.
  • LEAST SQUARES FIT： Minimization of the sum of the squares of the distances between a set of sample points and a smooth surface . The finite element method gives a solution that is a least squares fit to the equilibrium equations.
  • LINEAR DEPENDENCE： One or more rows (columns) of a matrix are linear combinations of the other rows (columns). This means that the matrix is singular.
  • LINEAR ANALYSIS： Linear Finite Element Analysis is based on the following assumptions: (1) Static; (2) Small displacements; (3) Material is linearly elastic.
  • LINEAR SYSTEM： When the coefficients of stiffness, mass and damping are all constant then the system is linear. Superposition can be used to solve the response equation.
  • LOADINGS：The loads applied to a structure that result in deflections and consequent strains and stresses.
  • LOCAL STRESSES： Areas of stress that are significantly different from (usually higher than) the general stress level.
  • LOWER BOUND SOLUTION UPPER BOUND SOLUTION： The assumed displacement form of the finite element solution gives a lower bound on the maximum displacements and strain energy (i.e. these are under estimated) for a given set of forces. This is the usual form of the finite element method. The assumed stress form of the finite element solution gives an upper bound on the maximum stresses and strain energy (i.e. these are over estimated) for a given set of displacements.
  • LUMPED MASS MODEL: When the coefficients of the mass matrix are combined to produce a diagonal matrix. The total mass and the position of the structures center of gravity are preserved.

M

  • MASS: The constant(s) of proportionality relating the acceleration(s) to the force(s). For a discrete parameter multi degree of freedom model this is usually given as a mass matrix.
  • MASS ELEMENT: An element lumped at a node representing the effect of a concentrated mass in different coordinate directions.
  • MASS MATRIX: The matrix relating acceleration to forces in a dynamic analysis. This can often be approximated as a diagonal matrix with no significant loss of accuracy.
  • MASTER FREEDOMS: The freedoms chosen to control the structural response when using a Guyan reduction or sub structuring methods.
  • MATERIAL LOSS FACTOR: A measure of the damping inherent within a material when it is dynamically loaded.
  • MATERIAL PROPERTIES: The physical properties required to define the material behavior for analysis purposes. For stress analysis typical required material properties are Young’s modulus, Poisson’s ratio, density and coefficient of linear expansion. The material properties must have been obtained by experiment.
  • MATERIAL STIFFNESS MATRIX MATERIAL FLEXIBILITY MATRIX: The material stiffness matrix allows the stresses to be found from a given set of strains at a point. The material flexibility is the inverse of this, allowing the strains to be found from a given set of stresses. Both of these matrices must be symmetric and positive definite.
  • MATRIX DISPLACEMENT METHOD: A form (the standard form) of the finite element method where displacements are assumed over the element. This gives a lower bound solution.
  • MATRIX FORCE METHOD: A form of the finite element method where stresses (internal forces) are assumed over the element. This gives an upper bound solution.
  • MATRIX INVERSE: If matrix A times matrix B gives the unit matrix then A is the inverse of B (B is the inverse of A). A matrix has no inverse if it is singular.
  • MATRIX NOTATION MATRIX ALGEBRA: A form of notation for writing sets of equations in a compact manner. Matrix notation highlights the generality of various classes of problem formulation and solution. Matrix algebra can be easily programmed on a digital computer.
  • MATRIX PRODUCTS: Two matrices A and B can be multiplied together if A is of size (j*k) and B is of size (k*l). The resulting matrix is of size (j*l).
  • MATRIX TRANSPOSE: The process of interchanging rows and columns of a matrix so that the j’th column becomes the j’th row.
  • MEAN SQUARE CONVERGENCE: A measure of the rate of convergence of a solution process. A mean square convergence indicates a rapid rate of convergence.

  • MEMBRANE: Membrane behavior is where the strains are constant from the center line of a beam or center surface of a plate or shell. Plane sections are assumed to remain plane. A membrane line element only has stiffness along the line, it has zero stiffness normal to the line. A membrane plate has zero stiffness normal to the plate. This can cause zero energy (no force required) displacements in these normal directions. If the stresses vary linearly along the normal to the centerline then this is called bending behavior.

  • Mesh (Grid): The elements and nodes, together, form a mesh (grid), which is the central data structure in FEA.

  • MESH DENSITY MESH REFINEMENT: The mesh density indicates the size of the elements in relation to the size of the body being analyzed. The mesh density need not be uniform all over the body There can be areas of mesh refinement (more dense meshes) in some parts of the body. Making the mesh finer is generally referred to as h -refinement. Making the element order higher is referred to as p -refinement.
  • MESH GENERATION ELEMENT GENERATION: The process of generating a mesh of elements over the structure. This is normally done automatically or semi-automatically.
  • MESH SPECIFICATION: The process of choosing and specifying a suitable mesh of elements for an analysis.
  • MESH SUITABILITY: The appropriate choice of element types and mesh density to give a solution to the required degree of accuracy.
  • MINDLIN ELEMENTS: A form of thick shell element.
  • MOBILITY: The ratio of the steady state velocity response to the value of the forcing function for a sinusoidal excitation.
  • MODAL DAMPING: The damping associated with the generalized displacements defined by the eigenvectors. Its value has no physical significance since the eigenvector contains an arbitrary normalizing factor.
  • MODAL MASS: The mass associated with the generalized displacements defined by the eigenvectors. Its value has no physical significance since the eigenvector contains an arbitrary normalizing factor but the ratio of modal stiffness to modal mass is always the eigenvalue.
  • MODAL STIFFNESS: The stiffness associated with the generalized displacements defined by the eigenvectors. Its value has no physical significance since the eigenvector contains an arbitrary normalizing factor but the ratio of modal stiffness to modal mass is always the eigenvalue.
  • MODAL TESTING: The experimental technique for measuring resonant frequencies (eigenvalues) and mode shapes (eigenvectors).
  • MODE PARTICIPATION FACTOR: The generalized force in each modal equation of a dynamic system.
  • MODE SHAPE: Same as the e igenvector. The mode shape often refers to the measure mode, found from a modal test.
  • MODELLING: The process of idealizing a system and its loading to produce a numerical (finite element) model.
  • MODIFIED NEWTON-RAPHSON: A form of the Newton-Raphson process f or solving non-linear equations where the tangent stiffness matrix is held constant for some steps. It is suitable for mildly non-linear problems.
  • MOHR COULOMB EQUIVALENT STRESS: A form of equivalent stress that includes the effects of friction in granular (e.g. sand) materials.
  • MULTI DEGREE OF FREEDOM: The system is defined by more than one force/displacement equation.
  • MULTI-POINT CONSTRAINTS: Where the constraint is defined by a relationship between more than one displacement at different node points.

N

  • NATURAL FREQUENCY: The frequency at which a structure will vibrate in the absence of any external forcing. If a model has n degrees of freedom then it has n natural frequencies. The eigenvalues of a dynamic system are the squares of the natural frequencies.
  • NATURAL MODE: Same as the eigenvector.
  • NEWMARK METHOD NEWMARK BETA METHOD: An implicit solution method for integrating second order equations of motion. It can be made unconditionally stable.
  • NEWTON COTES FORMULAE: A family of methods for numerically integrating a function.
  • NEWTON-RAPHSON NON-LINEAR SOLUTION: A general technique for solving non-linear equations. If the function and its derivative are known at any point then the Newton-Raphson method is second order convergent.
  • NODAL VALUES: The value of variables at the node points. For a structure typical possible nodal values are force, displacement, temperature, velocity, x, y, and z.
  • NODE: A node is a point in the domain, and is often the vertex of several elements. A node is also called a nodal point. computers to generate finite element mesh automatically. There are many different algorithms for automatic mesh generation. Click here to see some automatically generated mesh samples.
  • NON-CONFORMING ELEMENTS: Elements that do not satisfy compatibility either within the element or across element boundaries or both. Such elements are not generally reliable although they might give very good solutions in some circumstances.
  • NON-HOLONOMIC CONSTRAINTS: Constraints that can only be defined at the level of infinitesimal displacements. They cannot be integrated to give global constraints.
  • NON-LINEAR SYSTEM/ANALYSIS: Nonlinear Finite Element Analysis considers material nonlinearity and/or geometric nonlinearity of an engineering system. Geometric nonlinear analysis is also called large deformation analysis.
  • NON-STATIONARY RANDOM: A force or response that is random and its statistical properties vary with time.
  • NON-STRUCTURAL MASS: Mass that is present in the system and will affect the dynamic response but it is not a part of the structural mass (e.g. the payload).
  • NORM: A scalar measure of the magnitude of a vector or a matrix.
  • NUMERICAL INTEGRATION: The process of finding the approximate integral of a function by numerical sampling and summing. In the finite element method the element matrices are usually formed by the Gaussian quadrature form of numerical integration.

O

  • OPTIMAL SAMPLING POINTS: The minimum number of Gauss points required to integrate an element matrix. Also the Gauss points at which the stresses are most accurate (see reduced Gauss points).
  • OVER DAMPED SYSTEM: A system which has an equation of motion where the damping is greater than critical. It has an exponentially decaying, non-oscillatory impulse response.
  • OVERSTIFF SOLUTIONS: Lower bound solutions. These are associated with the assumed displacement method.

P

  • PARTICIPATION FACTOR: The fraction of the mass that is active for a given mode with a given distribution of dynamic loads. Often this is only defined for the specific load case of inertia (seismic) loads.
  • PATCH TEST: A test to prove that a mesh of distorted elements can represent constant stress situations and strain free rigid body motions (i.e. the mesh convergence requirements) exactly.
  • PDEs: partial differential equations.
  • PERIODIC RESPONSE FORCE: A response (force) that regularly repeats itself exactly.
  • PHASE ANGLE: The ratio of the in phase component of a signal to its out of phase component gives the tangent of the phase angle of the signal relative to some reference.
  • PLANE STRAIN/STRESS: A two dimensional analysis is plane stress if the stress in the third direction is assumed zero. This is valid if the dimension of the body in this direction is very small, e.g. a thin plate. A two dimensional analysis is plane strain if the strain in the third direction is assumed zero. This is valid if the dimension of the body in this direction is very large, e.g. a cross- sectional slice of a long body.
  • PLATE BENDING ELEMENTS: Two-dimensional shell elements where the in plane behavior of the element is ignored. Only the out of plane bending is considered.
  • POISSONS RATIO: The material property in Hooke s law relating strain in one direction arising from a stress in a perpendicular direction to this. Poissons' ratio can be defined in WELSIM material module.
  • POST-PROCESSING: The interrogation of the results after the analysis phase. This is usually done with a combination of graphics and numerics.
  • POTENTIAL ENERGY: The energy associated with the static behavior of a system. For a structure this is the strain energy.
  • POWER METHOD: A method for finding the lowest or the highest eigenvalue of a system.
  • PRANDTL-REUSS EQUATIONS: The equations relating an increment of stress to an increment of plastic strain for a metal undergoing plastic flow.
  • PREPROCESSING: The process of preparing finite element input data involving model creation, mesh generation,material definition, and load and boundary condition application.
  • PRIMARY COMPONENT: Those parts of the structure that are of direct interest for the analysis. Other parts are secondary components.
  • PRINCIPAL CURVATURE: The maximum and minimum radii of curvature at a point.
  • PRINCIPAL STRESSES: The maximum direct stress values at a point. They are the eigenvalues of the stress tensor.
  • PROPORTIONAL DAMPING: A damping matrix that is a linear combination of the mass and stiffness matrices. The eigenvectors of a proportionally damped system are identical to those of the undamped system.
  • P-METHOD: A method of finite element analysis that uses P- convergence to iteratively minimize the error of analysis.
  • QR METHOD: A technique for finding eigenvalues. This is currently the most stable method for finding eigenvalues but it is restricted in the size of problem that it can solve.
  • RANDOM VIBRATIONS: The applied loading is only known in terms of its statistical properties. The loading is nondeterministic in that its value is not known exactly at any time but its mean, mean square, variance and other statistical quantities are known.

R

  • RANK DEFICIENCY: A measure of how singular a matrix is.
  • RAYLEIGH DAMPING: Damping that is proportional to a linear combination of the stiffness and mass. This assumption has no physical basis but it is mathematically convenient to approximate low damping in this way when exact damping values are not known.
  • RAYLELGH QUOTIENT: The ratio of stiffness times displacement squared (2*strain energy) to mass times displacement squared. The minimum values of the Rayleigh quotient are the eigenvalues.
  • REACTION FORCES: The forces generated at support points when a structure is loaded. Reaction force is supported in WELSIM.
  • REFERENCE TEMPERATURE: The reference temperature defines the temperature at which strain in the design does not result from thermal expansion or contraction. For many situations, reference temperature is adequately defined as room temperature. Define reference temperature in the properties of an environment.
  • REDUCED INTEGRATION: If an element requires an l*m*n Gauss rule to integrate the element matrix exactly then (l-1)(m-1)(n-1) is the reduced integration rule. For many elements the stresses are most accurate at the reduced integration points. For some elements the matrices are best evaluated by use of the reduced integration points. Use of reduced integration for integrating the elements can lead to zero energy and hour glassing modes.
  • RESPONSE SPECTRUM METHOD: A method for characterizing a dynamic transient forcing function and the associated solution technique. It is used for seismic and shock type loads.
  • RIGID BODY DEFORMATIONS: A non-zero displacement pattern that h as zero strain energy associate with it.
  • RIGID BODY DISPLACEMENT: A non-zero displacement pattern that has zero strain energy associate with it.
  • RIGID BODY MODES: If a displaced shape does not give rise to any strain energy in the structure then this a rigid body mode. A general three-dimensional unsupported structure has 6 rigid body modes, 3 translation and 3 rotation.
  • RIGID LINKS/OFFSETS: This is a connection between two non-coincident nodes assuming that the connection is infinitely stiff. This allows the degrees of freedom at one of the nodes (the slave node) to be deleted from the system. It is a form of multi-point constraint.
  • ROUNDOFF ERROR: Computers have a fixed word length and hence only hold numbers to a certain number of significant figures. If two close numbers are subtracted one from another then the result loses the first set of significant figures and hence loses accuracy. This is round off error.

S

  • SECANT STIFFNESS: The stiffness defined by the slope of the line from the origin to the current point of interest on a load/deflection curve.
  • SECONDARY COMPONENTS: Components of a structure not of direct interest but they may have some influence of the behavior of the part of the structure that is of interest (the primary component) and have to be included in the analysis in some approximate form.
  • SEEPAGE FLOW: Flows in porous materials
  • SEISMIC ANALYSIS: The calculation of the dynamic displacement and stress response arising from earthquake excitations.
  • SELECTED REDUCED INTEGRATION: A form of Gaussian quadrature where different sets of Gauss points are used for different strain components.
  • SELF ADJOINT EQUATIONS: A form of matrix products that preserves symmetry of equations. The product A*B*A(transpose) is self -adjoint if the matrix B is symmetric. The result of the product will be symmetric for any form of A that is of a size compatible with B. This form o f equation occurs regularly within the finite element method. Typically it means that for a structural analysis the stiffness (and mass) matrices for any element or element assembly will be symmetric.
  • SELF EQUILIBRATING LOADS: A load set is self -equilibrating if all of its resultants are zero. Both translation and moment resultants are zero.
  • SEMI-LOOF ELEMENT: A form of thick shell element.
  • SHAKEDOWN: If a structure is loaded cyclically and initially undergoes some plastic deformation then it is said to shakedown if the behavior is entirely elastic after a small number of load cycles.
  • SIMULTANEOUS VECTOR ITERATION: A method for finding the first few eigenvalues and eigenvectors of a finite element system. This is also known as subspace vector iteration.
  • SINGLE DEGREE OF FREEDOM: The system is defined by a single force/displacement equation.
  • SINGLE POINT CONSTRAINT: Where the constraint is unique to a single node point.
  • SINGULAR MATRIX: A square matrix that cannot be inverted.
  • SKEW DISTORTION (ANGULAR DISTORTION): A measure of the angular distortion arising between two vectors that are at right angles in the basis space when these are mapped to the real coordinate space. If this angle approaches zero the element becomes ill-conditioned.
  • SOLUTION DIAGNOSTICS: Messages that are generated as the finite element solution progresses. These should always be checked for relevance but the are often only provided for information purposes
  • SOLUTION EFFICIENCY: A comparative measure between two solutions of a given problem defining which is the ‘best’. The measures can include accuracy, time of solution, memory requirements and disc storage space.
  • SPARSE MATRIX METHODS: Solution methods that exploit the sparse nature of finite element equations. Such methods include the frontal solution and Cholesky (skyline) factorization for direct solutions, conjugate gradient methods for iterative solutions and the Lanczos method and subspace iteration (simultaneous vector iteration) for eigenvalue solutions.
  • SPECTRAL DENSITY: The Fourier transform of the correlation function. In random vibrations it gives a measure of the significant frequency content in a system. White noise has a constant spectral density for all frequencies.
  • SPLINE CURVES: A curve fitting technique that preserves zero, first and second derivative continuity across segment boundaries.
  • STATIC ANALYSIS: Analysis of stresses and displacements in a structure when the applied loads do not vary with time.
  • STATICALLY DETERMINATE STRUCTURE: A structure where all of the unknowns can be found from equilibrium considerations alone.
  • STATICALLY EQUIVALENT LOADS: Equivalent nodal loads that have the same equilibrium resultants as the applied loads but do not necessarily do the same work as the applied loads.
  • STATICALLY INDETERMINATE STRUCTURE REDUNDANT: A structure where all of the unknowns can not be found from equilibrium considerations alone. The compatibility equations must also be used. In this case the structure is said to be redundant.
  • STATIONARY RANDOM EXCITATION: A force or response that is random but its statistical characteristics do not vary with time.
  • STEADY-STATE HEAT TRANSFER: Determination of the temperature distribution of a mechanical part having reached thermal equilibrium with the environmental conditions. There are no time varying changes in the resulting temperatures.
  • STIFFNESS: A set of values which represent the rigidity or softness of a particular element. Stiffness is determined by material type and geometry.
  • STIFFNESS MATRIX: The parameter(s) that relate the displacement(s) to the force(s). For a discrete parameter multi degree of freedom model this is usually given as a stiffness matrix.
  • STRAIN: A dimensionless quantity calculated as the ratio of deformation to the original size of the body.
  • STRAIN ENERGY: The energy stored in the system by the stiffness when it is displaced from its equilibrium position.
  • STRESS: The intensity of internal forces in a body (force per unit area) acting on a plane within the material of the body is called the stress on that plane.
  • STRESS ANALYSIS: The computation of stresses and displacements due to applied loads. The analysis may be elastic, inelastic, time dependent or dynamic.
  • STRESS AVERAGING STRESS SMOOTHING: The process of filtering the raw finite element stress results to obtain the most realistic estimates of the true state of stress.
  • STRESS CONCENTRATION: A local area of the structure where the stresses are significantly higher than the general stress level. A fine mesh of elements is required in such regions if accurate estimates of the stress concentration values are required.
  • STRESS CONTOUR PLOT: A plot of a stress component by a series of color filled contours representing regions of equal stress. WELSIM can plot stress contour.
  • STRESS DISCONTINUITIES/ERROR ESTIMATES: Lines along which the stresses are discontinuous. If the geometry or loading changes abruptly along a line then the true stress can be discontinuous. In a finite element solution the element assumptions means that the stresses will generally be discontinuous across element boundaries. The degree of discontinuity can then be used to form an estimate of the error in the stress within the finite element calculation.
  • STRESS EXTRAPOLATION: The process of taking the stress results at the optimum sampling points for an element and extrapolating these to the element node points.
  • STRESS INTENSITY FACTORS: A measure of the importance of the stress at a sharp crack tip (where the actual stress values will be infinite) used to estimate if the crack will propagate.
  • STRESS/STRAIN VECTOR/TENSOR: The stress (strain) vector is the components of stress (strain) written as a column vector. For a general three dimensional body this is a (6×1) matrix. The components of stress (strain) written in tensor form. For a general three dimensional body this forms a (3×3) matrix with the direct terms down the diagonal and the shear terms as the off-diagonals.
  • STRESS-STRAIN LAW: The material property behavior relating stress to strain. For a linear behavior this is Hookes law (linear elasticity). For elastic plastic behavior it is a combination of Hookes law and the Prandtl-Reuss equations.
  • SUBSPACE VECTOR ITERATION: A method for finding the first few eigenvalues and eigenvectors of a finite element system. This is also known as simultaneous vector iteration.
  • SUBSTRUCTURING: An efficient way of solving large finite element analysis problems by breaking the model into several parts or substructures, analyzing each one individually, and then combining them for the final results.
  • SUBSTRUCTURING SUPER ELEMENT METHOD: Substructuring is a form of equation solution method where the structure is split into a series of smaller structures -the substructures. These are solved to eliminate the internal freedoms and the complete problem solved by only assembling the freedoms on the common boundaries between the substructures. The intermediate solution where the internal freedoms of a substructure have been eliminated gives the super element matrix for the substructure.
  • SURFACE MODELING: The geometric modeling technique in which the model is created in terms of its surfaces only without any volume definition.

T

  • TEMPERATURE CONTOUR PLOTS: A plot showing contour lines connecting points of equal temperature.
  • TETRAHEDRON/TETRAHEDRAL ELEMENT: A three dimensional four sided solid element with triangular faces.
  • THERMAL CAPACITY: The material property defining the thermal inertia of a material. It relates the rate of change of temperature with time to heat flux.
  • THERMAL CONDUCTIVITY: The material property relating temperature gradient to heat flux. Temperature-dependent thermal conductivity is supported in WELSIM.
  • THERMAL LOADS: The equivalent loads on a structure arising from thermal strains. These in turn arise from a temperature change.
  • THERMAL STRAINS: The components of strain arising from a change in temperature.
  • THERMAL STRESS ANALYSIS: The computation of stresses and displacements due to change in temperature.
  • THIN/THICK SHELL ELEMENT: In a shell element the geometry is very much thinner in one direction than the other two. It can then be assumed stresses can only vary linearly at most in the thickness direction. If the through thickness shear strains can be taken as zero then a thin shell model is formed. This uses the Kirchoff shell theory If the transverse shear strains are not ignored then a thick shell model is formed. This uses the Mindlin shell theory. For the finite element method the thick shell theory generates the most reliable form of shell elements. There are two forms of such elements, the Mindlin shell and the Semi-Loof shell.
  • TIME DOMAIN: The structures forcing function and the consequent response is defined in terms of time histories. The Fourier transform of the time domain gives the corresponding quantity in the frequency domain.
  • TRANSIENT FORCE: A forcing function that varies for a short period of time and then settles to a constant value.
  • TRANSIENT RESPONSE: The component of the system response that does not repeat itself regularly with time.
  • TRANSITION ELEMENT: Special elements that have sides with different numbers of nodes. They are used to couple elements with different orders of interpolation, typically a transition element with two nodes on one edge and three on another is used to couple a 4-node quad to an 8-node quad.
  • TRANSIENT HEAT TRANSFER: Heat transfer problems in which temperature distribution varies as a function of time.
  • TRIANGULAR ELEMENTS: Two dimensional or surface elements that have three edges.
  • TRUSS ELEMENT: A one dimensional line element defined by two nodes resisting only axial loads.

U

  • ULTIMATE STRESS: The failure stress (or equivalent stress) for the material.
  • UNDAMPED NATURAL FREQUENCY: The square root of the ratio of the stiffness to the mass (the square root of the eigenvalue). It is the frequency at which an undamped system vibrates naturally. A system with n degrees of freedom has n natural frequencies.
  • UNDER DAMPED SYSTEM: A system which has an equation of motion where the damping is less than critical. It has an oscillatory impulse response.
  • UPDATED/TOTAL LAGRANGIAN: The updated Lagrangian coordinate system is one where the stress directions are referred to the last known equilibrium state. The total Lagrangian coordinate system is one where the stress directions are referred to the initial geometry. Both algorithms are supported in WELSIM.

V

  • VARIABLE BANDWIDTH (SKYLINE): A sparse matrix where the bandwidth is not constant. Some times called a skyline matrix.
  • VIRTUAL DISPLACEMENTS: An arbitrary imaginary change of the system configuration consistent with its constraints.
  • VIRTUAL WORK/DISPLACEMENTS/FORCES: Techniques for using work arguments to establish equilibrium equations from compatibility equations (virtual displacements) and to establish compatibility equations from equilibrium (virtual forces).
  • VISCOUS DAMPING: The damping is viscous when the damping force is proportional to the velocity.
  • VOLUME/VOLUMETRIC DISTORTION: The distortion measured by the determinant of the Jacobian matrix, det J.
  • VON MISES STRESS: An “averaged” stress value calculated by adding the squares of the 3 component stresses (X, Y and Z directions) and taking the square root of their sums. This value allows for a quick method to locate probable problem areas with one plot.
  • VON MISES/TRESCA EQUIVALENT STRESS: Equivalent stress measures to represent the maximum shear stress in a material. These are used to characterize flow failures (e.g. plasticity and creep) in WELSIM. From test results the VonMises form seems more accurate but the Tresca form is easier to handle.

W

  • WHIRLING STABILITY: The stability of rotating systems where centrifugal and Coriolis are also present.
  • WILSON THETA METHOD: An implicit solution method for integrating second order equations of motion. It can be made unconditionally stable.

Y

  • YOUNG’S MODULUS: The material property relating a uniaxial stress to the corresponding strain.

Z

  • ZERO ENERGY/STIFFNESS MODES: Non-zero patterns of displacements that have no energy associated with them. No forces are required to generate such modes, Rigid body motions are zero energy modes. Buckling modes at their buckling loads are zero energy modes. If the elements are not fully integrated they will have zero energy displacement modes. If a structure has one or more zero energy modes then the matrix is singular.
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Glossary

A

  • ACCELERATION： The second time derivative of the displacement (the first time derivative of the velocity).
  • ADAPTIVE FINITE ELEMENT METHOD/ADAPTIVE MESHING： An adaptive finite element solver iteratively performs finite element analysis, determines the areas of the mesh where the solution is not sufficiently accurate and refines the mesh in those areas until the solution obtains the prescribed degree of accuracy. Adaptive Meshing involves automatically improving the mesh where necessary to meet specified convergence criteria.
  • ASPECT RATIO: The ratio of the longest to shortest side lengths on an element.
  • ASSEMBLY: Geometric:Two or more parts mated together. FEA: The process of assembling the element matrices together to form the global matrix. Typically element stiffness matrices are assembled to form the complete stiffness matrix of the structure.
  • AUTOMATIC MESH GENERATION: The process of generating a mesh of elements over the volume that is being analyzed. There are two forms of automatic mesh generation: Free Meshing -Where the mesh has no structure to it. Free meshing generally uses triangular and tetrahedral elements. Mapped Meshing -Where large regions, if not all, of the volume is covered with regular meshes. This can use any form of element. Free meshing can be used to fill any shape. Mapped meshing can only be used on some shapes without elements being excessively distorted.
  • AXISYMMETRY: If a shape can be defined by rotating a cross- section about a line (e.g. a cone) then it is said to be axisymmetric. This can be used to simplify the analysis of the system. Such models are sometimes called two and a half dimensional since a 2D cross- section represents a 3D body.

B

  • BARLOW POINTS： The set of Gauss integration points that give the best estimates of the stress for an element. For triangles and tetrahedra these are the full Gauss integration points. For quadrilateral and brick elements they are the reduced Gauss points.
  • BASIS SPACE： When an element is being constructed it is derived from a simple regular shape in non-dimensional coordinates. The coordinates used to define the simple shape form the basis space. In its basis space a general quadrilateral is a 2×2 square and a general triangle is an isosceles triangle with unit side lengths.
  • BEAM ELEMENT: A line element that has both translational and rotational degrees of freedom. It represents both membrane and bending actions.
  • BENDING: Bending behavior is where the strains vary linearly from the centerline of a beam or center surface of a plate or shell.There is zero strain on the centerline for pure bending. Plane sections are assumed to remain plane. If the stresses are constant normal to the centerline then this is called membrane behavior.
  • BENDING STRESS: A compressive and/or tensile stress resulting from the application of a nonaxial force to a structural member.
  • BODY FORCE VECTOR: Mechanical loadings within the interior of the volume, typically inertia loadings in a stiffness analysis.
  • BOUNDARY CONDITIONS: The boundary conditions of a function are values of the function at the edge of the range of some of its variables. Knowledge of some of the boundary conditions is needed to solve an engineering problem or to find an unknown function.
  • BOUNDARY ELEMENT/INTEGRAL: A method of solving differential equations by taking exact solutions to the field equations loaded by a point source and then finding the strengths of sources distributed around the boundary of the body required to satisfy the boundary conditions on the body.
  • BUBBLE FUNCTIONS: Element shape functions that are zero along the edges of the element. They are non-zero within the interior of the element.
  • BUCKLING (SNAP THROUGH): The situation where the elastic stiffness of the structure is cancelled by the effects of compressive stress within the structure. If the effect of this causes the structure to suddenly displace a large amount in a direction normal to the load direction then it is classical bifurcation buckling. If there is a sudden large movement in the direction of the loading it is snap through buckling.

C

  • CAE: computer aided engineering.
  • CENTRAL DIFFERENCE METHOD: A method for numerically integrating second order dynamic equations of motion. It is widely used as a technique for solving non-linear dynamic problems.
  • CHARACTERISTIC VALUE: Same as the eigenvalue.
  • CHARACTERISTIC VECTOR: Same as the eigenvector.
  • CHOLESKY FACTORISATION (SKYLINE): A method of solving a set of simultaneous equations that is especially well suited to the finite element method. It is sometimes called a skyline solution. Choose to optimize the profile o f the matrix if a renumbering scheme is used.
  • COEFFICIENT OF VISCOUS DAMPING: The system parameter relating force to velocity.
  • COMPATIBILITY OF STRAINS: Compatibility of strain is satisfied if strains that are continuous before loading are continuous after.
  • COMPLETE DISPLACEMENT FIELD: When the functions interpolating the field variable (typically the displacements) form a complete nth order polynomial in all directions.
  • COMPLEX EIGENVALUES: The eigenvectors of a damped system. For proportionally damped systems they are the same as the undamped eigenvectors. For non-proportionally damped systems with damping in all modes less th an critical they are complex numbers and occur as complex conjugate pairs.
  • COMPLEX EIGENVECTORS: The eigenvalues of any damped system. If the damping is less than critical they will occur as complex conjugate pairs even for proportionally damped systems. The real part of the complex eigenvalue is a measure of the damping in the mode and should always be negative. The imaginary part is a measure of the resonant frequency.
  • COMPOSITE MATERIAL: A material that is made up of discrete components, typically a carbon-epoxy composite material or a glass-fiber material. Layered material and foam materials are also forms of composite materials.
  • COMPUTATIONAL FLUID DYNAMICS (CFD): A computer-based numerical study of turbulent fluid flow using approximate methods such as the finite element method, the fine difference method, the boundary element method, the finite volume methods, and so on.
  • CONDITION NUMBER: The ratio of the highest eigenvalue to the lowest eigenvalue of a matrix. The exponent of this number gives a measure of the number of digits required in the computation to maintain numerical accuracy. The higher the condition number the more chance of numerical error and the slower the rate of convergence for iterative solutions.
  • CONDITIONAL/UNCONDITIONAL STABILITY: Any scheme for numerically integrating dynamic equations of motion in a step-by- step form is conditionally stable if there is a maximum time step value that can be used. It is unconditionally stable (but not necessarily accurate) if any length of time step can be used.
  • CONJUGATE GRADIENT METHOD: A method for solving simultaneous equations iteratively. It is closely related to the Lanczos method for finding the first few eigenvalues and eigenvectors of a set of equations.
  • CONSISTENT DISPLACEMENTS AND FORCES: The displacements and forces act at the same point and in the same direction so that the sum of their products give a work quantity. If consistent displacements and forces are used the resulting stiffness and mass matrices are symmetric.
  • CONSTANT STRAIN CONSTANTSTRESS: For structural analysis an element must be able to reproduce a state of constant stress and strain under a suitable loading to ensure that it will converge to the correct solution. This is tested for using the patch test.
  • CONSTITUTIVE RELATIONSHIPS: The equations defining the material behavior for an infinitesimal volume of material. For structures these are the stress -strain laws and include Hookes law for elasticity and the Prandle-Reuss equations for plasticity.
  • CONSTRAINT EQUATIONS (MULTI POINT CONSTRAINTS): If one group of variables can be defined in terms of another group then the relationship between the two are constraint equations. Typically the displacements on the face of an element can be constrained to remain plane but the plane itself can move.
  • CONSTRAINTS: Known values of, or relationships between, the displacements in the coordinate system.
  • CONTACT PROBLEMS: A contact problem occurs when two bodies that are originally apart can come together, or two bodies that are originally connected can separate.
  • CONTINUOUS MASS MODELS: The system mass is distributed between the degrees of freedom. The mass matrix is not diagonal.
  • CONTOUR PLOTTING: A graphical representation of the variation of a field variable over a surface, such as stress, displacement, or temperature. A contour line is a line of constant value for the variable. A contour band is an area of a single color for values of the variable within two limit values.
  • CONVERGENCE REQUIREMENTS: For a structural finite element to converge as the mesh is refined it must be able to represent a state of constant stress and strain free rigid body movements exactly. There are equivalent requirements for other problem types.
  • CRANK-NICHOLSON SCHEME: A method for numerically integrating first order dynamic equations of motion. It is widely used as a technique for solving thermal transient problems.
  • CRITICAL ENERGY RELEASE: This is a material property defining the minimum energy that a propagating crack must release in order for it to propagate. Three critical energies, or modes of crack propagation, have been identified. Mode 1 is the two surfaces of the crack moving apart. Mode 2 is where the two surfaces slide from front to back. Mode 3 is where the to surfaces slide sideways.
  • CRITICALLY DAMPED SYSTEM CRITICAL DAMPING: The dividing line between under damped and over damped systems where the equation of motion has a damping value that is equal to the critical damping.
  • CYCLIC SYMMETRY: A generalization of axisymmetry. The structure is composed of a series of identical sectors that are arranged circumferentially to form a ring. A turbine disc with blades attached is atypical example.

D

  • DAMPED EIGENVALUES: Same as complex eigenvalues.
  • DAMPED EIGENVECTORS: Same as complex eigenvectors.
  • DAMPED NATURAL FREQUENCY: The frequency at which the damped system vibrates naturally when only an initial disturbance is applied.
  • DAMPING: Any mechanism that dissipates energy in a vibrating system.
  • DAMPING FACTOR (DECAY FACTOR): The damping factor is the ratio of the actual damping to the critical damping. It is often specified as a percentage. If the damping factor is less than one then the system can undergo free vibrations. The free vibrations will decay to zero with time. If the damping factor is greater than one then the decay is exponential and no vibrations occur. For most structures the damping factor is very small.
  • DEGENERATE ELEMENTS: Elements that are defined as one shape in the basis space but they are a simpler shape in the real space. A quadrilateral can degenerate into a triangle. A brick element can degenerate into a wedge, a pyramid or a tetrahedron. Degenerate elements should be avoided in practice.
  • DEGREES OF FREEDOM: The number of equations of equilibrium for the system. In dynamics, the number of displacement quantities which must be considered in order to represent the effects of all of the significant inertia forces. Degrees of freedom define the ability of a given node to move in any direction in space. There are six types of DOF for any given node: 3 possible translations (one each in the X,Y and Z directions) and 3 possible rotations (one rotation about each of the X,Y, and X axes). DOF are defined and restricted by the elements and constraints associated with each node.
  • DET(J) DET J: The Jacobian matrix is used to relate derivatives in the basis space to the real space. The determinant of the Jacobian – det(j) -is a measure of the distortion of the element when mapping from the basis to the real space.
  • DEVIATORIC STRESS STRESS DEVIATORS: A measure of stress where the hydrostatic stress has been subtracted from the actual stress. Material failures that are flow failures (plasticity and creep) fail independently of the hydrostatic stress. The failure is a function of the deviatoric stress.
  • DIAGONAL GENERALIZED MATRIX: The eigenvectors of a system can be used to define a coordinate transformation such that, in these generalized coordinates the coefficient matrices (typically mass and stiffness) are diagonal.
  • DIE-AWAY LENGTH: If there is a stress concentration in a structure the high stress will reduce rapidly with distance from the peak value. The distance over which it drops to some small value is called the die-away length. A fine mesh is required over this die-away length for accurate stress results.
  • DIRECT INTEGRATION: The name for various techniques for numerically integrating equations of motion. These are either implicit or explicit methods and include central difference, Crank-Nicholson, Runge-Kutta, Newmark beta and Wilson theta.
  • DISCRETE PARAMETER MODELS (DISCRETISED APPROACH): The model is defined in terms of an ordinary differential equation and the system has a finite number of degrees of freedom.
  • DISCRETIZATION: The process of dividing geometry into smaller pieces (finite elements) to prepare for analysis, i.e. Meshing.
  • DISPLACEMENT METHOD (DISPLACEMENT SOLUTION) :A form of discrete parameter model where the displacements of the system are the basic unknowns.
  • DISPLACEMENT: The distance, translational and rotational, that a node travels from its initial position to its post-analysis position. The total displacement is represented by components in each of the 3 translational directions and the 3 rotational directions.
  • DISPLACEMENT PLOTS: Plots showing the deformed shape of the structure. For linear small deflection problems the displacements are usually multiplied by a magnifying factor before plotting the deformed shape.
  • DISPLACEMENT VECTOR: The nodal displacements written as a column vector.

  • DOMAIN: In mathematics, a domain is the set of independent variables for which a function is defined. In finite element analysis, a domain is a continuous system (region) over which the laws of physics govern. In structural engineering, a domain could be a beam or a complete building frame. In mechanical engineering, a domain could be a piece of machine parts or a thermal field.

  • DRUCKER-PRAGER EQUIVALENT STRESSES: An equivalent stress measure for friction materials (typically sand). The effect of hydrostatic stress is included in the equivalent stress.

  • DYNAMIC ANALYSIS: An analysis that includes the effect of the variables changing with time as well as space.

  • DYNAMIC FLEXIBILITY MATRIX: The factor relating the steady state displacement response of a system to a sinusoidal force input. It is the same as the recep tance.

  • DYNAMIC MODELLING: A modeling process where consideration as to time effects in addition to spatial effects are included. A dynamic model can be the same as a static model or it can differ significantly depending upon the nature of the problem.
  • DYNAMIC RESPONSE: The time dependent response of a dynamic system in terms of its displacement, velocity or acceleration at any given point of the system.
  • DYNAMIC STIFFNESS MATRIX: If the structure is vibrating steadily at a frequency w then the dynamic stiffness is (K+iwC w2M) It is the inverse of the dynamic flexibility matrix.
  • DYNAMIC STRESSES：Stresses that vary with time and space.
  • DYNAMIC SUBSTRUCTURING： Special forms of substructuring used within a dynamic analysis. Dynamic substructuring is always approximate and causes some loss of accuracy in the dynamic solution.

E

  • EIGENVALUE PROBLEM： Problems that require calculation of eigenvalues and eigenvectors for their solution. Typically solving free vibration problems or finding buckling loads.
  • ELASTIC FOUNDATION： If a structure is sitting on a flexible foundation the supports are treated as a continuous elastic foundation. The elastic foundation can have a significant effect upon the structural response.
  • ELASTIC STIFFNESS： If the relationship between loads and displacements is linear then the problem is elastic. For a multi-degree of freedom system the forces and displacements are related by the elastic stiffness matrix.
  • ELECTRIC FIELDS： Electro-magnetic and electro-static problems form electric field problems.

  • ELEMENT： An element is a portion of the problem domain, and is typically some simple shape like a triangle or quadrilateral in 2D, or tetrahedron or hex solid in 3D.

  • ELEMENT ASSEMBLY： Individual element matrices have to be assembled into the complete stiffness matrix. This is basically a process of summing the element matrices. This summation has to be of the correct form. For the stiffness method the summation is based upon the fact that element displacements at common nodes must be the same.

  • ELEMENT STRAINS/STRESSES： Stresses and strains within elements are usually defined at the Gauss points (ideally at the Barlow points) and the node points. The most accurate estimates are at the reduced Gauss points (more specifically the Barlow points). Stresses and strains are usually calculated here and extrapolated to the node points.
  • ENERGY METHODS HAMILTONS PRINCIPLE： Methods for defining equations of equilibrium and compatibility through consideration of possible variations of the energies of the system. The general form is Hamiltons principle and sub-sets of this are the principle of virtual work including the principle of virtual displacements (PVD) and the principle of virtual forces (PVF).
  • ENGINEERING/MATHEMATICAL NORMALIZATION： Each eigenvector (mode shape or normal mode) can be multiplied by an arbitrary constant and still satisfy the eigenvalue equation. Various methods of scaling the eigenvector are used Engineering normalization -The vector is scaled so that the largest absolute value of any term in the eigenvector is unity. This is useful for inspecting printed tables of eigenvectors. Mathematical normalization -The vector is scaled so that the diagonal modal mass matrix is the unit matrix. The diagonal modal stiffness matrix is the system eigenvalues. This is useful for response calculations.
  • EQUILIBRIUM EQUATIONS：Internal forces and external forces must balance. At the infinitesimal level the stresses and the body forces must balance. The equations of equilibrium define these force balance conditions.
  • EQUILIBRIUM FINITE ELEMENTS： Most of the current finite elements used for structural analysis are defined by assuming displacement variations over the element. An alternative approach assumes the stress variation over the element. This leads to equilibrium finite elements.
  • EQUIVALENT MATERIAL PROPERTIES： Equivalent material properties are defined where real material properties are smeared over the volume of the element. Typically, for composite materials the discrete fiber and matrix material properties are smeared to give average equivalent material properties.
  • EQUIVALENT STRESS： A three dimensional solid has six stress components. If material properties have been found experimentally by a uniaxial stress test then the real stress system is related to this by combining the six stress components to a single equivalent stress. There are various forms of equivalent stress for different situations. Common ones are Tresca, Von-Mises, Mohr-Coulomb and Drucker-Prager.
  • EULERIAN/LAGRANGIAN METHOD： For non-linear large deflection problems the equations can be defined in various ways. If the material is flowing though a fixed grid the equations are defined in Eulerian coordinates. Here the volume of the element is constant but the mass in the element can change. If the grid moves with the body then the equations are defined in Lagrangian coordinates. Here the mass in the element is fixed but the volume changes.
  • EXACT SOLUTIONS： Solutions that satisfy the differential equations and the associated boundary conditions exactly. There are very few such solutions and they are for relatively simple geometries and loadings.
  • EXPLICIT/IMPLICIT METHOD： These are methods for integrating equations of motion. Explicit methods can deal with highly non-linear systems but need small steps. Implicit methods can deal with mildly nonlinear problems but with large steps.
  • EXTRAPOLATION INTERPOLATION： The process of estimating a value of a variable from a tabulated set of values. For interpolation values inside the table are estimated. For extrapolation values outside the table are estimated. Interpolation is generally accurate and extrapolation is only accurate for values slightly outside the table. It becomes very inaccurate for other cases.

F

  • FACETED GEOMETRY： If a curved line or surface is modeled by straight lines or flat surfaces then the modeling is said to produce a faceted geometry.
  • FAST FOURIER TRANSFORM： A method for calculating Fourier transforms that is computationally very efficient.
  • FIELD PROBLEMS： Problems that can be defined by a set of partial differential equations are field problems. Any such problem can be solved approximately by the finite element method.
  • FINITE DIFFERENCES： A numerical method for solving partial differential equations by expressing them in a difference form rather than an integral form. Finite difference methods are very similar to finite element methods and in some cases are identical.
  • FINITE ELEMENT MODELING (FEM)： The process of setting up a model for analysis, typically involving graphical generation of the model geometry, meshing it into finite elements, defining material properties, and applying loads and boundary conditions.
  • FINITE VOLUME METHODS： A technique related to the finite element method. The equations are integrated approximately using t he weighted residual method, but a different form of weighting function is used from that in the finite element method. For the finite element method the Galerkin form of the weighted residual method is used.
  • FIXED BOUNDARY CONDITIONS： All degrees of freedom are restrained for this condition. The nodes on the fixed boundary can not move: translation or rotation.
  • FLEXIBILITY MATRIX FORCE METHOD： The conventional form of the finite element treats the displacements as unknowns, which leads to a stiffness matrix form. Alternative methods treating the stresses (internal forces) as unknowns lead to force methods with an associated flexibility matrix. The inverse of the stiffness matrix is the flexibility matrix.
  • FORCED RESPONSE： The dynamic motion results from a time varying forcing function.
  • FORCING FUNCTIONS： The dynamic forces that are applied to the system.
  • FOURIER EXPANSIONS FOURIER SERIES： Functions that repeat themselves in a regular manner can be expanded in terms of a Fourier series.
  • FOURIER TRANSFORM： A method for finding the frequency content of a time varying signal. If the signal is periodic it gives the same result as the Fourier series.
  • FOURIER TRANSFORM PAIR：The Fourier transform and its inverse which, together, allow the complete system to be transformed freely in either direction between the time domain and the frequency domain.
  • FRAMEWORK ANALYSIS： If a structure is idealized as a series interconnected line elements then this forms a framework analysis model. If the connections between the line elements a re pins then it is a pin-jointed framework analysis. If the joints are rigid then the lines must be beam elements.
  • FREE VIBRATION： The dynamic motion which results from specified initial conditions. The forcing function is zero.
  • FREQUENCY DOMAIN： The structures forcing function and the consequent response is defined in terms of their frequency content. The inverse Fourier transform of the frequency domain gives the corresponding quantity in the time domain.
  • FRONTAL SOLUTION WAVEFRONT SOLUTION： A form of solving the finite element equations using Gauss elimination that is very efficient for the finite element form of equations.

G

  • GAP/CONTACT ELEMENT: These are special forms of non-linear element that have a very high stiffness in compression and a low stiffness in tension. They are used to model contact conditions between surfaces. Most of these elements also contain a model for sliding friction between the contacting surfaces. Some gap elements are just line springs between points and others are more general forms of quadrilateral or brick element elements. The line spring elements should only be used in meshes of first order finite elements.

  • GAUSS POINT EXTRAPOLATION GAUSS POINT STRESSES: Stresses calculated internally within the element at the Gauss integration points are called the Gauss point stresses. These stresses are usually more accurate at these points than the nodal points.

  • GAUSS POINTS GAUSS WEIGHTS: The Gauss points are the sample points used within the elements for the numerical integration of the matrices and loadings. They are also the points at which the stresses can be recovered. The Gauss weights are associated factors used in the numerical integration process. They represent the volume of influence of the Gauss points. The positions of the Gauss points, together with the associated Gauss weights, are available in tables for integrations of polynomials of various orders.

  • GAUSSIAN ELIMINATION: A form of solving a large set of simultaneous equations. Within most finite element systems a form of Gaussian elimination forms the basic solution process.
  • GAUSSIAN INTEGRATION GAUSSIAN QUADRATURE: A form of numerically integrating functions that is especially efficient for integrating polynomials. The functions are evaluated at the Gauss points, multiplied by the Gauss weights and summed to give the integral.
  • GENERALIZED COORDINATES: A set of linearly independent displacement coordinates which are consistent with the constraints and are just sufficient to describe any arbitrary configuration of the system. Generalized coordinates are usually patterns of displacements, typically the system eigenvectors.
  • GENERALIZED MASS: The mass associated with a generalized displacement.
  • GENERALIZED STIFFNESS: The stiffness associated with a generalized displacement.
  • GEOMETRIC PROPERTIES: Various shape dependent properties of real structures, such as thickness, cross sectional area, sectional moments of inertia, centroid location and others that are applied as properties of finite elements.
  • GEOMETRIC/STRESS STIFFNESS: The component of the stiffness matrix that arises from the rotation of the internal stresses in a large deflection problem. This stiffness is positive for tensile stresses and negative for compressive stresses. If the compressive stresses are sufficiently high then the structure will buckle when the geometric stiffness cancels the elastic stiffness.
  • GEOMETRICAL ERRORS: Errors in the geometrical representation of the model. These generally arise from the approximations inherent in the finite element approximation.

  • GLOBAL STIFFNESS MATRIX: The assembled stiffness matrix of the complete structure.

  • GROSS DEFORMATIONS: Deformations sufficiently high to make it necessary to include their effect in the solution process. The problem requires a large deflection non-linear analysis.

  • GOVERNING EQUATIONS: The governing equations for a system are the equations derived from the physics of the system. Many engineering systems can be described by governing equations, which determine the system's characteristics and behaviors.
  • GUARD VECTORS: The subspace iteration (simultaneous vector iteration) method uses extra guard vectors in addition to the number of vectors requested by the user. These guard the desired vectors from being contaminated by the higher mode vectors and speed up convergence.
  • GUI: GUI stands for graphical user interface, which provides a visual tool to build a finite element model for a domain with complex geometry and boundary conditions.

H

  • HARDENING STRUCTURE: A structure where the stiffness increases with load.
  • HARMONIC LOADING: A dynamic loading that is periodic and can be represented by a Fourier series.
  • HEAT CONDUCTION: The analysis of the steady state heat flow within solids and fluids. The equilibrium balance between internal and external heat flows.
  • HERMITIAN SHAPE FUNCTIONS: Shape functions that provide both variable and variable first derivative continuity (displacement and slope continuity in structural terms) across element boundaries.
  • HEXAHEDRON ELEMENTS: Type of 3D element which has six quadrilateral faces.
  • HIGH/LOW ASPECT RATIO: The ratio of the longest side length of a body to the shortest is termed its aspect ratio. Generally bodies with high aspect ratios (long and thin) are more ill conditioned for numerical solution than bodies with an aspect ratio of one.
  • HOOKES LAW: The material property equations relating stress to strain for linear elasticity. They involve the material properties of Young’s modulus and Poisson ratio.
  • HOURGLASS MODE: Zero energy modes of low order quadrilateral and brick elements that arise from using reduced integration. These modes can propagate through the complete body.
  • H-CONVERGENCE: Convergence towards a more accurate solution by subdividing the elements into a number of smaller elements. This approach is referred to as H-convergence because of improved discretization due to reduced element size.
  • H-METHOD: A finite element method which requires an increasing number of elements to improve the solution.
  • H/P-REFINEMENT: Making the mesh finer over parts or all of the body is termed h-refinement. Making the element order higher is termed p-refinement.
  • HYBRID ELEMENTS: Elements that use stress interpolation within their volume and displacement interpolation around their boundary.
  • HYDROSTATIC STRESS: The stress arising from a uniform pressure load on a cube of material. It is the average value of the direct stress components at any point in the body.
  • HYSTERETIC DAMPING: A damping model representing internal material loss damping. The energy loss per unit cycle is independent of frequency. It is only valid for harmonic response.

I

  • ILL-CONDITIONING ERRORS: Numerical (rounding) errors that arise when using ill-conditioned equations.
  • ILL-CONDITIONING ILL-CONDITIONED EQUATIONS: Equations that are sensitive to rounding errors in a numerical operation. The numerical operation must also be defined. Equations can be ill conditioned for solving simultaneous equations but not for finding eigenvalues.
  • IMPULSE RESPONSE FUNCTION: The response of the system to an applied impulse.
  • IMPULSE RESPONSE MATRIX: The matrix of all system responses to all possible impulses. It is always symmetric for linear systems. It is the inverse Fourier transform of the dynamic flexibility matrix.
  • INCREMENTAL SOLUTION: A solutions process that involves applying the loading in small increments and finding the equilibrium conditions at the end of each step. Such solutions are generally used for solving non-linear problems.
  • INELASTIC MATERIAL BEHAVIOR: A material behavior where residual stresses or strains can remain in the body after a loading cycle, typically plasticity and creep.
  • INERTANCE (ACCELERANCE): The ratio of the steady state acceleration response to the value of the forcing function for a sinusoidal excitation.
  • INERTIA FORCE: The force that is equal to the mass times the acceleration.
  • INITIAL BUCKLING: The load at which a structure first buckles.
  • INITIAL STRAINS: The components of the strains that are non-elastic. Typically thermal strain and plastic strain.
  • INTEGRATION BY PARTS: A method of integrating a function where high order derivative terms are partially integrated to reduce their order.
  • INTERPOLATION FUNCTIONS SHAPE FUNCTIONS: The polynomial functions used to define the form of interpolation within an element. When these are expressed as interpolations associated with each node they become the element shape functions.
  • ISOPARAMETRIC ELEMENT: Elements that use the same shape functions (interpolations) to define the geometry as were used to define the displacements. If these elements satisfy the convergence requirements of constant stress representation and strain free rigid body motions for one geometry then it will satisfy the conditions for any geometry.
  • ISOTROPIC MATERIAL: Materials where the material properties are independent of the co-ordinate system.

J

  • JACOBI METHOD: A method for finding eigenvalues and eigenvectors of a symmetric matrix.
  • JACOBIAN MATRIX: A square matrix relating derivatives of a variable in one coordinate system to the derivatives of the same variable in a second coordinate system. It arises when the chain rule for differentiation is written in matrix form.
  • J-INTEGRAL METHODS: A method for finding the stress intensity factor for fracture mechanics problems.
  • JOINTS: The interconnections between components. Joints can be difficult to model in finite element terms but they can significantly affect dynamic behavior.

K

  • KINEMATIC BOUNDARY CONDITIONS: The necessary displacement boundary conditions for a structural analysis. These are the essential boundary conditions in a finite element analysis.
  • KINEMATICALLY EQUIVALENT FORCES (LOADS): A method for finding equivalent nodal loads when the actual load is distributed over a surface of a volume. The element shape functions are used so that the virtual work done by the equivalent loads is equal to the virtual work done by the real loads over the same virtual displacements. This gives the most accurate load representation for the finite element model. These are the non-essential stress boundary conditions in a finite element analysis.
  • KINEMATICALLY EQUIVALENT MASS: If the mass and stiffness are defined by the same displacement assumptions then a kinematically equivalent mass matrix is produced. This is not a diagonal (lumped) mass matrix.
  • KINETIC ENERGY: The energy stored in the system arising from its velocity. In some cases it can also be a function of the structural displacements.

L

  • LAGRANGE INTERPOLATION LAGRANGE SHAPE FUNCTIONS： A method of interpolation over a volume by means of simple polynomials. This is the basis of most of the shape function definitions for elements.
  • LAGRANGE MULTIPLIER TECHNIQUE： A method for introducing constraints into an analysis where the effects of the constraint are represented in terms of the unknown Lagrange multiplying factors.
  • LANCZOS METHOD： A method for finding the first few eigenvalues and eigenvectors of a set of equations. It is very well suited to the form of equations generated by the finite element method. It is closely related to the method of conjugate gradients used for solving simultaneous equations iteratively.
  • LEAST SQUARES FIT： Minimization of the sum of the squares of the distances between a set of sample points and a smooth surface . The finite element method gives a solution that is a least squares fit to the equilibrium equations.
  • LINEAR DEPENDENCE： One or more rows (columns) of a matrix are linear combinations of the other rows (columns). This means that the matrix is singular.
  • LINEAR ANALYSIS： Linear Finite Element Analysis is based on the following assumptions: (1) Static; (2) Small displacements; (3) Material is linearly elastic.
  • LINEAR SYSTEM： When the coefficients of stiffness, mass and damping are all constant then the system is linear. Superposition can be used to solve the response equation.
  • LOADINGS：The loads applied to a structure that result in deflections and consequent strains and stresses.
  • LOCAL STRESSES： Areas of stress that are significantly different from (usually higher than) the general stress level.
  • LOWER BOUND SOLUTION UPPER BOUND SOLUTION： The assumed displacement form of the finite element solution gives a lower bound on the maximum displacements and strain energy (i.e. these are under estimated) for a given set of forces. This is the usual form of the finite element method. The assumed stress form of the finite element solution gives an upper bound on the maximum stresses and strain energy (i.e. these are over estimated) for a given set of displacements.
  • LUMPED MASS MODEL: When the coefficients of the mass matrix are combined to produce a diagonal matrix. The total mass and the position of the structures center of gravity are preserved.

M

  • MASS: The constant(s) of proportionality relating the acceleration(s) to the force(s). For a discrete parameter multi degree of freedom model this is usually given as a mass matrix.
  • MASS ELEMENT: An element lumped at a node representing the effect of a concentrated mass in different coordinate directions.
  • MASS MATRIX: The matrix relating acceleration to forces in a dynamic analysis. This can often be approximated as a diagonal matrix with no significant loss of accuracy.
  • MASTER FREEDOMS: The freedoms chosen to control the structural response when using a Guyan reduction or sub structuring methods.
  • MATERIAL LOSS FACTOR: A measure of the damping inherent within a material when it is dynamically loaded.
  • MATERIAL PROPERTIES: The physical properties required to define the material behavior for analysis purposes. For stress analysis typical required material properties are Young’s modulus, Poisson’s ratio, density and coefficient of linear expansion. The material properties must have been obtained by experiment.
  • MATERIAL STIFFNESS MATRIX MATERIAL FLEXIBILITY MATRIX: The material stiffness matrix allows the stresses to be found from a given set of strains at a point. The material flexibility is the inverse of this, allowing the strains to be found from a given set of stresses. Both of these matrices must be symmetric and positive definite.
  • MATRIX DISPLACEMENT METHOD: A form (the standard form) of the finite element method where displacements are assumed over the element. This gives a lower bound solution.
  • MATRIX FORCE METHOD: A form of the finite element method where stresses (internal forces) are assumed over the element. This gives an upper bound solution.
  • MATRIX INVERSE: If matrix A times matrix B gives the unit matrix then A is the inverse of B (B is the inverse of A). A matrix has no inverse if it is singular.
  • MATRIX NOTATION MATRIX ALGEBRA: A form of notation for writing sets of equations in a compact manner. Matrix notation highlights the generality of various classes of problem formulation and solution. Matrix algebra can be easily programmed on a digital computer.
  • MATRIX PRODUCTS: Two matrices A and B can be multiplied together if A is of size (j*k) and B is of size (k*l). The resulting matrix is of size (j*l).
  • MATRIX TRANSPOSE: The process of interchanging rows and columns of a matrix so that the j’th column becomes the j’th row.
  • MEAN SQUARE CONVERGENCE: A measure of the rate of convergence of a solution process. A mean square convergence indicates a rapid rate of convergence.

  • MEMBRANE: Membrane behavior is where the strains are constant from the center line of a beam or center surface of a plate or shell. Plane sections are assumed to remain plane. A membrane line element only has stiffness along the line, it has zero stiffness normal to the line. A membrane plate has zero stiffness normal to the plate. This can cause zero energy (no force required) displacements in these normal directions. If the stresses vary linearly along the normal to the centerline then this is called bending behavior.

  • Mesh (Grid): The elements and nodes, together, form a mesh (grid), which is the central data structure in FEA.

  • MESH DENSITY MESH REFINEMENT: The mesh density indicates the size of the elements in relation to the size of the body being analyzed. The mesh density need not be uniform all over the body There can be areas of mesh refinement (more dense meshes) in some parts of the body. Making the mesh finer is generally referred to as h -refinement. Making the element order higher is referred to as p -refinement.
  • MESH GENERATION ELEMENT GENERATION: The process of generating a mesh of elements over the structure. This is normally done automatically or semi-automatically.
  • MESH SPECIFICATION: The process of choosing and specifying a suitable mesh of elements for an analysis.
  • MESH SUITABILITY: The appropriate choice of element types and mesh density to give a solution to the required degree of accuracy.
  • MINDLIN ELEMENTS: A form of thick shell element.
  • MOBILITY: The ratio of the steady state velocity response to the value of the forcing function for a sinusoidal excitation.
  • MODAL DAMPING: The damping associated with the generalized displacements defined by the eigenvectors. Its value has no physical significance since the eigenvector contains an arbitrary normalizing factor.
  • MODAL MASS: The mass associated with the generalized displacements defined by the eigenvectors. Its value has no physical significance since the eigenvector contains an arbitrary normalizing factor but the ratio of modal stiffness to modal mass is always the eigenvalue.
  • MODAL STIFFNESS: The stiffness associated with the generalized displacements defined by the eigenvectors. Its value has no physical significance since the eigenvector contains an arbitrary normalizing factor but the ratio of modal stiffness to modal mass is always the eigenvalue.
  • MODAL TESTING: The experimental technique for measuring resonant frequencies (eigenvalues) and mode shapes (eigenvectors).
  • MODE PARTICIPATION FACTOR: The generalized force in each modal equation of a dynamic system.
  • MODE SHAPE: Same as the e igenvector. The mode shape often refers to the measure mode, found from a modal test.
  • MODELLING: The process of idealizing a system and its loading to produce a numerical (finite element) model.
  • MODIFIED NEWTON-RAPHSON: A form of the Newton-Raphson process f or solving non-linear equations where the tangent stiffness matrix is held constant for some steps. It is suitable for mildly non-linear problems.
  • MOHR COULOMB EQUIVALENT STRESS: A form of equivalent stress that includes the effects of friction in granular (e.g. sand) materials.
  • MULTI DEGREE OF FREEDOM: The system is defined by more than one force/displacement equation.
  • MULTI-POINT CONSTRAINTS: Where the constraint is defined by a relationship between more than one displacement at different node points.

N

  • NATURAL FREQUENCY: The frequency at which a structure will vibrate in the absence of any external forcing. If a model has n degrees of freedom then it has n natural frequencies. The eigenvalues of a dynamic system are the squares of the natural frequencies.
  • NATURAL MODE: Same as the eigenvector.
  • NEWMARK METHOD NEWMARK BETA METHOD: An implicit solution method for integrating second order equations of motion. It can be made unconditionally stable.
  • NEWTON COTES FORMULAE: A family of methods for numerically integrating a function.
  • NEWTON-RAPHSON NON-LINEAR SOLUTION: A general technique for solving non-linear equations. If the function and its derivative are known at any point then the Newton-Raphson method is second order convergent.
  • NODAL VALUES: The value of variables at the node points. For a structure typical possible nodal values are force, displacement, temperature, velocity, x, y, and z.
  • NODE: A node is a point in the domain, and is often the vertex of several elements. A node is also called a nodal point. computers to generate finite element mesh automatically. There are many different algorithms for automatic mesh generation. Click here to see some automatically generated mesh samples.
  • NON-CONFORMING ELEMENTS: Elements that do not satisfy compatibility either within the element or across element boundaries or both. Such elements are not generally reliable although they might give very good solutions in some circumstances.
  • NON-HOLONOMIC CONSTRAINTS: Constraints that can only be defined at the level of infinitesimal displacements. They cannot be integrated to give global constraints.
  • NON-LINEAR SYSTEM/ANALYSIS: Nonlinear Finite Element Analysis considers material nonlinearity and/or geometric nonlinearity of an engineering system. Geometric nonlinear analysis is also called large deformation analysis.
  • NON-STATIONARY RANDOM: A force or response that is random and its statistical properties vary with time.
  • NON-STRUCTURAL MASS: Mass that is present in the system and will affect the dynamic response but it is not a part of the structural mass (e.g. the payload).
  • NORM: A scalar measure of the magnitude of a vector or a matrix.
  • NUMERICAL INTEGRATION: The process of finding the approximate integral of a function by numerical sampling and summing. In the finite element method the element matrices are usually formed by the Gaussian quadrature form of numerical integration.

O

  • OPTIMAL SAMPLING POINTS: The minimum number of Gauss points required to integrate an element matrix. Also the Gauss points at which the stresses are most accurate (see reduced Gauss points).
  • OVER DAMPED SYSTEM: A system which has an equation of motion where the damping is greater than critical. It has an exponentially decaying, non-oscillatory impulse response.
  • OVERSTIFF SOLUTIONS: Lower bound solutions. These are associated with the assumed displacement method.

P

  • PARTICIPATION FACTOR: The fraction of the mass that is active for a given mode with a given distribution of dynamic loads. Often this is only defined for the specific load case of inertia (seismic) loads.
  • PATCH TEST: A test to prove that a mesh of distorted elements can represent constant stress situations and strain free rigid body motions (i.e. the mesh convergence requirements) exactly.
  • PDEs: partial differential equations.
  • PERIODIC RESPONSE FORCE: A response (force) that regularly repeats itself exactly.
  • PHASE ANGLE: The ratio of the in phase component of a signal to its out of phase component gives the tangent of the phase angle of the signal relative to some reference.
  • PLANE STRAIN/STRESS: A two dimensional analysis is plane stress if the stress in the third direction is assumed zero. This is valid if the dimension of the body in this direction is very small, e.g. a thin plate. A two dimensional analysis is plane strain if the strain in the third direction is assumed zero. This is valid if the dimension of the body in this direction is very large, e.g. a cross- sectional slice of a long body.
  • PLATE BENDING ELEMENTS: Two-dimensional shell elements where the in plane behavior of the element is ignored. Only the out of plane bending is considered.
  • POISSONS RATIO: The material property in Hooke s law relating strain in one direction arising from a stress in a perpendicular direction to this. Poissons' ratio can be defined in WELSIM material module.
  • POST-PROCESSING: The interrogation of the results after the analysis phase. This is usually done with a combination of graphics and numerics.
  • POTENTIAL ENERGY: The energy associated with the static behavior of a system. For a structure this is the strain energy.
  • POWER METHOD: A method for finding the lowest or the highest eigenvalue of a system.
  • PRANDTL-REUSS EQUATIONS: The equations relating an increment of stress to an increment of plastic strain for a metal undergoing plastic flow.
  • PREPROCESSING: The process of preparing finite element input data involving model creation, mesh generation,material definition, and load and boundary condition application.
  • PRIMARY COMPONENT: Those parts of the structure that are of direct interest for the analysis. Other parts are secondary components.
  • PRINCIPAL CURVATURE: The maximum and minimum radii of curvature at a point.
  • PRINCIPAL STRESSES: The maximum direct stress values at a point. They are the eigenvalues of the stress tensor.
  • PROPORTIONAL DAMPING: A damping matrix that is a linear combination of the mass and stiffness matrices. The eigenvectors of a proportionally damped system are identical to those of the undamped system.
  • P-METHOD: A method of finite element analysis that uses P- convergence to iteratively minimize the error of analysis.
  • QR METHOD: A technique for finding eigenvalues. This is currently the most stable method for finding eigenvalues but it is restricted in the size of problem that it can solve.
  • RANDOM VIBRATIONS: The applied loading is only known in terms of its statistical properties. The loading is nondeterministic in that its value is not known exactly at any time but its mean, mean square, variance and other statistical quantities are known.

R

  • RANK DEFICIENCY: A measure of how singular a matrix is.
  • RAYLEIGH DAMPING: Damping that is proportional to a linear combination of the stiffness and mass. This assumption has no physical basis but it is mathematically convenient to approximate low damping in this way when exact damping values are not known.
  • RAYLELGH QUOTIENT: The ratio of stiffness times displacement squared (2*strain energy) to mass times displacement squared. The minimum values of the Rayleigh quotient are the eigenvalues.
  • REACTION FORCES: The forces generated at support points when a structure is loaded. Reaction force is supported in WELSIM.
  • REFERENCE TEMPERATURE: The reference temperature defines the temperature at which strain in the design does not result from thermal expansion or contraction. For many situations, reference temperature is adequately defined as room temperature. Define reference temperature in the properties of an environment.
  • REDUCED INTEGRATION: If an element requires an l*m*n Gauss rule to integrate the element matrix exactly then (l-1)(m-1)(n-1) is the reduced integration rule. For many elements the stresses are most accurate at the reduced integration points. For some elements the matrices are best evaluated by use of the reduced integration points. Use of reduced integration for integrating the elements can lead to zero energy and hour glassing modes.
  • RESPONSE SPECTRUM METHOD: A method for characterizing a dynamic transient forcing function and the associated solution technique. It is used for seismic and shock type loads.
  • RIGID BODY DEFORMATIONS: A non-zero displacement pattern that h as zero strain energy associate with it.
  • RIGID BODY DISPLACEMENT: A non-zero displacement pattern that has zero strain energy associate with it.
  • RIGID BODY MODES: If a displaced shape does not give rise to any strain energy in the structure then this a rigid body mode. A general three-dimensional unsupported structure has 6 rigid body modes, 3 translation and 3 rotation.
  • RIGID LINKS/OFFSETS: This is a connection between two non-coincident nodes assuming that the connection is infinitely stiff. This allows the degrees of freedom at one of the nodes (the slave node) to be deleted from the system. It is a form of multi-point constraint.
  • ROUNDOFF ERROR: Computers have a fixed word length and hence only hold numbers to a certain number of significant figures. If two close numbers are subtracted one from another then the result loses the first set of significant figures and hence loses accuracy. This is round off error.

S

  • SECANT STIFFNESS: The stiffness defined by the slope of the line from the origin to the current point of interest on a load/deflection curve.
  • SECONDARY COMPONENTS: Components of a structure not of direct interest but they may have some influence of the behavior of the part of the structure that is of interest (the primary component) and have to be included in the analysis in some approximate form.
  • SEEPAGE FLOW: Flows in porous materials
  • SEISMIC ANALYSIS: The calculation of the dynamic displacement and stress response arising from earthquake excitations.
  • SELECTED REDUCED INTEGRATION: A form of Gaussian quadrature where different sets of Gauss points are used for different strain components.
  • SELF ADJOINT EQUATIONS: A form of matrix products that preserves symmetry of equations. The product A*B*A(transpose) is self -adjoint if the matrix B is symmetric. The result of the product will be symmetric for any form of A that is of a size compatible with B. This form o f equation occurs regularly within the finite element method. Typically it means that for a structural analysis the stiffness (and mass) matrices for any element or element assembly will be symmetric.
  • SELF EQUILIBRATING LOADS: A load set is self -equilibrating if all of its resultants are zero. Both translation and moment resultants are zero.
  • SEMI-LOOF ELEMENT: A form of thick shell element.
  • SHAKEDOWN: If a structure is loaded cyclically and initially undergoes some plastic deformation then it is said to shakedown if the behavior is entirely elastic after a small number of load cycles.
  • SIMULTANEOUS VECTOR ITERATION: A method for finding the first few eigenvalues and eigenvectors of a finite element system. This is also known as subspace vector iteration.
  • SINGLE DEGREE OF FREEDOM: The system is defined by a single force/displacement equation.
  • SINGLE POINT CONSTRAINT: Where the constraint is unique to a single node point.
  • SINGULAR MATRIX: A square matrix that cannot be inverted.
  • SKEW DISTORTION (ANGULAR DISTORTION): A measure of the angular distortion arising between two vectors that are at right angles in the basis space when these are mapped to the real coordinate space. If this angle approaches zero the element becomes ill-conditioned.
  • SOLUTION DIAGNOSTICS: Messages that are generated as the finite element solution progresses. These should always be checked for relevance but the are often only provided for information purposes
  • SOLUTION EFFICIENCY: A comparative measure between two solutions of a given problem defining which is the ‘best’. The measures can include accuracy, time of solution, memory requirements and disc storage space.
  • SPARSE MATRIX METHODS: Solution methods that exploit the sparse nature of finite element equations. Such methods include the frontal solution and Cholesky (skyline) factorization for direct solutions, conjugate gradient methods for iterative solutions and the Lanczos method and subspace iteration (simultaneous vector iteration) for eigenvalue solutions.
  • SPECTRAL DENSITY: The Fourier transform of the correlation function. In random vibrations it gives a measure of the significant frequency content in a system. White noise has a constant spectral density for all frequencies.
  • SPLINE CURVES: A curve fitting technique that preserves zero, first and second derivative continuity across segment boundaries.
  • STATIC ANALYSIS: Analysis of stresses and displacements in a structure when the applied loads do not vary with time.
  • STATICALLY DETERMINATE STRUCTURE: A structure where all of the unknowns can be found from equilibrium considerations alone.
  • STATICALLY EQUIVALENT LOADS: Equivalent nodal loads that have the same equilibrium resultants as the applied loads but do not necessarily do the same work as the applied loads.
  • STATICALLY INDETERMINATE STRUCTURE REDUNDANT: A structure where all of the unknowns can not be found from equilibrium considerations alone. The compatibility equations must also be used. In this case the structure is said to be redundant.
  • STATIONARY RANDOM EXCITATION: A force or response that is random but its statistical characteristics do not vary with time.
  • STEADY-STATE HEAT TRANSFER: Determination of the temperature distribution of a mechanical part having reached thermal equilibrium with the environmental conditions. There are no time varying changes in the resulting temperatures.
  • STIFFNESS: A set of values which represent the rigidity or softness of a particular element. Stiffness is determined by material type and geometry.
  • STIFFNESS MATRIX: The parameter(s) that relate the displacement(s) to the force(s). For a discrete parameter multi degree of freedom model this is usually given as a stiffness matrix.
  • STRAIN: A dimensionless quantity calculated as the ratio of deformation to the original size of the body.
  • STRAIN ENERGY: The energy stored in the system by the stiffness when it is displaced from its equilibrium position.
  • STRESS: The intensity of internal forces in a body (force per unit area) acting on a plane within the material of the body is called the stress on that plane.
  • STRESS ANALYSIS: The computation of stresses and displacements due to applied loads. The analysis may be elastic, inelastic, time dependent or dynamic.
  • STRESS AVERAGING STRESS SMOOTHING: The process of filtering the raw finite element stress results to obtain the most realistic estimates of the true state of stress.
  • STRESS CONCENTRATION: A local area of the structure where the stresses are significantly higher than the general stress level. A fine mesh of elements is required in such regions if accurate estimates of the stress concentration values are required.
  • STRESS CONTOUR PLOT: A plot of a stress component by a series of color filled contours representing regions of equal stress. WELSIM can plot stress contour.
  • STRESS DISCONTINUITIES/ERROR ESTIMATES: Lines along which the stresses are discontinuous. If the geometry or loading changes abruptly along a line then the true stress can be discontinuous. In a finite element solution the element assumptions means that the stresses will generally be discontinuous across element boundaries. The degree of discontinuity can then be used to form an estimate of the error in the stress within the finite element calculation.
  • STRESS EXTRAPOLATION: The process of taking the stress results at the optimum sampling points for an element and extrapolating these to the element node points.
  • STRESS INTENSITY FACTORS: A measure of the importance of the stress at a sharp crack tip (where the actual stress values will be infinite) used to estimate if the crack will propagate.
  • STRESS/STRAIN VECTOR/TENSOR: The stress (strain) vector is the components of stress (strain) written as a column vector. For a general three dimensional body this is a (6×1) matrix. The components of stress (strain) written in tensor form. For a general three dimensional body this forms a (3×3) matrix with the direct terms down the diagonal and the shear terms as the off-diagonals.
  • STRESS-STRAIN LAW: The material property behavior relating stress to strain. For a linear behavior this is Hookes law (linear elasticity). For elastic plastic behavior it is a combination of Hookes law and the Prandtl-Reuss equations.
  • SUBSPACE VECTOR ITERATION: A method for finding the first few eigenvalues and eigenvectors of a finite element system. This is also known as simultaneous vector iteration.
  • SUBSTRUCTURING: An efficient way of solving large finite element analysis problems by breaking the model into several parts or substructures, analyzing each one individually, and then combining them for the final results.
  • SUBSTRUCTURING SUPER ELEMENT METHOD: Substructuring is a form of equation solution method where the structure is split into a series of smaller structures -the substructures. These are solved to eliminate the internal freedoms and the complete problem solved by only assembling the freedoms on the common boundaries between the substructures. The intermediate solution where the internal freedoms of a substructure have been eliminated gives the super element matrix for the substructure.
  • SURFACE MODELING: The geometric modeling technique in which the model is created in terms of its surfaces only without any volume definition.

T

  • TEMPERATURE CONTOUR PLOTS: A plot showing contour lines connecting points of equal temperature.
  • TETRAHEDRON/TETRAHEDRAL ELEMENT: A three dimensional four sided solid element with triangular faces.
  • THERMAL CAPACITY: The material property defining the thermal inertia of a material. It relates the rate of change of temperature with time to heat flux.
  • THERMAL CONDUCTIVITY: The material property relating temperature gradient to heat flux. Temperature-dependent thermal conductivity is supported in WELSIM.
  • THERMAL LOADS: The equivalent loads on a structure arising from thermal strains. These in turn arise from a temperature change.
  • THERMAL STRAINS: The components of strain arising from a change in temperature.
  • THERMAL STRESS ANALYSIS: The computation of stresses and displacements due to change in temperature.
  • THIN/THICK SHELL ELEMENT: In a shell element the geometry is very much thinner in one direction than the other two. It can then be assumed stresses can only vary linearly at most in the thickness direction. If the through thickness shear strains can be taken as zero then a thin shell model is formed. This uses the Kirchoff shell theory If the transverse shear strains are not ignored then a thick shell model is formed. This uses the Mindlin shell theory. For the finite element method the thick shell theory generates the most reliable form of shell elements. There are two forms of such elements, the Mindlin shell and the Semi-Loof shell.
  • TIME DOMAIN: The structures forcing function and the consequent response is defined in terms of time histories. The Fourier transform of the time domain gives the corresponding quantity in the frequency domain.
  • TRANSIENT FORCE: A forcing function that varies for a short period of time and then settles to a constant value.
  • TRANSIENT RESPONSE: The component of the system response that does not repeat itself regularly with time.
  • TRANSITION ELEMENT: Special elements that have sides with different numbers of nodes. They are used to couple elements with different orders of interpolation, typically a transition element with two nodes on one edge and three on another is used to couple a 4-node quad to an 8-node quad.
  • TRANSIENT HEAT TRANSFER: Heat transfer problems in which temperature distribution varies as a function of time.
  • TRIANGULAR ELEMENTS: Two dimensional or surface elements that have three edges.
  • TRUSS ELEMENT: A one dimensional line element defined by two nodes resisting only axial loads.

U

  • ULTIMATE STRESS: The failure stress (or equivalent stress) for the material.
  • UNDAMPED NATURAL FREQUENCY: The square root of the ratio of the stiffness to the mass (the square root of the eigenvalue). It is the frequency at which an undamped system vibrates naturally. A system with n degrees of freedom has n natural frequencies.
  • UNDER DAMPED SYSTEM: A system which has an equation of motion where the damping is less than critical. It has an oscillatory impulse response.
  • UPDATED/TOTAL LAGRANGIAN: The updated Lagrangian coordinate system is one where the stress directions are referred to the last known equilibrium state. The total Lagrangian coordinate system is one where the stress directions are referred to the initial geometry. Both algorithms are supported in WELSIM.

V

  • VARIABLE BANDWIDTH (SKYLINE): A sparse matrix where the bandwidth is not constant. Some times called a skyline matrix.
  • VIRTUAL DISPLACEMENTS: An arbitrary imaginary change of the system configuration consistent with its constraints.
  • VIRTUAL WORK/DISPLACEMENTS/FORCES: Techniques for using work arguments to establish equilibrium equations from compatibility equations (virtual displacements) and to establish compatibility equations from equilibrium (virtual forces).
  • VISCOUS DAMPING: The damping is viscous when the damping force is proportional to the velocity.
  • VOLUME/VOLUMETRIC DISTORTION: The distortion measured by the determinant of the Jacobian matrix, det J.
  • VON MISES STRESS: An “averaged” stress value calculated by adding the squares of the 3 component stresses (X, Y and Z directions) and taking the square root of their sums. This value allows for a quick method to locate probable problem areas with one plot.
  • VON MISES/TRESCA EQUIVALENT STRESS: Equivalent stress measures to represent the maximum shear stress in a material. These are used to characterize flow failures (e.g. plasticity and creep) in WELSIM. From test results the VonMises form seems more accurate but the Tresca form is easier to handle.

W

  • WHIRLING STABILITY: The stability of rotating systems where centrifugal and Coriolis are also present.
  • WILSON THETA METHOD: An implicit solution method for integrating second order equations of motion. It can be made unconditionally stable.

Y

  • YOUNG’S MODULUS: The material property relating a uniaxial stress to the corresponding strain.

Z

  • ZERO ENERGY/STIFFNESS MODES: Non-zero patterns of displacements that have no energy associated with them. No forces are required to generate such modes, Rigid body motions are zero energy modes. Buckling modes at their buckling loads are zero energy modes. If the elements are not fully integrated they will have zero energy displacement modes. If a structure has one or more zero energy modes then the matrix is singular.
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Welcome

WELSIM was born out of a vision to create a general-purpose simulation utility that could successfully enable a wide range of engineering and science communities to conduct simulation with more confidence. Customers use our software to help ensure the integrity of their innovations. WELSIM comes with an all-in-one user interface and self-integrated features. It is a long-term-support product that aims to accurately model engineering problems using the prestigious open source solvers.

finite_element_analysis_welsim_exhaust_manifold_rst

Why WELSIM

  • Support 3D structural, thermal, fluid, and electromagnetic analyses that reveal physics-based results. Convenient data interface to export mesh or result files.
  • No wait. You can download and use WELSIM immediately.
  • The secure software program and no collection of your data. No need for an internet connection to run the program.
  • The ease-of-use graphical interface requires no learning curve.
  • Friendly pricing options. Free trial. No hidden fees. No commitments.

Where to start

Engineers can do a thousand things with the WELSIM simulation solutions. We recommend starting with:

  • Quick start to quickly review the steps of using WELSIM.
  • Windows and Linux installation guides to install the software on your computer.

If you already use WELSIM:

  • User's manual - learn about WELSIM user interfaces and how to use them for everything else.
  • Theory - learn about math theory and numerical algorithms used in WELSIM.

If you are interested in our free engineering software:

  • CurveFitter - learn about the curve fitting tool.
  • MatEditor - learn about the engineering material data tool.
  • UnitConverter - learn about the engineering unit convertion tool.
  • BeamSection - learn about the beam cross-section tool.

Last Updated: Jan. 8th, 2024

\ No newline at end of file + WelSim Documentation
Skip to content

Welcome

WELSIM was born out of a vision to create a general-purpose simulation utility that could successfully enable a wide range of engineering and science communities to conduct simulation with more confidence. Customers use our software to help ensure the integrity of their innovations. WELSIM comes with an all-in-one user interface and self-integrated features. It is a long-term-support product that aims to accurately model engineering problems using the prestigious open source solvers.

finite_element_analysis_welsim_exhaust_manifold_rst

Why WELSIM

  • Support 3D structural, thermal, fluid, and electromagnetic analyses that reveal physics-based results. Convenient data interface to export mesh or result files.
  • No wait. You can download and use WELSIM immediately.
  • The secure software program and no collection of your data. No need for an internet connection to run the program.
  • The ease-of-use graphical interface requires no learning curve.
  • Friendly pricing options. Free trial. No hidden fees. No commitments.

Where to start

Engineers can do a thousand things with the WELSIM simulation solutions. We recommend starting with:

  • Quick start to quickly review the steps of using WELSIM.
  • Windows and Linux installation guides to install the software on your computer.

If you already use WELSIM:

  • User's manual - learn about WELSIM user interfaces and how to use them for everything else.
  • Theory - learn about math theory and numerical algorithms used in WELSIM.

If you are interested in our free engineering software:

  • CurveFitter - learn about the curve fitting tool.
  • MatEditor - learn about the engineering material data tool.
  • UnitConverter - learn about the engineering unit convertion tool.
  • BeamSection - learn about the beam cross-section tool.

Last Updated: Oct. 14th, 2024

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WELSIM licensing guide

Preface

This document contains information for running the WELSIM License Manager with all WelSimulation LLC products.

Supported hardware platforms

This document details information about licensing WelSimulation LLC products on the hardware platforms listed below.

  • Linux x64 (linx64)
  • Windows x64 (winx64)

For specific operating system requirements, contact the customer support for the product and platform you are running.

Conventions used in this document

Computer prompts and responses and user input are printed using this font:

/welsim_com/shared_files/licensing/welslic_admin
+ WelSim licensing guide - WelSim Documentation      
 
 
  
 
  
 
 
 
 
  
 
 
 
 
 
  
 
 
 
 
 
WELSIM licensing guide
 
Preface
 
This document contains information for running the WELSIM License Manager with all WelSimulation LLC products. 
 
Supported hardware platforms
 
This document details information about licensing WelSimulation LLC products on the hardware platforms listed below. 
 
     
  • Linux x64 (linx64)
    •  
  • Windows x64 (winx64)
    •  
 
For specific operating system requirements, contact the customer support for the product and platform you are running.
 
Conventions used in this document
 
Computer prompts and responses and user input are printed using this font:
 
/welsim_com/shared_files/licensing/welslic_admin
 
 
Wild card arguments and variables are italicized. 
 Commands appear in bold face.
 
Introduction
 
WelSimulation LLC uses the internal license manager for all of its licensed products. The communication between the WELSIM applications and license manager occurs through an internal process. The communication is nearly transparent; you should not see any noticeable difference in your day-to-day operation of WELSIM products.
 
You do not need to run the license manager installation. The license manager is installed together with the WELSIM application package.
 
The licensing process
 
The licensing process for WELSIM is as follows:
 
     
  1. Install the software. 
    2.  
  2. Start the software and generate your unique Computer ID, send the Computer ID to info@welsim.com.
    3.  
  3. After you receive your license file, run the License Manager Wizard from Toolbar of WELSIM application.
    4.  
  4. Set up the licensing environment and input license. See Activating the WELSIM.
    5.  
 
Explanation of licensing terms
 
The main components of the licensing are:
 
     
  • License file
    •  
  • Application program (WELSIM)
    •  
 
These components are explained in more detail in the following sections.
 
The license file
 
Licensing data is stored in a text file called the license file. The license file is created by WelSimulation LLC and is installed by the end user. It contains information about the version, signature, and date.
 
The default and recommended location for the WELSIM license file (wsimkey.dat) is in the %APPDATA%/WELSIM directory. The application can automatically place the license file at this location after activation. End users can manually copy the license file to that directory, although are not suggested. 
 
License file format
 
License files usually contain eight lines. You cannot modify any these data items in the license files.
 
 
Note
 
Everything in the license key should be entered exactly as supplied. All data in the license file is case sensitive, unless otherwise indicated.
 
 
Application line
 
The application line specifies the application name. Normally a license file for WELSIM application uses the “[WELSIM]”. The example of the application line is: 
[WELSIM]
 
 
License version line
 
The license version line specifies the version of current license file. The example of the this line is shown below: 
license_verion = 100
 
 
License signature line
 
A license signature line describes the password key to use a product. The example of the signature line is: 
license_signature = Tvp919deAq5od+nCUjRF15mgeBIKCLgscLgvR8eFYAlBrqqcjETIyuY0Lu/brYbOKYrIPOXqFzWn8asLqieImA== 
@@ -15,4 +15,4 @@
 to_sw_version = 100
 from_date = 2023-07-02
 to_date = 2024-07-02
-
 
Recognizing a WELSIM license file
 
If you receive a license file and are not sure if it is a WELSIM license file, you can determine if it is by looking at the contents of the license file. If it is a WELSIM license file, then
 
     
  • In the first line of the license file, the string field is WELSIM.
    •  
 
Installing the WELSIM license manager
 
The WelSim License Manager is included in the WELSIM application installation. As the user installs the application, the license manager is already installed.
 
Troubleshooting
 
This section lists problems and error messages that you may encounter while setting up licensing. The possible error messages are:
 
     
  • LICENSE_FILE_NOT_FOUND
    •  
  • LICENSE_SERVER_NOT_FOUND 
    •  
  • ENVIRONMENT_VARIABLE_NOT_DEFINED 
    •  
  • FILE_FORMAT_NOT_RECOGNIZED 
    •  
  • LICENSE_MALFORMED 
    •  
  • PRODUCT_NOT_LICENSED
    •  
  • PRODUCT_EXPIRED 
    •  
  • LICENSE_CORRUPTED 
    •  
  • IDENTIFIERS_MISMATCH
    •  
 
An example of the license message error message is shown in Figure [fig:ch10_license_not_found].
 
finite_element_analysis_welsim_license_not_found
 
 
  
 
  
 
 
 
         
\ No newline at end of file
+

Recognizing a WELSIM license file

If you receive a license file and are not sure if it is a WELSIM license file, you can determine if it is by looking at the contents of the license file. If it is a WELSIM license file, then

  • In the first line of the license file, the string field is WELSIM.

Installing the WELSIM license manager

The WelSim License Manager is included in the WELSIM application installation. As the user installs the application, the license manager is already installed.

Troubleshooting

This section lists problems and error messages that you may encounter while setting up licensing. The possible error messages are:

  • LICENSE_FILE_NOT_FOUND
  • LICENSE_SERVER_NOT_FOUND
  • ENVIRONMENT_VARIABLE_NOT_DEFINED
  • FILE_FORMAT_NOT_RECOGNIZED
  • LICENSE_MALFORMED
  • PRODUCT_NOT_LICENSED
  • PRODUCT_EXPIRED
  • LICENSE_CORRUPTED
  • IDENTIFIERS_MISMATCH

An example of the license message error message is shown in Figure [fig:ch10_license_not_found].

finite_element_analysis_welsim_license_not_found

\ No newline at end of file diff --git a/install/linux/index.html b/install/linux/index.html index df26883..e499b69 100755 --- a/install/linux/index.html +++ b/install/linux/index.html @@ -1,8 +1,8 @@ - Linux installation guide - WelSim Documentation
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Linux installation guide

Installation prerequisites for Linux

This document describes the steps necessary to correctly install and configure WELSIM application on Linux platforms. These products include:

  • WELSIM Application
  • License manager

System prerequisites

WELSIM application is supported on the Linux platforms and operating system levels listed in Table below.

Platform Operating system Availability
Linux x64 Ubuntu 22.04 LTS or higher Download

Note

  1. If you run WELSIM on Ubuntu, we recommand Ubuntu 22.04 LTS or higher with the latest libstdc++ and libfortran libraries.

Disk space and memory requirements

You will need the disk space shown in Table below for installation and proper functioning.

Product Disk space Memory
WELSIM application at least 1 GB at least 4 GB

Platform details

For all 64-bit Linux platforms, the libraries listed below should be installed.

  • libxcb-xinerama0
  • libstdc++
  • gcc-c++
  • glibc
  • libfortran
  • openmpi-bin
  • libomp-dev

Installing the WELSIM for a Linux system

This section explains how to download and install WELSIM.

You can install WELSIM as root, or non-root; however, if you are root user, you can install the application in the system directory. The application can be used by different users.

Product download instructions

To download the installation files from our website, you will need to agree the US Export Restrictions. You only need to download one installer file.

  1. From the website1, select the Linux version of WELSIM and click the download button on the webpage.
  2. The downloaded installer file has the name like: WelSim%version%SetupUbuntu.run. For example, the installer of 2024R1 is WelSim28SetupUbuntu.run.
  3. Begin the product installation as described in the next section.

Production installation

1.Navigate to the directory where you placed the installer file. Run the commands below in a terminal window. Note that we take the version of 2024R1 as an example, if you are installing a different version, replace the installer name in the command line below. 

$ chmod +x WelSim28SetupUbuntu.run
+ Linux installation guide - WelSim Documentation      
 
 
  
 
  
 
 
 
 
  
 
 
 
 
 
  
 
 
 
 
 
Linux installation guide
 
Installation prerequisites for Linux
 
This document describes the steps necessary to correctly install and configure WELSIM application on Linux platforms. These products include:
 
     
  • WELSIM Application
    •  
  • License manager
    •  
 
System prerequisites
 
WELSIM application is supported on the Linux platforms and operating system levels listed in Table below.
 
  
 Platform Operating system Availability 
   
 Linux x64 Ubuntu 22.04 LTS or higher Download 
  
 
 
Note
 
     
  1. If you run WELSIM on Ubuntu, we recommand Ubuntu 22.04 LTS or higher with the latest libstdc++ and libfortran libraries.
    2.  
 
 
Disk space and memory requirements
 
You will need the disk space shown in Table below for installation and proper functioning. 
 
  
 Product Disk space Memory 
   
 WELSIM application at least 1 GB at least 4 GB 
  
 
Platform details
 
For all 64-bit Linux platforms, the libraries listed below should be installed. 
 
     
  • libxcb-xinerama0
    •  
  • libstdc++
    •  
  • gcc-c++
    •  
  • glibc
    •  
  • libfortran
    •  
  • openmpi-bin
    •  
  • libomp-dev
    •  
 
Installing the WELSIM for a Linux system
 
This section explains how to download and install WELSIM. 
 
You can install WELSIM as root, or non-root; however, if you are root user, you can install the application in the system directory. The application can be used by different users.
 
Product download instructions
 
To download the installation files from our website, you will need to agree the US Export Restrictions. You only need to download one installer file.
 
     
  1. From the website1, select the Linux version of WELSIM and click the download button on the webpage.
    2.  
  2. The downloaded installer file has the name like: WelSim%version%SetupUbuntu.run. For example, the installer of 2024R1 is WelSim28SetupUbuntu.run.
    3.  
  3. Begin the product installation as described in the next section.
    4.  
 
Production installation
 
1.Navigate to the directory where you placed the installer file. Run the commands below in a terminal window. Note that we take the version of 2024R1 as an example, if you are installing a different version, replace the installer name in the command line below. 
 
$ chmod +x WelSim28SetupUbuntu.run
 $ ./WelSim28SetupUbuntu.run
 
 
 
Note
 
Running the installer requires the libxcb-xinerama0 library installed in your system. 
 
 
2.The WELSIM installation Launcher appears as shown below.
 
finite_element_analysis_welsim_linux_install1
 
3.Click the Next button to start the installation on your computer.
 
4.The installation folder setting appears as shown below. You can input your designated directory or keep the default one. After specifying the directory, Click Next.
 
finite_element_analysis_welsim_linux_install2
 
5.The component selection interface appears as shown below. You can select the components that you want to install. The user can keep the default selection, and know the occupied disk space for this installation. Click Next.
 
finite_element_analysis_welsim_linux_install3
 
6.The license agreement appears as shown below. Read the agreement, and if you agree to the terms and conditions, select I Agree. Click Next. 
 
finite_element_analysis_welsim_linux_install4
 
7.The installation needs your conformation to start as shown below. Click Install. 
 
finite_element_analysis_welsim_linux_install5
 
8.The installation completed as shown below. Click Next. 
 
finite_element_analysis_welsim_linux_install6
 
Starting the software on Linux
 
After installation, starting the WELSIM software application is straightforward. Here are steps:
 
1.Install the dependencies to your Ubuntu OS 
sudo apt update
 sudo apt upgrade
 sudo apt install openmpi-bin libomp-dev
 
 
2.Allocate the installed WELSIM application folder, double click the executable file runWelSim. 
 
 
Note
 
If the WELSIM does not start, the executable file may have no exectuable attribute on your machine. You could open a terminal window and type commends below. 
$ chmod +x runWelSim.sh
 $ ./runWelSim.sh 
-
 
 
3.WELSIM application starts, the GUI shows the system information in Figure below.
 
finite_element_analysis_welsim_linux_run
 
Uninstalling the software
 
To uninstall WELSIM, you can browse file explorer into the installation folder, and double click on the Uninstaller. Following the instructions on the Uninstaller, you can remove the application from your computer. 
 
You also can simply delete the installation folder to uninstall the WELSIM.
 
 
 
     
  1.  
    https://welsim.com/download ↩
     
    2.  
 
 
 
  
 
  
 
 
 
         
\ No newline at end of file
+

3.WELSIM application starts, the GUI shows the system information in Figure below.

finite_element_analysis_welsim_linux_run

Uninstalling the software

To uninstall WELSIM, you can browse file explorer into the installation folder, and double click on the Uninstaller. Following the instructions on the Uninstaller, you can remove the application from your computer.

You also can simply delete the installation folder to uninstall the WELSIM.

  1. https://welsim.com/download ↩

\ No newline at end of file diff --git a/install/windows/index.html b/install/windows/index.html index b2aa2c7..d526fc1 100755 --- a/install/windows/index.html +++ b/install/windows/index.html @@ -1 +1 @@ - Windows installation guide - WelSim Documentation
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Windows installation guide

Installation prerequisites for Windows

This document describes the steps essential to correctly install and configure WELSIM on Windows platform.

System prerequisites

WELSIM is supported on the following Windows platforms and operating system levels.

Platform Operating System Platform Architecture Availability
x64 Windows 11 winx64 Download

Disk space and memory requirements

You will need the disk space shown in Table [tab:ch11_win_disk_space] for installation and proper functioning. The numbers listed here are the maximum amount of disk space you will need.

Product Disk Space Memory
WELSIM 1 GB at least 4GB

Software prerequisites

You need to have the following software installed on your system. These software prerequisites will be installed automatically when you launch the product installation. If you have finished an installation successfully, the prerequisites executable are located under the %Installed Folder%\Prerequisites directory.

  • Microsoft Visual C++ 2015-2022 Redistributable(x64)
  • Intel Visual Fortran Redistributables, 2022
  • Microsoft MPI Redistributable, 10.0

Digital signatures

WELSIM installer and executable files are signed with digital certificates. The signer name is: WelSimulation LLC.

Platform details

Compiler requirements for Windows systems

The compiler requirements for Windows systems are listed in Table [tab:ch12_win_compiler_req].

No. WELSIM Compilers
1 Visual Studio 2022 (including the Microsoft C++ compiler)
2 Intel Visual Fortran 2022 compiler

Note

Those compilers are not required if you only use WELSIM application.

Installing the WELSIM for a Windows system

This section includes the steps required for installing WELSIM and licensing configuration on one Windows machine.

Downloading the installation file

To download the installation files from our website, you will need to agree the US Export Restrictions.

You only need to download one installer file.

  1. From the website, select the Windows version of WELSIM and click the download button on the webpage.
  2. The downloaded installer file has the name: WelSim28Setup.exe
  3. Begin the product installation as described in the next section.

Installing WELSIM

  1. Navigate to the directory where you placed the installer file. Run the installer by double click.
  2. The WELSIM installation Launcher appears as shown in Figure below. finite_element_analysis_welsim_windows_install1
  3. Click the Next button to start the installation on your computer.
  4. The license agreement appears as shown in Figure below. Read the agreement, and if you agree to the terms and conditions, select I Agree. Click Next. finite_element_analysis_welsim_windows_install2
  5. The installation folder setting appears as shown in the figure below. You can input your designated directory or keep the default one. After specifying the directory, Click Next. finite_element_analysis_welsim_windows_install3
  6. The prerequesites libraries installation appears as shown in the figure below. Your system requires these libraries to run the WELSIM application. Click Yes. finite_element_analysis_welsim_windows_install4 finite_element_analysis_welsim_windows_install5 finite_element_analysis_welsim_windows_install6
  7. The installation completed as shown in the figure below. Click Finish. finite_element_analysis_welsim_windows_install7

Note

WELSIM relies on the latest version of Microsoft MPI. If the Microsoft MPI redistributable installation conflicts with your pre-existing MS MPI libraries, please uninstall the pre-existing MPI from the Control Panel and reinstall the WELSIM.

Activating the WELSIM

In this section, assuming you already received the license file wsimkey.dat. To activate WELSIM on your computer with client licensing, you can follow the steps below:

  1. Start WELSIM application on your computer.
  2. Click the License Manager from the menu: HELP -> License Manager
  3. WELSIM License Manager user interface appears. There are five buttons on the interface:
    1. Generate Computer ID: generate user's unique ID for license key generation.
    2. Evaluate: click to continue using the trial version.
    3. Exit: quit the License Manager with no software activation.
    4. Buy Now: open your default internet browser and direct your visit to the pricing page.
    5. Enter Code: If you have received the license key file, click this button to import the license file.
  4. If the user are running software at the first time, generate the Computer ID by clicking the button of “Generate Computer ID”, and send this string (format of xxxx-xxxx-xxxx-xxxx) to info@welsim.com. The user will receive the license key within 24 hours.
  5. After receiving the license file (wsimkey.dat), click “Enter Code” button to import the license. In the License Code interface, the user can paste the license content from clipboard, or directly import the license from file.
  6. Click OK button to activate the WELSIM. A successfully activated software is shown in figure below.

finite_element_analysis_welsim_windows_install13

Starting the software

After installation, starting the WELSIM software is straightforward. Here are three methods:

  1. Double click the shortcut of WELSIM, if you toggle the option “Create Desktop Shortcut” during the last step of installation.
  2. Click the shortcut of WELSIM from the Start menu. From Start -> WELSIM ->WELSIM v1.8.
  3. Browse the directory of installation, double click the runWelSim.exe file.

As shown in the figure below, WESLIM application is started successfully on the Windows operation system. finite_element_analysis_welsim_windows_install12

Uninstalling the software

Uninstalling the software is straightforward. The user can run the unint.exe from one of methods below:

  1. Click the shortcut of WELSIM uninstaller from the Start menu. From Start -> WELSIM ->Uninstall.
  2. Browse the directory of installation, double click the uninst.exe file.
  3. Unstall the WELSIM application from the system Control Panel.
\ No newline at end of file + Windows installation guide - WelSim Documentation
Skip to content

Windows installation guide

Installation prerequisites for Windows

This document describes the steps essential to correctly install and configure WELSIM on Windows platform.

System prerequisites

WELSIM is supported on the following Windows platforms and operating system levels.

Platform Operating System Platform Architecture Availability
x64 Windows 11 winx64 Download

Disk space and memory requirements

You will need the disk space shown in Table [tab:ch11_win_disk_space] for installation and proper functioning. The numbers listed here are the maximum amount of disk space you will need.

Product Disk Space Memory
WELSIM 1 GB at least 4GB

Software prerequisites

You need to have the following software installed on your system. These software prerequisites will be installed automatically when you launch the product installation. If you have finished an installation successfully, the prerequisites executable are located under the %Installed Folder%\Prerequisites directory.

  • Microsoft Visual C++ 2015-2022 Redistributable(x64)
  • Intel Visual Fortran Redistributables, 2022
  • Microsoft MPI Redistributable, 10.0

Digital signatures

WELSIM installer and executable files are signed with digital certificates. The signer name is: WelSimulation LLC.

Platform details

Compiler requirements for Windows systems

The compiler requirements for Windows systems are listed in Table [tab:ch12_win_compiler_req].

No. WELSIM Compilers
1 Visual Studio 2022 (including the Microsoft C++ compiler)
2 Intel Visual Fortran 2022 compiler

Note

Those compilers are not required if you only use WELSIM application.

Installing the WELSIM for a Windows system

This section includes the steps required for installing WELSIM and licensing configuration on one Windows machine.

Downloading the installation file

To download the installation files from our website, you will need to agree the US Export Restrictions.

You only need to download one installer file.

  1. From the website, select the Windows version of WELSIM and click the download button on the webpage.
  2. The downloaded installer file has the name: WelSim28Setup.exe
  3. Begin the product installation as described in the next section.

Installing WELSIM

  1. Navigate to the directory where you placed the installer file. Run the installer by double click.
  2. The WELSIM installation Launcher appears as shown in Figure below. finite_element_analysis_welsim_windows_install1
  3. Click the Next button to start the installation on your computer.
  4. The license agreement appears as shown in Figure below. Read the agreement, and if you agree to the terms and conditions, select I Agree. Click Next. finite_element_analysis_welsim_windows_install2
  5. The installation folder setting appears as shown in the figure below. You can input your designated directory or keep the default one. After specifying the directory, Click Next. finite_element_analysis_welsim_windows_install3
  6. The prerequesites libraries installation appears as shown in the figure below. Your system requires these libraries to run the WELSIM application. Click Yes. finite_element_analysis_welsim_windows_install4 finite_element_analysis_welsim_windows_install5 finite_element_analysis_welsim_windows_install6
  7. The installation completed as shown in the figure below. Click Finish. finite_element_analysis_welsim_windows_install7

Note

WELSIM relies on the latest version of Microsoft MPI. If the Microsoft MPI redistributable installation conflicts with your pre-existing MS MPI libraries, please uninstall the pre-existing MPI from the Control Panel and reinstall the WELSIM.

Activating the WELSIM

In this section, assuming you already received the license file wsimkey.dat. To activate WELSIM on your computer with client licensing, you can follow the steps below:

  1. Start WELSIM application on your computer.
  2. Click the License Manager from the menu: HELP -> License Manager
  3. WELSIM License Manager user interface appears. There are five buttons on the interface:
    1. Generate Computer ID: generate user's unique ID for license key generation.
    2. Evaluate: click to continue using the trial version.
    3. Exit: quit the License Manager with no software activation.
    4. Buy Now: open your default internet browser and direct your visit to the pricing page.
    5. Enter Code: If you have received the license key file, click this button to import the license file.
  4. If the user are running software at the first time, generate the Computer ID by clicking the button of “Generate Computer ID”, and send this string (format of xxxx-xxxx-xxxx-xxxx) to info@welsim.com. The user will receive the license key within 24 hours.
  5. After receiving the license file (wsimkey.dat), click “Enter Code” button to import the license. In the License Code interface, the user can paste the license content from clipboard, or directly import the license from file.
  6. Click OK button to activate the WELSIM. A successfully activated software is shown in figure below.

finite_element_analysis_welsim_windows_install13

Starting the software

After installation, starting the WELSIM software is straightforward. Here are three methods:

  1. Double click the shortcut of WELSIM, if you toggle the option “Create Desktop Shortcut” during the last step of installation.
  2. Click the shortcut of WELSIM from the Start menu. From Start -> WELSIM ->WELSIM v1.8.
  3. Browse the directory of installation, double click the runWelSim.exe file.

As shown in the figure below, WESLIM application is started successfully on the Windows operation system. finite_element_analysis_welsim_windows_install12

Uninstalling the software

Uninstalling the software is straightforward. The user can run the unint.exe from one of methods below:

  1. Click the shortcut of WELSIM uninstaller from the Start menu. From Start -> WELSIM ->Uninstall.
  2. Browse the directory of installation, double click the uninst.exe file.
  3. Unstall the WELSIM application from the system Control Panel.
\ No newline at end of file diff --git a/legal/LGPL/index.html b/legal/LGPL/index.html index f95f81d..ec9104a 100755 --- a/legal/LGPL/index.html +++ b/legal/LGPL/index.html @@ -1 +1 @@ - GNU Lesser Genreal Public License (LGPL) - WelSim Documentation
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GNU Lesser Genreal Public License (LGPL)

Version 3 GNU Lesser General Public License

Version 3, 29 June 2007

Copyright © 2007 Free Software Foundation, Inc. http://fsf.org/

Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed.

This version of the GNU Lesser General Public License incorporates the terms and conditions of version 3 of the GNU General Public License, supplemented by the additional permissions listed below.

  1. Additional Definitions. As used herein, “this License” refers to version 3 of the GNU Lesser General Public License, and the “GNU GPL” refers to version 3 of the GNU General Public License.

    “The Library” refers to a covered work governed by this License, other than an Application or a Combined Work as defined below.

    An “Application” is any work that makes use of an interface provided by the Library, but which is not otherwise based on the Library. Defining a subclass of a class defined by the Library is deemed a mode of using an interface provided by the Library.

    A “Combined Work” is a work produced by combining or linking an Application with the Library. The particular version of the Library with which the Combined Work was made is also called the “Linked Version”.

    The “Minimal Corresponding Source” for a Combined Work means the Corresponding Source for the Combined Work, excluding any source code for portions of the Combined Work that, considered in isolation, are based on the Application, and not on the Linked Version.

    The “Corresponding Application Code” for a Combined Work means the object code and/or source code for the Application, including any data and utility programs needed for reproducing the Combined Work from the Application, but excluding the System Libraries of the Combined Work.

  2. Exception to Section 3 of the GNU GPL. You may convey a covered work under sections 3 and 4 of this License without being bound by section 3 of the GNU GPL.

  3. Conveying Modified Versions.

    If you modify a copy of the Library, and, in your modifications, a facility refers to a function or data to be supplied by an Application that uses the facility (other than as an argument passed when the facility is invoked), then you may convey a copy of the modified version:

    1. under this License, provided that you make a good faith effort to ensure that, in the event an Application does not supply the function or data, the facility still operates, and performs whatever part of its purpose remains meaningful, or

    2. under the GNU GPL, with none of the additional permissions of this License applicable to that copy.

  4. Object Code Incorporating Material from Library Header Files. The object code form of an Application may incorporate material from a header file that is part of the Library. You may convey such object code under terms of your choice, provided that, if the incorporated material is not limited to numerical parameters, data structure layouts and accessors, or small macros, inline functions and templates (ten or fewer lines in length), you do both of the following:

    1. Give prominent notice with each copy of the object code that the Library is used in it and that the Library and its use are covered by this License.

    2. Accompany the object code with a copy of the GNU GPL and this license document.

  5. Combined Works. You may convey a Combined Work under terms of your choice that, taken together, effectively do not restrict modification of the portions of the Library contained in the Combined Work and reverse engineering for debugging such modifications, if you also do each of the following:

    1. Give prominent notice with each copy of the Combined Work that the Library is used in it and that the Library and its use are covered by this License.
    2. Accompany the Combined Work with a copy of the GNU GPL and this license document.
    3. For a Combined Work that displays copyright notices during execution, include the copyright notice for the Library among these notices, as well as a reference directing the user to the copies of the GNU GPL and this license document.

    4. Do one of the following:

      1. Convey the Minimal Corresponding Source under the terms of this License, and the Corresponding Application Code in a form suitable for, and under terms that permit, the user to recombine or relink the Application with a modified version of the Linked Version to produce a modified Combined Work, in the manner specified by section 6 of the GNU GPL for conveying Corresponding Source.

      2. Use a suitable shared library mechanism for linking with the Library. A suitable mechanism is one that (a) uses at run time a copy of the Library already present on the user's computer system, and (b) will operate properly with a modified version of the Library that is interface-compatible with the Linked Version.

    5. Provide Installation Information, but only if you would otherwise be required to provide such information under section 6 of the GNU GPL, and only to the extent that such information is necessary to install and execute a modified version of the Combined Work produced by recombining or relinking the Application with a modified version of the Linked Version. (If you use option 4d0, the Installation Information must accompany the Minimal Corresponding Source and Corresponding Application Code. If you use option 4d1, you must provide the Installation Information in the manner specified by section 6 of the GNU GPL for conveying Corresponding Source.)

  6. Combined Libraries. You may place library facilities that are a work based on the Library side by side in a single library together with other library facilities that are not Applications and are not covered by this License, and convey such a combined library under terms of your choice, if you do both of the following:

    1. Accompany the combined library with a copy of the same work based on the Library, uncombined with any other library facilities, conveyed under the terms of this License.
    2. Give prominent notice with the combined library that part of it is a work based on the Library, and explaining where to find the accompanying uncombined form of the same work.

  7. Revised Versions of the GNU Lesser General Public License. The Free Software Foundation may publish revised and/or new versions of the GNU Lesser General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns.

    Each version is given a distinguishing version number. If the Library as you received it specifies that a certain numbered version of the GNU Lesser General Public License “or any later version” applies to it, you have the option of following the terms and conditions either of that published version or of any later version published by the Free Software Foundation. If the Library as you received it does not specify a version number of the GNU Lesser General Public License, you may choose any version of the GNU Lesser General Public License ever published by the Free Software Foundation.

    If the Library as you received it specifies that a proxy can decide whether future versions of the GNU Lesser General Public License shall apply, that proxy's public statement of acceptance of any version is permanent authorization for you to choose that version for the Library.

Version 2.1

GNU LESSER GENERAL PUBLIC LICENSE (LGPL) Version 2.1, February 1999 Copyright © 1991, 1999, Free Software Foundation, Inc. 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA

WelSimulation LLC will provide you with a complete machine-readable copy of the source code, valid for three years. The source code can be obtained by contacting WelSimulation LLC at info@welsim.com.

Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. NO WARRANTY BECAUSE THE LIBRARY IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY FOR THE LIBRARY, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE LIBRARY "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE LIBRARY IS WITH YOU. SHOULD THE LIBRARY PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.

GNU Lesser General Public License

Version 2.1

Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed.

Preamble

The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public Licenses are intended to guarantee your freedom to share and change free software--to make sure the software is free for all its users.

This license, the Lesser General Public License, applies to some specially designated software packages--typically libraries--of the Free Software Foundation and other authors who decide to use it. You can use it too, but we suggest you first think carefully about whether this license or the ordinary General Public License is the better strategy to use in any particular case, based on the explanations below.

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  • ABAQUS is a registered trademark of ABAQUS, Inc

  • Copyright 1984-1989, 1994 Adobe Systems Incorporated. Copyright 1988, 1994 Digital Equipment Corporation. Permission to use,copy,modify,distribute and sell this software and its documentation for any purpose and without fee is hereby granted, provided that the above copyright notices appear in all copies and that both those copyright notices and this permission notice appear in supporting documentation, and that the names of Adobe Systems and Digital Equipment Corporation not be used in advertising or publicity pertaining to distribution of the software without specific, written prior permission. Adobe Systems & Digital Equipment Corporation make no representations about the suitability of this software for any purpose. It is provided "as is" without express or implied warranty.

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License

WELSIM License

WELSIM SOFTWARE LICENSE AGREEMENT Copyright (C) 2017-2024 WELSIMULATION LLC Version effective date: August 10, 2017

READ THIS SOFTWARE LICENSE AGREEMENT CAREFULLY BEFORE PROCEEDING. THIS IS A LEGALLY BINDING CONTRACT BETWEEN LICENSEE AND LICENSOR FOR LICENSEE TO USE THE PROGRAM(S), AND IT INCLUDES DISCLAIMERS OF WARRANTY AND LIMITATIONS OF LIABILITY. WELSIMULATION LLC IS WILLING TO LICENSE THE SOFTWARE ONLY UPON THE CONDITION THAT YOU ACCEPT ALL OF THE TERMS CONTAINED IN THIS SOFTWARE LICENSE AGREEMENT. PLEASE READ THE TERMS CAREFULLY. BY CLICKING ON "I AGREE" OR BY INSTALLING THE SOFTWARE, YOU WILL INDICATE YOUR AGREEMENT WITH THEM. IF YOU ARE ENTERING INTO THIS AGREEMENT ON BEHALF OF A COMPANY OR OTHER LEGAL ENTITY, YOUR ACCEPTANCE REPRESENTS THAT YOU HAVE THE AUTHORITY TO BIND SUCH ENTITY TO THESE TERMS, IN WHICH CASE "YOU" OR "YOUR" SHALL REFER TO YOUR ENTITY. IF YOU DO NOT AGREE WITH THESE TERMS, OR IF YOU DO NOT HAVE THE AUTHORITY TO BIND YOUR ENTITY, THEN WELSIMULATION LLC IS UNWILLING TO LICENSE THE SOFTWARE, AND YOU SHOULD NOT INSTALL THE SOFTWARE.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

THE ACCOMPANYING PROGRAM IS PROVIDED UNDER THE TERMS OF THIS COMMON PUBLIC LICENSE ("AGREEMENT"). ANY USE, REPRODUCTION OR DISTRIBUTION OF THE PROGRAM CONSTITUTES RECIPIENT'S ACCEPTANCE OF THIS AGREEMENT.

This software is provided 'as-is', without any express or implied warranty. In no event will the authors be held liable for any damages or consequences arising from the use of this software.

  1. Parties. The parties to this Agreement are you, the licensee ("You") and WELSIMULATION LLC. If You are not acting on behalf of Yourself as an individual, then "You" means Your company or organization. A company or organization shall in either case mean a single business entity, and shall not include its affiliates or wholly owned subsidiaries.

  2. The Software. The accompanying materials including, but not limited to, source code, binary executables, documentation, images, and scripts, which are distributed by WELSIMULATION LLC, and derivatives of that collection and/or those files are referred to herein as the "Software".

  3. Restrictions. WELSIMULATION LLC encourages You to promote use of the Software. However this Agreement does not grant permission to use the trade names, trademarks, service marks, or product names of WELSIMULATION LLC, except as required for reasonable and customary use in describing the origin of the Software. In particular, You cannot use any of these marks in any way that might state or imply that WELSIMULATION LLC endorses Your work, or might state or imply that You created the Software covered by this Agreement. Except as expressly provided herein, you may not:

    1. modify or translate the Software;
    2. reverse engineer, decompile, or disassemble the Software, except to the extent this restriction is expressly prohibited by applicable law;
    3. create derivative works based on the Software;
    4. merge the Software with another product;
    5. copy the Software; or
    6. remove or obscure any proprietary rights notices or labels on the Software.

  4. Ownership. WELSIMULATION LLC and its suppliers own the Software and all intellectual property rights embodied therein, including copyrights and valuable trade secrets embodied in the Software's design and coding methodology. The Software is protected by United States copyright laws and international treaty provisions. This Agreement provides You only a limited use license, and no ownership of any intellectual property.

  5. Infringement Indemnification. You shall defend or settle, at Your expense, any action brought against WELSIMULATION LLC based upon the claim that any modifications to the Software or combination of the Software with products infringes or violates any third party right; provided, however, that: (i) WELSIMULATION LLC shall notify Licensee promptly in writing of any such claim; (ii) WELSIMULATION LLC shall not enter into any settlement or compromise any such claim without Your prior written consent; (iii) You shall have sole control of any such action and settlement negotiations; and (iv) WELSIMULATION LLC shall provide You with commercially reasonable information and assistance, at Your request and expense, necessary to settle or defend such claim. You agree to pay all damages and costs finally awarded against WELSIMULATION LLC attributable to such claim.

  6. No warranty The program is provided on an 'as is' basis, without warranties or conditions of any kind, either express or implied including, without limitation, any warranties or conditions of title, non-infringement, merchantability or fitness for a particular purpose. Each Recipient is solely responsible for determining the appropriateness of using and distributing the Program and assumes all risks associated with its exercise of rights under this Agreement, including but not limited to the risks and costs of program errors, compliance with applicable laws, damage to or loss of data, programs or equipment, and unavailability or interruption of operations.

  7. Licensee Outside The U.S. If You are located outside the U.S.,then the following provisions shall apply: (i) The parties confirm that this Agreement and all related documentation is and will be in the English language; and (ii) You are responsible for complying with any local laws in your jurisdiction which might impact your right to import, export or use the Software, and You represent that You have complied with any regulations or registration procedures required by applicable law to make this license enforceable.

  8. Assignment. Except as expressly provided herein neither this Agreement nor any rights granted hereunder, nor the use of any of the software may be assigned, or otherwise transferred, in whole or in part, by Licensee, without the prior written consent of WELSIMULATION LLC. WELSIMULATION LLC may assign this Agreement in the event of a merger or sale of all or substantially all of the stock of assets of WELSIMULATION LLC without the consent of Licensee. Any attempted assignment will be void and of no effect unless permitted by the foregoing. This Agreement shall inure to the benefit of the parties permitted successors and assigns.

  9. Miscellaneous. This Agreement constitutes the entire understanding of the parties with respect to the subject matter of this Agreement and merges all prior communications, representations, and agreements. WELSIMULATION LLC reserves the right to change this Agreement at any time, which change shall be effective immediately.

  10. General If any provision of this Agreement is invalid or unenforceable under applicable law, it shall not affect the validity or enforceability of the remainder of the terms of this Agreement, and without further action by the parties hereto, such provision shall be reformed to the minimum extent necessary to make such provision valid and enforceable.

If Recipient institutes patent litigation against a Contributor with respect to a patent applicable to software (including a cross-claim or counterclaim in a lawsuit), then any patent licenses granted by that Contributor to such Recipient under this Agreement shall terminate as of the date such litigation is filed. In addition, if Recipient institutes patent litigation against any entity (including a cross-claim or counterclaim in a lawsuit) alleging that the Program itself (excluding combinations of the Program with other software or hardware) infringes such Recipient's patent(s), then such Recipient's rights granted under Section 3(b) shall terminate as of the date such litigation is filed.

All Recipient's rights under this Agreement shall terminate if it fails to comply with any of the material terms or conditions of this Agreement and does not cure such failure in a reasonable period of time after becoming aware of such noncompliance. If all Recipient's rights under this Agreement terminate, Recipient agrees to cease use and distribution of the Program as soon as reasonably practicable. However, Recipient's obligations under this Agreement and any licenses granted by Recipient relating to the Program shall continue and survive.

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License

WELSIM License

WELSIM SOFTWARE LICENSE AGREEMENT Copyright (C) 2017-2024 WELSIMULATION LLC Version effective date: August 10, 2017

READ THIS SOFTWARE LICENSE AGREEMENT CAREFULLY BEFORE PROCEEDING. THIS IS A LEGALLY BINDING CONTRACT BETWEEN LICENSEE AND LICENSOR FOR LICENSEE TO USE THE PROGRAM(S), AND IT INCLUDES DISCLAIMERS OF WARRANTY AND LIMITATIONS OF LIABILITY. WELSIMULATION LLC IS WILLING TO LICENSE THE SOFTWARE ONLY UPON THE CONDITION THAT YOU ACCEPT ALL OF THE TERMS CONTAINED IN THIS SOFTWARE LICENSE AGREEMENT. PLEASE READ THE TERMS CAREFULLY. BY CLICKING ON "I AGREE" OR BY INSTALLING THE SOFTWARE, YOU WILL INDICATE YOUR AGREEMENT WITH THEM. IF YOU ARE ENTERING INTO THIS AGREEMENT ON BEHALF OF A COMPANY OR OTHER LEGAL ENTITY, YOUR ACCEPTANCE REPRESENTS THAT YOU HAVE THE AUTHORITY TO BIND SUCH ENTITY TO THESE TERMS, IN WHICH CASE "YOU" OR "YOUR" SHALL REFER TO YOUR ENTITY. IF YOU DO NOT AGREE WITH THESE TERMS, OR IF YOU DO NOT HAVE THE AUTHORITY TO BIND YOUR ENTITY, THEN WELSIMULATION LLC IS UNWILLING TO LICENSE THE SOFTWARE, AND YOU SHOULD NOT INSTALL THE SOFTWARE.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

THE ACCOMPANYING PROGRAM IS PROVIDED UNDER THE TERMS OF THIS COMMON PUBLIC LICENSE ("AGREEMENT"). ANY USE, REPRODUCTION OR DISTRIBUTION OF THE PROGRAM CONSTITUTES RECIPIENT'S ACCEPTANCE OF THIS AGREEMENT.

This software is provided 'as-is', without any express or implied warranty. In no event will the authors be held liable for any damages or consequences arising from the use of this software.

  1. Parties. The parties to this Agreement are you, the licensee ("You") and WELSIMULATION LLC. If You are not acting on behalf of Yourself as an individual, then "You" means Your company or organization. A company or organization shall in either case mean a single business entity, and shall not include its affiliates or wholly owned subsidiaries.

  2. The Software. The accompanying materials including, but not limited to, source code, binary executables, documentation, images, and scripts, which are distributed by WELSIMULATION LLC, and derivatives of that collection and/or those files are referred to herein as the "Software".

  3. Restrictions. WELSIMULATION LLC encourages You to promote use of the Software. However this Agreement does not grant permission to use the trade names, trademarks, service marks, or product names of WELSIMULATION LLC, except as required for reasonable and customary use in describing the origin of the Software. In particular, You cannot use any of these marks in any way that might state or imply that WELSIMULATION LLC endorses Your work, or might state or imply that You created the Software covered by this Agreement. Except as expressly provided herein, you may not:

    1. modify or translate the Software;
    2. reverse engineer, decompile, or disassemble the Software, except to the extent this restriction is expressly prohibited by applicable law;
    3. create derivative works based on the Software;
    4. merge the Software with another product;
    5. copy the Software; or
    6. remove or obscure any proprietary rights notices or labels on the Software.

  4. Ownership. WELSIMULATION LLC and its suppliers own the Software and all intellectual property rights embodied therein, including copyrights and valuable trade secrets embodied in the Software's design and coding methodology. The Software is protected by United States copyright laws and international treaty provisions. This Agreement provides You only a limited use license, and no ownership of any intellectual property.

  5. Infringement Indemnification. You shall defend or settle, at Your expense, any action brought against WELSIMULATION LLC based upon the claim that any modifications to the Software or combination of the Software with products infringes or violates any third party right; provided, however, that: (i) WELSIMULATION LLC shall notify Licensee promptly in writing of any such claim; (ii) WELSIMULATION LLC shall not enter into any settlement or compromise any such claim without Your prior written consent; (iii) You shall have sole control of any such action and settlement negotiations; and (iv) WELSIMULATION LLC shall provide You with commercially reasonable information and assistance, at Your request and expense, necessary to settle or defend such claim. You agree to pay all damages and costs finally awarded against WELSIMULATION LLC attributable to such claim.

  6. No warranty The program is provided on an 'as is' basis, without warranties or conditions of any kind, either express or implied including, without limitation, any warranties or conditions of title, non-infringement, merchantability or fitness for a particular purpose. Each Recipient is solely responsible for determining the appropriateness of using and distributing the Program and assumes all risks associated with its exercise of rights under this Agreement, including but not limited to the risks and costs of program errors, compliance with applicable laws, damage to or loss of data, programs or equipment, and unavailability or interruption of operations.

  7. Licensee Outside The U.S. If You are located outside the U.S.,then the following provisions shall apply: (i) The parties confirm that this Agreement and all related documentation is and will be in the English language; and (ii) You are responsible for complying with any local laws in your jurisdiction which might impact your right to import, export or use the Software, and You represent that You have complied with any regulations or registration procedures required by applicable law to make this license enforceable.

  8. Assignment. Except as expressly provided herein neither this Agreement nor any rights granted hereunder, nor the use of any of the software may be assigned, or otherwise transferred, in whole or in part, by Licensee, without the prior written consent of WELSIMULATION LLC. WELSIMULATION LLC may assign this Agreement in the event of a merger or sale of all or substantially all of the stock of assets of WELSIMULATION LLC without the consent of Licensee. Any attempted assignment will be void and of no effect unless permitted by the foregoing. This Agreement shall inure to the benefit of the parties permitted successors and assigns.

  9. Miscellaneous. This Agreement constitutes the entire understanding of the parties with respect to the subject matter of this Agreement and merges all prior communications, representations, and agreements. WELSIMULATION LLC reserves the right to change this Agreement at any time, which change shall be effective immediately.

  10. General If any provision of this Agreement is invalid or unenforceable under applicable law, it shall not affect the validity or enforceability of the remainder of the terms of this Agreement, and without further action by the parties hereto, such provision shall be reformed to the minimum extent necessary to make such provision valid and enforceable.

If Recipient institutes patent litigation against a Contributor with respect to a patent applicable to software (including a cross-claim or counterclaim in a lawsuit), then any patent licenses granted by that Contributor to such Recipient under this Agreement shall terminate as of the date such litigation is filed. In addition, if Recipient institutes patent litigation against any entity (including a cross-claim or counterclaim in a lawsuit) alleging that the Program itself (excluding combinations of the Program with other software or hardware) infringes such Recipient's patent(s), then such Recipient's rights granted under Section 3(b) shall terminate as of the date such litigation is filed.

All Recipient's rights under this Agreement shall terminate if it fails to comply with any of the material terms or conditions of this Agreement and does not cure such failure in a reasonable period of time after becoming aware of such noncompliance. If all Recipient's rights under this Agreement terminate, Recipient agrees to cease use and distribution of the Program as soon as reasonably practicable. However, Recipient's obligations under this Agreement and any licenses granted by Recipient relating to the Program shall continue and survive.

\ No newline at end of file diff --git a/mateditor/mat_core_loss/index.html b/mateditor/mat_core_loss/index.html index 553c6a4..542256a 100755 --- a/mateditor/mat_core_loss/index.html +++ b/mateditor/mat_core_loss/index.html @@ -1,4 +1,4 @@ - Core loss model - WelSim Documentation
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Core loss model

The core loss combines eddy current losses and hysteresis losses for a transient solution type. It is a post-processing calculation, based on already calculated transient magnetic field quantities. It is applicable for the evaluation of core losses in steel laminations (frequently used in applications such as electric machines, transformers) or in power ferrites.

Hysteresis loss is associated with loss density fields in 2D and 3D eddy current solutions only. Hysteresis loss is short for magnetic hysteresis loss and represents power loss in some magnetic materials (electric steels or ferrites) in alternating (sinusoidal) magnetic fields. This loss is due to a phenomenon called "magnetic viscosity" which causes the B and H fields to have a phase shift between them. In the B-H plane, for linear materials, the relationship between these two fields describes an ellipse. The hysteresis loss is proportional to the area of the ellipse.

Core loss models for an electromagnetic material

MatEditor provides two core loss models: electrical steel and power ferrite. The coefficients are given in the table below.

Type Associated properties
Electrical Steel Hystersis coefficient \(K_h\), Classcial eddy coefficient \(K_c\), Excess coefficient \(K_e\).
Power Ferrite Steinmetz coefficients \(C_m\), \(X\), and \(Y\).
WelSim/docs

Core loss model

The core loss combines eddy current losses and hysteresis losses for a transient solution type. It is a post-processing calculation, based on already calculated transient magnetic field quantities. It is applicable for the evaluation of core losses in steel laminations (frequently used in applications such as electric machines, transformers) or in power ferrites.

Hysteresis loss is associated with loss density fields in 2D and 3D eddy current solutions only. Hysteresis loss is short for magnetic hysteresis loss and represents power loss in some magnetic materials (electric steels or ferrites) in alternating (sinusoidal) magnetic fields. This loss is due to a phenomenon called "magnetic viscosity" which causes the B and H fields to have a phase shift between them. In the B-H plane, for linear materials, the relationship between these two fields describes an ellipse. The hysteresis loss is proportional to the area of the ellipse.

Core loss models for an electromagnetic material

MatEditor provides two core loss models: electrical steel and power ferrite. The coefficients are given in the table below.

Type Associated properties
Electrical Steel Hystersis coefficient \(K_h\), Classcial eddy coefficient \(K_c\), Excess coefficient \(K_e\).
Power Ferrite Steinmetz coefficients \(C_m\), \(X\), and \(Y\).

Note

In Transient Solver, X must be less than Y.

Calculate core loss coefficients from loss curves

This section introduces how to calculate core loss coefficients for electrical steel and power ferrite materials according to the given P-B test data.

  1. Add P-B Test Data material property, and edit the frequency-based data. You also can import the data from a plain text or Excel file. Check the data curves by clicking the row of frequency. Click the header of the frequency column displays all curves in the chart.
    finite_element_analysis_mateditor_pbtestdata

  2. Add Core Loss Model material property, and set the Core Loss Model Type of the property to Electrical Steel or Power Ferrite.
    finite_element_analysis_mateditor_core_loss_model_type

  3. Add Curve Fitting sub-property from the RMB context menu.
    finite_element_analysis_mateditor_core_loss_add_curve_fitting

  4. Solve the curve fit from the RMB context menu.
    finite_element_analysis_mateditor_core_loss_fit_context_menu

  5. If the solve succeeds. The calculated parameters will be shown in the table.
    finite_element_analysis_mateditor_core_loss_curve_fit_solved

  6. Copy the solved values to the properties from RMB context menu. You also can review the calculated curves in the chart.
    finite_element_analysis_mateditor_core_loss_fit_all_curves

  7. Display curves in the logarithmic axis (optional).
    finite_element_analysis_mateditor_core_loss_fit_all_curves_in_log

Computation of electrical steel core loss from loss curves

The iron-core loss without DC flux bias is expressed as the following:

\[ p_v=P_h+P_c+P_e=K_{f} f (B_m)^2 + K_c (fB_m)^2 + K_e(fB_m)^{1.5} = K_1B_m^2+K_2B_m^{1.5} \]

where

  • \(B_m\) is the amplitude of the AC flux component,
  • \(f\) is the frequency,
  • \(K_h\) is the hysteresis core loss coefficient,
  • \(K_c\) is the eddy-current core loss coefficient, and
  • \(K_e\) is the excess core loss coefficient,
  • \(K_1=K_ff+K_cf^2\),
  • \(K_2=K_ef^{1.5}\).

Minimize the quadratic form to obtain \(K_h\) , \(K_c\), and \(K_e\) directly.

\[ err(K_h,K_c,K_e)=\sum_{i=1}^m \sum_{j=1}^{n_i} \left[p_{ij}-\left(K_{h}f_{i}B_{mij}^2 +K_{c}\left(fB_{mij}\right)^{2}+ K_{e}\left(f_iB_{mij}\right)^{1.5} \right) \right]^2=min \]

where \(m\) is the number of loss curves, \(n_i\) is the number of points of the \(i\)-th loss curve, and \(p_{ij} = f(f_i , B_{mij})\) is two dimensional lookup table for loss curves.

Note

Since the manufacturer-provided loss curve is obtained under sinusoidal flux conditions at a given frequency, these coefficients can be derived in the frequency domain.

Computation of power ferrite core loss from loss curves

The principles of the computation algorithm are summarized as follows. The iron-core loss is expressed as the Steinmetz approximation

\[ p_v=C_m f^x B_m^y \]

where \(p_v\) is the average power density, \(f\) is the excitation frequency, and \(B_m\) is the peak flux density, is commonly used to characterize core loss data for sinusoidal excitation, but can also be applied to square-wave data.

To linearize the equation for curve fitting, we used base-10 logarithms. The equation above can be rewritten to

\[ log(p_v)=c + x\cdot log(f) + y \cdot(B_m) \]

where \(c=log(C_m)\).

Minimize the quadratic form to obtain \(C\), \(x\) and \(y\).

\[ err(C_m,x,y)=\sum_{i=1}^{m}\sum_{j=1}^{n_i}\left[log(p_{vij})-\left(c+xlog(f_i)+ylog(B_{mij}) \right) \right]^2=min \]

where \(m\) is the number of loss curves, \(n_i\) is the number of points of the \(i\)-th loss curve, and \(P_{vij} = f(f_i , B_{mij})\) is two dimensional lookup table for multi-frequency loss curves. Then \(C_m\) is calculated from the equation \(c=log(C_m)\).

\ No newline at end of file +* Ke - Excess -->

Calculate core loss coefficients from loss curves

This section introduces how to calculate core loss coefficients for electrical steel and power ferrite materials according to the given P-B test data.

  1. Add P-B Test Data material property, and edit the frequency-based data. You also can import the data from a plain text or Excel file. Check the data curves by clicking the row of frequency. Click the header of the frequency column displays all curves in the chart.
    finite_element_analysis_mateditor_pbtestdata

  2. Add Core Loss Model material property, and set the Core Loss Model Type of the property to Electrical Steel or Power Ferrite.
    finite_element_analysis_mateditor_core_loss_model_type

  3. Add Curve Fitting sub-property from the RMB context menu.
    finite_element_analysis_mateditor_core_loss_add_curve_fitting

  4. Solve the curve fit from the RMB context menu.
    finite_element_analysis_mateditor_core_loss_fit_context_menu

  5. If the solve succeeds. The calculated parameters will be shown in the table.
    finite_element_analysis_mateditor_core_loss_curve_fit_solved

  6. Copy the solved values to the properties from RMB context menu. You also can review the calculated curves in the chart.
    finite_element_analysis_mateditor_core_loss_fit_all_curves

  7. Display curves in the logarithmic axis (optional).
    finite_element_analysis_mateditor_core_loss_fit_all_curves_in_log

Computation of electrical steel core loss from loss curves

The iron-core loss without DC flux bias is expressed as the following:

\[ p_v=P_h+P_c+P_e=K_{f} f (B_m)^2 + K_c (fB_m)^2 + K_e(fB_m)^{1.5} = K_1B_m^2+K_2B_m^{1.5} \]

where

Minimize the quadratic form to obtain \(K_h\) , \(K_c\), and \(K_e\) directly.

\[ err(K_h,K_c,K_e)=\sum_{i=1}^m \sum_{j=1}^{n_i} \left[p_{ij}-\left(K_{h}f_{i}B_{mij}^2 +K_{c}\left(fB_{mij}\right)^{2}+ K_{e}\left(f_iB_{mij}\right)^{1.5} \right) \right]^2=min \]

where \(m\) is the number of loss curves, \(n_i\) is the number of points of the \(i\)-th loss curve, and \(p_{ij} = f(f_i , B_{mij})\) is two dimensional lookup table for loss curves.

Note

Since the manufacturer-provided loss curve is obtained under sinusoidal flux conditions at a given frequency, these coefficients can be derived in the frequency domain.

Computation of power ferrite core loss from loss curves

The principles of the computation algorithm are summarized as follows. The iron-core loss is expressed as the Steinmetz approximation

\[ p_v=C_m f^x B_m^y \]

where \(p_v\) is the average power density, \(f\) is the excitation frequency, and \(B_m\) is the peak flux density, is commonly used to characterize core loss data for sinusoidal excitation, but can also be applied to square-wave data.

To linearize the equation for curve fitting, we used base-10 logarithms. The equation above can be rewritten to

\[ log(p_v)=c + x\cdot log(f) + y \cdot(B_m) \]

where \(c=log(C_m)\).

Minimize the quadratic form to obtain \(C\), \(x\) and \(y\).

\[ err(C_m,x,y)=\sum_{i=1}^{m}\sum_{j=1}^{n_i}\left[log(p_{vij})-\left(c+xlog(f_i)+ylog(B_{mij}) \right) \right]^2=min \]

where \(m\) is the number of loss curves, \(n_i\) is the number of points of the \(i\)-th loss curve, and \(P_{vij} = f(f_i , B_{mij})\) is two dimensional lookup table for multi-frequency loss curves. Then \(C_m\) is calculated from the equation \(c=log(C_m)\).

\ No newline at end of file diff --git a/mateditor/mat_file_format/index.html b/mateditor/mat_file_format/index.html index 7176d57..b3ff75b 100755 --- a/mateditor/mat_file_format/index.html +++ b/mateditor/mat_file_format/index.html @@ -1 +1 @@ - Material file format - WelSim Documentation
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Material library file format

Material library data follows the MatML 3.1 Schema for saving material data to external libraries on disk. More information about MatML can be found at http://matml.org. For an example of the format see the Export individual data item in the Perform Basic Tasks in Material section and then open the file with a text/xml editor.

\ No newline at end of file + Material file format - WelSim Documentation
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Material library file format

Material library data follows the MatML 3.1 Schema for saving material data to external libraries on disk. More information about MatML can be found at http://matml.org. For an example of the format see the Export individual data item in the Perform Basic Tasks in Material section and then open the file with a text/xml editor.

\ No newline at end of file diff --git a/mateditor/mat_gui/index.html b/mateditor/mat_gui/index.html index 9d21ac9..a7ec6d7 100755 --- a/mateditor/mat_gui/index.html +++ b/mateditor/mat_gui/index.html @@ -1,3 +1,3 @@ - Graphical user interface - WelSim Documentation
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Graphical user interface

The MatEditor workspace is an independent interface and display relavant items as you configured.

Layout reference

Presented below are two layout configurations for the MatEditor view. The first configuration is displayed by clicking on "Library" tab in toolbox. The second configure is shown by clicking on "Build" tab in toolbox. You can switch this two layout mode by clicking the tabs.

finite_element_analysis_mateditor_gui1

finite_element_analysis_mateditor_gui2

Legend Name Description
A Menu Bar Operations for MatEditor.
B Toolbar Selected operations that often used for MatEditor.
C Material Outline Pane Material items that are created in MatEditor.
D Library Outline Pane Displays the available prebuild material sources.
E Property Outline Pane Displays the available material property sources that can be included into a material.
F Properties Pane Displays the properties of the current material.
G Table Pane Shows the tabular data for the selected item in the Properties pane.
H Chart Pane Shows the chart of the item selected in the Properties pane.

The following items in the menu bar are provided by MatEditor:

File

  • New: Create a new material object in the tree window.
  • Open: Retrieve material data from an external XML file. This command remove all existing material data in the system.
  • Save: Save current material data into an external XML file.
  • Save as: Save current material data into an designated folder and in a specific XML file name.
  • Export material data: Output selected material data into an exteral XML file.
  • Import material data: Input material data from an external XML file. The existing material data will not be removed.
  • Exit: Close the software.

Edit

  • Activate: Set the selected material object as current.
  • Duplicate: Create a new material object and copy all propeties from the selected to the newly created material.
  • Delete: Remove the selected material object(s).
  • Delete all: Remove all material objects.

Units

This menu provides all avilable unit systems and units. Once one unit (system) is chosen, the default unit is determined. The units for the newly created material data will be automatically set to the chosen unit(system).

Help

  • Help: Direct the user to the online user manual.
  • About: Display the software and hardware information dialog.

Toolbar

The following item in the toolbar is provided by MatEditor:

Icon Name Description
finite_element_analysis_mateditor_icon_new New Create a new material object in the tree window.
finite_element_analysis_mateditor_icon_open Open Retrieve material data from an external XML file. This command remove all existing material data in the system.
finite_element_analysis_mateditor_icon_save Save Save current material data into an external XML file.
finite_element_analysis_mateditor_icon_help Help Direct the user to the online user manual.
finite_element_analysis_mateditor_icon_about About Display the software and hardware information dialog.

Toolbox

MatEditor Toolbox contains two tabs: Library and Build. These two tabs function as:

  • Library: contains default material data that allows user to directly use. Clicking this tab displays the Library Outline Pane.
  • Build: contains all supported material properties that enable user to compose material data. Clicking this tab displays the Property Outline Pane.

Material outline pane

The Outline pane shows an outline of the contents of the created material data source. You can perform the following actions in this pane:

  • Create a new material
  • Delete a material
  • Rename a material
  • Edit a material
  • Duplicate a material

Items status

The itmes column shows the name of the items contained in the data source. When the name of material object is in bold, the material is activated for editing.

Library outline pane

The Library Outline pane shows an outline of availble predefined materials. These materials are grouped into several categories.

finite_element_analysis_mateditor_library_outline

Property outline pane

The Property Outline pane shows an outline of availble material properties. These material properties are grouped into several categories.

finite_element_analysis_mateditor_property_outline

Properties pane

The Properties pane shows the properties for the item selected in the Property Outline pane. You can perform the following actions in this pane:

  • Add additional properties, tabular data (from the Property Outline and Table panes)
  • Delete a property
  • Modify constant data
  • Suppress a property

Property column

The property column lists the properties for the item selected in the Property Outline pane. Clicking a property will change the contents of the Table pane and Chart pane.

Material property

The status of the material property is indicated as follows:

  • finite_element_analysis_mateditor_icon_property: The material property is described in a single property data (see the Material Definitions topic).
WelSim/docs

Graphical user interface

The MatEditor workspace is an independent interface and display relavant items as you configured.

Layout reference

Presented below are two layout configurations for the MatEditor view. The first configuration is displayed by clicking on "Library" tab in toolbox. The second configure is shown by clicking on "Build" tab in toolbox. You can switch this two layout mode by clicking the tabs.

finite_element_analysis_mateditor_gui1

finite_element_analysis_mateditor_gui2

Legend Name Description
A Menu Bar Operations for MatEditor.
B Toolbar Selected operations that often used for MatEditor.
C Material Outline Pane Material items that are created in MatEditor.
D Library Outline Pane Displays the available prebuild material sources.
E Property Outline Pane Displays the available material property sources that can be included into a material.
F Properties Pane Displays the properties of the current material.
G Table Pane Shows the tabular data for the selected item in the Properties pane.
H Chart Pane Shows the chart of the item selected in the Properties pane.

The following items in the menu bar are provided by MatEditor:

File

  • New: Create a new material object in the tree window.
  • Open: Retrieve material data from an external XML file. This command remove all existing material data in the system.
  • Save: Save current material data into an external XML file.
  • Save as: Save current material data into an designated folder and in a specific XML file name.
  • Export material data: Output selected material data into an exteral XML file.
  • Import material data: Input material data from an external XML file. The existing material data will not be removed.
  • Exit: Close the software.

Edit

  • Activate: Set the selected material object as current.
  • Duplicate: Create a new material object and copy all propeties from the selected to the newly created material.
  • Delete: Remove the selected material object(s).
  • Delete all: Remove all material objects.

Units

This menu provides all avilable unit systems and units. Once one unit (system) is chosen, the default unit is determined. The units for the newly created material data will be automatically set to the chosen unit(system).

Help

  • Help: Direct the user to the online user manual.
  • About: Display the software and hardware information dialog.

Toolbar

The following item in the toolbar is provided by MatEditor:

Icon Name Description
finite_element_analysis_mateditor_icon_new New Create a new material object in the tree window.
finite_element_analysis_mateditor_icon_open Open Retrieve material data from an external XML file. This command remove all existing material data in the system.
finite_element_analysis_mateditor_icon_save Save Save current material data into an external XML file.
finite_element_analysis_mateditor_icon_help Help Direct the user to the online user manual.
finite_element_analysis_mateditor_icon_about About Display the software and hardware information dialog.

Toolbox

MatEditor Toolbox contains two tabs: Library and Build. These two tabs function as:

  • Library: contains default material data that allows user to directly use. Clicking this tab displays the Library Outline Pane.
  • Build: contains all supported material properties that enable user to compose material data. Clicking this tab displays the Property Outline Pane.

Material outline pane

The Outline pane shows an outline of the contents of the created material data source. You can perform the following actions in this pane:

  • Create a new material
  • Delete a material
  • Rename a material
  • Edit a material
  • Duplicate a material

Items status

The itmes column shows the name of the items contained in the data source. When the name of material object is in bold, the material is activated for editing.

Library outline pane

The Library Outline pane shows an outline of availble predefined materials. These materials are grouped into several categories.

finite_element_analysis_mateditor_library_outline

Property outline pane

The Property Outline pane shows an outline of availble material properties. These material properties are grouped into several categories.

finite_element_analysis_mateditor_property_outline

Properties pane

The Properties pane shows the properties for the item selected in the Property Outline pane. You can perform the following actions in this pane:

  • Add additional properties, tabular data (from the Property Outline and Table panes)
  • Delete a property
  • Modify constant data
  • Suppress a property

Property column

The property column lists the properties for the item selected in the Property Outline pane. Clicking a property will change the contents of the Table pane and Chart pane.

Material property

The status of the material property is indicated as follows:

  • finite_element_analysis_mateditor_icon_property: The material property is described in a single property data (see the Material Definitions topic).

Value column

The value column is used to change data for a property or indicates that the data for the property is tabular (finite_element_analysis_mateditor_icon_tabular).

Unit column

The unit column displays the unit of the data shown in the value column . If the column is editable (see Units Menu), changing the unit will convert the value into the selected unit (there is no net change in the data, so the solution is still valid).

Suppression column

The suppression column shows the suppression status of the item and may also be used to switch the status (see Suppression).

Table pane

The Table pane shows the tabular data for the item selected in the Properties pane. If there are independent variables (for instance, Temperature) for the selected item and the item is constant, you may change it to a table by entering a value into the independent variables data cell. If a row is shown with an index of *, you may add additional rows of data.

finite_element_analysis_mateditor_table

Note

You also can change the unit by clicking the header of table

Chart pane

The Chart pane shows the chart of the selected item in the Properties pane. The chart data is idenital to the table data.

\ No newline at end of file + Indicates that the collection of property data requires attention (see the Validation and Filtering topics). -->

Value column

The value column is used to change data for a property or indicates that the data for the property is tabular (finite_element_analysis_mateditor_icon_tabular).

Unit column

The unit column displays the unit of the data shown in the value column . If the column is editable (see Units Menu), changing the unit will convert the value into the selected unit (there is no net change in the data, so the solution is still valid).

Suppression column

The suppression column shows the suppression status of the item and may also be used to switch the status (see Suppression).

Table pane

The Table pane shows the tabular data for the item selected in the Properties pane. If there are independent variables (for instance, Temperature) for the selected item and the item is constant, you may change it to a table by entering a value into the independent variables data cell. If a row is shown with an index of *, you may add additional rows of data.

finite_element_analysis_mateditor_table

Note

You also can change the unit by clicking the header of table

Chart pane

The Chart pane shows the chart of the selected item in the Properties pane. The chart data is idenital to the table data.

\ No newline at end of file diff --git a/mateditor/mat_hyperelasticity_curvefit/index.html b/mateditor/mat_hyperelasticity_curvefit/index.html index ea9e515..cd65028 100755 --- a/mateditor/mat_hyperelasticity_curvefit/index.html +++ b/mateditor/mat_hyperelasticity_curvefit/index.html @@ -1 +1 @@ - Curve fitting - WelSim Documentation
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Curve Fitting

Calculate material constants from test data

This section introduces how to calculate material coefficients for the selected hyperelastic models according to the given uniaxial, biaxial, shear, and volumetric test data. Enginering strain and stress pair is used for input data.

  1. Add Uniaxial Test Data, Biaxial Test Data, or Shear Test Data material property, and edit the strain-stress data. You also can import the data from a plain text or Excel file. Set the temperature value if it is available. Check the data points by clicking the row of temperature.
    finite_element_analysis_mateditor_hyperelastic_testdata

  2. Add one of hyperelastic material properties from the toolbox, the supported hyperelastic models include Neo-Hookean, Mooney-Rivlin, Arruda-Boyce, Blatz-Ko, Gent, Ogden, Polynomial, and Yeoh. An example of Mooney-Rivlin 9 is given here.
    finite_element_analysis_mateditor_hyperelastic_mooneyrivlin9_properties

  3. Add Curve Fitting sub-property from the RMB context menu.
    finite_element_analysis_mateditor_mooneyrivlin9_add_curvefit

  4. Solve the curve fit from the RMB context menu.
    finite_element_analysis_mateditor_mooneyrivlin9_solve_curvefit

  5. If the solve succeeds. The calculated parameters will be shown in the table.
    finite_element_analysis_mateditor_mooneyrivlin9_curvefit_solved

  6. Copy the solved values to the properties from RMB context menu. You also can review the calculated curves in the chart.
    finite_element_analysis_mateditor_mooneyrivlin9_curves

Note

  1. The test data should cover the entire strain range in the following simulation.
  2. It is recommended to input all uniaxial, biaxial, and shear test data if those data are available from the experiments.
\ No newline at end of file + Curve fitting - WelSim Documentation
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Curve Fitting

Calculate material constants from test data

This section introduces how to calculate material coefficients for the selected hyperelastic models according to the given uniaxial, biaxial, shear, and volumetric test data. Enginering strain and stress pair is used for input data.

  1. Add Uniaxial Test Data, Biaxial Test Data, or Shear Test Data material property, and edit the strain-stress data. You also can import the data from a plain text or Excel file. Set the temperature value if it is available. Check the data points by clicking the row of temperature.
    finite_element_analysis_mateditor_hyperelastic_testdata

  2. Add one of hyperelastic material properties from the toolbox, the supported hyperelastic models include Neo-Hookean, Mooney-Rivlin, Arruda-Boyce, Blatz-Ko, Gent, Ogden, Polynomial, and Yeoh. An example of Mooney-Rivlin 9 is given here.
    finite_element_analysis_mateditor_hyperelastic_mooneyrivlin9_properties

  3. Add Curve Fitting sub-property from the RMB context menu.
    finite_element_analysis_mateditor_mooneyrivlin9_add_curvefit

  4. Solve the curve fit from the RMB context menu.
    finite_element_analysis_mateditor_mooneyrivlin9_solve_curvefit

  5. If the solve succeeds. The calculated parameters will be shown in the table.
    finite_element_analysis_mateditor_mooneyrivlin9_curvefit_solved

  6. Copy the solved values to the properties from RMB context menu. You also can review the calculated curves in the chart.
    finite_element_analysis_mateditor_mooneyrivlin9_curves

Note

  1. The test data should cover the entire strain range in the following simulation.
  2. It is recommended to input all uniaxial, biaxial, and shear test data if those data are available from the experiments.
\ No newline at end of file diff --git a/mateditor/mat_io/index.html b/mateditor/mat_io/index.html index 4f4bce7..4442c80 100644 --- a/mateditor/mat_io/index.html +++ b/mateditor/mat_io/index.html @@ -1 +1 @@ - Mutually exclusive properties 1 - WelSim Documentation
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Mutually exclusive properties 1

Some properties are mutually exclusive of each other and require that only one property in the mutually exclusive set be unsuppressed. The addition or removing of the suppression for one of these properties automatically suppresses the other mutually exclusive properties.

For example, defining Isotropic Elasticity and Orthotropic Elasticity for the same material represents redundant elasticity behavior. Only one behavior can be active for the material. When such a conflict occurs, the property defined last is used and the previously defined, conflicting property is automatically suppressed.

The properties that are mutually exclusive are grouped in the following table.

Group Material Property
Elastic properties Isotropic Elasticity, Orthotropic Elasticity, Anisotropic Elasticity, Mooney-Rivlin, Neo-Hookean, Polynomial, Yeoh, Ogden, Arruda-Boyce, Gent, Blatz-Ko, Ogden Foam, Extended Tube, Mullins Effect
Plastic properties Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening
Thermal conductivity properties Thermal Conductivity Isotropic, Thermal Conductivity Orthotropic
Resistivity properties Isotropic Resistivity, Orthotropic Resistivity
Electric permittivity properties Isotropic Relative Permittivity, Orthotropic Relative Permittivity
Dielectric loss properties Isotropic Dielectric Loss Tangent, Orthotropic Dielectric Loss Tangent
Magnetic permeability properties Isotropic Relative Permeability, Orthotropic Relative Permeability
Magnetic loss properties Isotropic Relative Imaginary Permeability, Isotropic Magnetic Loss Tangent, Orthotropic Magnetic Loss Tangent
\ No newline at end of file + Mutually exclusive properties 1 - WelSim Documentation
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Mutually exclusive properties 1

Some properties are mutually exclusive of each other and require that only one property in the mutually exclusive set be unsuppressed. The addition or removing of the suppression for one of these properties automatically suppresses the other mutually exclusive properties.

For example, defining Isotropic Elasticity and Orthotropic Elasticity for the same material represents redundant elasticity behavior. Only one behavior can be active for the material. When such a conflict occurs, the property defined last is used and the previously defined, conflicting property is automatically suppressed.

The properties that are mutually exclusive are grouped in the following table.

Group Material Property
Elastic properties Isotropic Elasticity, Orthotropic Elasticity, Anisotropic Elasticity, Mooney-Rivlin, Neo-Hookean, Polynomial, Yeoh, Ogden, Arruda-Boyce, Gent, Blatz-Ko, Ogden Foam, Extended Tube, Mullins Effect
Plastic properties Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening
Thermal conductivity properties Thermal Conductivity Isotropic, Thermal Conductivity Orthotropic
Resistivity properties Isotropic Resistivity, Orthotropic Resistivity
Electric permittivity properties Isotropic Relative Permittivity, Orthotropic Relative Permittivity
Dielectric loss properties Isotropic Dielectric Loss Tangent, Orthotropic Dielectric Loss Tangent
Magnetic permeability properties Isotropic Relative Permeability, Orthotropic Relative Permeability
Magnetic loss properties Isotropic Relative Imaginary Permeability, Isotropic Magnetic Loss Tangent, Orthotropic Magnetic Loss Tangent
\ No newline at end of file diff --git a/mateditor/mat_io_openradioss/index.html b/mateditor/mat_io_openradioss/index.html index d2bfd18..cd4bd28 100644 --- a/mateditor/mat_io_openradioss/index.html +++ b/mateditor/mat_io_openradioss/index.html @@ -1 +1 @@ - OpenRadioss format - WelSim Documentation
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OpenRadioss format

The format of exported material scripts is based on the OpenRadioss version 2022, more details please refer to the OpenRadioss user reference manual.

The import of OpenRadioss scripts is not supported yet in MatEditor/WELSIM.

Supported OpenRadioss units

At present, MatEditor supports eight types of unit systems commonly used in engineering simulation, which are as follows.

  • Metric kg-m-s
  • Metric g-cm-s
  • Metrickg-mm-s
  • Metric tonne-mm-s
  • Metric decatonne-mm-s
  • Metric kg-um-s
  • US Customary lbm-ft-s
  • US Customary lbm-in-s
  • Metric g-cm-us

Supported OpenRadioss materials

Basic

  • Density
  • Linear Elasticity

Hyperelasticity and Viscoelasticity

  • LAW34 — Boltzmann
  • LAW35 — Maxwell-Kelvin-Voigt
  • LAW40 — Maxwell-Kelvin
  • LAW42 — Odgen ½/3
  • LAW92 — Arruda-Boyce
  • LAW94 — Yeoh ½/3
  • LAW100 — Polynomial, Neo-Hookean, Mooney-Rivlin2

Plasticity

  • LAW2 — Johnson-Cook
  • PLAS_ZERIL — Zerilli-Armstrng
  • LAW32 — Hill
  • LAW36 — Rate-Dependent Multilinear Hardening
  • LAW44 — Cowper-Symonds
  • LAW93 — Orthotropic Hill
  • LAW48 — Zhao
  • LAW49 — Steinberg-Guinan
  • LAW52 — Gurson
  • LAW57 — Barlet3
  • LAW78 — Yoshida-Uemori
  • LAW79 — Johnson-Holmquist
  • LAW84 — Swift-Voce
  • LAW103 — Hensel-Spittel
  • LAW110 — Vegter

Failure Models

  • ALTER — Glass Failure
  • BIQUD — BiQuadratic
  • COCKCROFT — Cockcroft
  • CONNECT-Connect
  • EMC — ExtendedMohr-Coulomb
  • ENERGY-Energy
  • FABRIC — Fabric
  • FLD — Forming Limit Diagram
  • GURSON — Gurson
  • HASHIN — Hashin
  • HC_DSSE — Ladeveze Delamination
  • JOHNSON-Johnson-Cook
  • MULLINS_OR — Mullins Effect
  • NXT — NXT
  • ORTHBIQUAD — Orthotropic Biquad
  • ORTHSTRAIN — Orthotropic Strain
  • PUCK — Puck
  • TBUTCHER — Tuler-Butcher
  • TENSSTRAIN — Tensile Strain
  • WILKINS — Wilkins
  • WIERZBICKI — Wierzbicki

Equation of State (EOS)

  • Compaction EOS
  • Gruneisen EOS
  • Ideal Gas EOS
  • Linear EOS
  • LSZK EOS
  • Murnaghan EOS
  • NASG EOS
  • Nobel-Abel EOS
  • Osborne EOS
  • Polynomial EOS
  • Puff EOS
  • Stiff-Gas EOS

Fluids

  • LAW06 - Kinematic Viscosity
  • ALE - ALE

More materials will be added upon user request.

\ No newline at end of file + OpenRadioss format - WelSim Documentation
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OpenRadioss format

The format of exported material scripts is based on the OpenRadioss version 2022, more details please refer to the OpenRadioss user reference manual.

The import of OpenRadioss scripts is not supported yet in MatEditor/WELSIM.

Supported OpenRadioss units

At present, MatEditor supports eight types of unit systems commonly used in engineering simulation, which are as follows.

  • Metric kg-m-s
  • Metric g-cm-s
  • Metrickg-mm-s
  • Metric tonne-mm-s
  • Metric decatonne-mm-s
  • Metric kg-um-s
  • US Customary lbm-ft-s
  • US Customary lbm-in-s
  • Metric g-cm-us

Supported OpenRadioss materials

Basic

  • Density
  • Linear Elasticity

Hyperelasticity and Viscoelasticity

  • LAW34 — Boltzmann
  • LAW35 — Maxwell-Kelvin-Voigt
  • LAW40 — Maxwell-Kelvin
  • LAW42 — Odgen ½/3
  • LAW92 — Arruda-Boyce
  • LAW94 — Yeoh ½/3
  • LAW100 — Polynomial, Neo-Hookean, Mooney-Rivlin2

Plasticity

  • LAW2 — Johnson-Cook
  • PLAS_ZERIL — Zerilli-Armstrng
  • LAW32 — Hill
  • LAW36 — Rate-Dependent Multilinear Hardening
  • LAW44 — Cowper-Symonds
  • LAW93 — Orthotropic Hill
  • LAW48 — Zhao
  • LAW49 — Steinberg-Guinan
  • LAW52 — Gurson
  • LAW57 — Barlet3
  • LAW78 — Yoshida-Uemori
  • LAW79 — Johnson-Holmquist
  • LAW84 — Swift-Voce
  • LAW103 — Hensel-Spittel
  • LAW110 — Vegter

Failure Models

  • ALTER — Glass Failure
  • BIQUD — BiQuadratic
  • COCKCROFT — Cockcroft
  • CONNECT-Connect
  • EMC — ExtendedMohr-Coulomb
  • ENERGY-Energy
  • FABRIC — Fabric
  • FLD — Forming Limit Diagram
  • GURSON — Gurson
  • HASHIN — Hashin
  • HC_DSSE — Ladeveze Delamination
  • JOHNSON-Johnson-Cook
  • MULLINS_OR — Mullins Effect
  • NXT — NXT
  • ORTHBIQUAD — Orthotropic Biquad
  • ORTHSTRAIN — Orthotropic Strain
  • PUCK — Puck
  • TBUTCHER — Tuler-Butcher
  • TENSSTRAIN — Tensile Strain
  • WILKINS — Wilkins
  • WIERZBICKI — Wierzbicki

Equation of State (EOS)

  • Compaction EOS
  • Gruneisen EOS
  • Ideal Gas EOS
  • Linear EOS
  • LSZK EOS
  • Murnaghan EOS
  • NASG EOS
  • Nobel-Abel EOS
  • Osborne EOS
  • Polynomial EOS
  • Puff EOS
  • Stiff-Gas EOS

Fluids

  • LAW06 - Kinematic Viscosity
  • ALE - ALE

More materials will be added upon user request.

\ No newline at end of file diff --git a/mateditor/mat_mutually_exclusive/index.html b/mateditor/mat_mutually_exclusive/index.html index ad7d2a6..59a91b5 100755 --- a/mateditor/mat_mutually_exclusive/index.html +++ b/mateditor/mat_mutually_exclusive/index.html @@ -1 +1 @@ - Mutually exclusive properties - WelSim Documentation
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Mutually exclusive properties

Some properties are mutually exclusive of each other and require that only one property in the mutually exclusive set be unsuppressed. The addition or removing of the suppression for one of these properties automatically suppresses the other mutually exclusive properties.

For example, defining Isotropic Elasticity and Orthotropic Elasticity for the same material represents redundant elasticity behavior. Only one behavior can be active for the material. When such a conflict occurs, the property defined last is used and the previously defined, conflicting property is automatically suppressed.

The properties that are mutually exclusive are grouped in the following table.

Group Material Property
Elastic properties Isotropic Elasticity, Orthotropic Elasticity, Anisotropic Elasticity, Mooney-Rivlin, Neo-Hookean, Polynomial, Yeoh, Ogden, Arruda-Boyce, Gent, Blatz-Ko, Ogden Foam, Extended Tube, Mullins Effect
Plastic properties Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening
Thermal conductivity properties Thermal Conductivity Isotropic, Thermal Conductivity Orthotropic
Resistivity properties Isotropic Resistivity, Orthotropic Resistivity
Electric permittivity properties Isotropic Relative Permittivity, Orthotropic Relative Permittivity
Dielectric loss properties Isotropic Dielectric Loss Tangent, Orthotropic Dielectric Loss Tangent
Magnetic permeability properties Isotropic Relative Permeability, Orthotropic Relative Permeability
Magnetic loss properties Isotropic Relative Imaginary Permeability, Isotropic Magnetic Loss Tangent, Orthotropic Magnetic Loss Tangent
\ No newline at end of file + Mutually exclusive properties - WelSim Documentation
Skip to content

Mutually exclusive properties

Some properties are mutually exclusive of each other and require that only one property in the mutually exclusive set be unsuppressed. The addition or removing of the suppression for one of these properties automatically suppresses the other mutually exclusive properties.

For example, defining Isotropic Elasticity and Orthotropic Elasticity for the same material represents redundant elasticity behavior. Only one behavior can be active for the material. When such a conflict occurs, the property defined last is used and the previously defined, conflicting property is automatically suppressed.

The properties that are mutually exclusive are grouped in the following table.

Group Material Property
Elastic properties Isotropic Elasticity, Orthotropic Elasticity, Anisotropic Elasticity, Mooney-Rivlin, Neo-Hookean, Polynomial, Yeoh, Ogden, Arruda-Boyce, Gent, Blatz-Ko, Ogden Foam, Extended Tube, Mullins Effect
Plastic properties Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening
Thermal conductivity properties Thermal Conductivity Isotropic, Thermal Conductivity Orthotropic
Resistivity properties Isotropic Resistivity, Orthotropic Resistivity
Electric permittivity properties Isotropic Relative Permittivity, Orthotropic Relative Permittivity
Dielectric loss properties Isotropic Dielectric Loss Tangent, Orthotropic Dielectric Loss Tangent
Magnetic permeability properties Isotropic Relative Permeability, Orthotropic Relative Permeability
Magnetic loss properties Isotropic Relative Imaginary Permeability, Isotropic Magnetic Loss Tangent, Orthotropic Magnetic Loss Tangent
\ No newline at end of file diff --git a/mateditor/mat_overview/index.html b/mateditor/mat_overview/index.html index 1ec17e7..589ef97 100644 --- a/mateditor/mat_overview/index.html +++ b/mateditor/mat_overview/index.html @@ -1,5 +1,5 @@ - Overview - WelSim Documentation
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Overview

Material Module serves as a database for material properties used in analysis projects. The module not only provides a material library but allow you to create a material using the given properties. The properties view of a Material object is the primary user interface designed to let you create, save, and retrieve material models. The well-defined material object can be saved and used in the subsequent projects.

finite_element_analysis_material_suppression

Note

The WELSIM Material module and MatEditor share the same features. For the completed and latest content, you can refer to the manual of MatEditor.

Graphical user interface

The ease-of-use Material Module contains the following graphical user interface components:

  • Toolbox: provdies two options (Library and Build tabs) for you to edit material data.
  • Library outline pane: lists predefined materials for you to quickly add material data.
  • Property outline pane: shows an outline of the contents of the togglable material properties. You can add a property data entry to the material by toggling on the property entry or remove property by toggling off the property entry.
  • Properties view pane: displays all properties that are going to be added to the Material Object. You can tune the property values at this pane.
  • Table pane: allows you to define and review tabular data for material properies.
  • Chart pane: displays the property tabular data in vivid.

Predefined materials

WELSIM also provide predefined materials, which covers most of commonly used materials. Users can choose these materials and apply to the successive finite element analysis.

Category Materials
General Materials Structural Steel, Stainless Steel, Aluminum Alloy, Concrete, Copper Alloy, Gray Cast Iron, Titanium Alloy
Nonlinear Materials Aluminum Alloy NL, Concrete NL, Copper Alloy NL, Stainless Steel NL, Structural Steel NL, Titanium Alloy NL
Hyperelastic Materials Elastomer Mooney-Rivlin, Elastomer Neo-Hookean, Elastomer Ogden, Elastomer Yeoh, Neoprene Rubber
Thermal Materials Brass, Bronze, Copper, Diamond, Ferrite, Nodular Cast Iron, Solder, Teflon, Tungsten, Wood
Electromagnetic Materials SS416, Supermendure
Other Materials Water Liquid, Argon, Ash

Material properties

The supported material properties are listed in the table below.

Category Materials
Basic Density, Isotropic Thermal Expansion, Isotropic Instantaneous Thermal Expansion, Orthotropic Thermal Expansion, Orthotropic Instantaneous Thermal Expansion, Constant Damping Coefficient
Linear Elastic Isotropic Elasticity, Orthotropic Elasticity, Viscoelastic
Hyperelastic Test Data Uniaxial Test Data, Biaxial Test Data, Shear Test Data, Volumetric Test Data, SimpleShear Test Data, Uniaxial Tension Test Data, Uniaxial Compression Test Data
Hyperelastic Arruda-Boyce, Blatz-Ko, Gent, Mooney-Rivlin 2, Mooney-Rivlin 3, Mooney-Rivlin 5, Mooney-Rivlin 9, Neo-Hookean, Ogden 1st Order, Ogden 2nd Order, Ogden 3rd Order, Polynomial 1st Order, Polynomial 2nd Order, Polynomial 3rd Order, Yeoh 1st Order, Yeoh 2nd Order, Yeoh 3rd Order
Plasticity Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening, Anand Viscoplasticity
Creep Strain Hardening, Time Hardening, Generalized Exponential, Generalized Graham, Generalized Blackburn, Modified Time Hardening, Modified Strain Hardening, Generalized Garofalo, Exponential Form, Norton, Combined Time Hardening, Rational Polynomial, Generalized Time Hardening
Visco-elastic Prony Shear Relaxation, Prony Volumetric Relaxation
Other Mechanical Strain Life Parameters, Compressive Ultimate Strength, Compressive Yield Strength, LaRc0304 Constants, Orthotropic Strain Limits, Orthotropic Stress Limits, Puck Constants, Tensile Ultimate Strength, Tensile Yield Strength, Tsai-Wu Constants, Shape Memory Effect, Drucker-Prager Strength Piecewise, Drucker-Prager Strength Linear, Ideal Gas EOS, Crushable Foam, Nonlinear Elastic Model Damage, Plakin Special Hardening, Tensile Pressure Failure, Crack Softening Failure
Thermal Enthalpy, Isotropic Thermal Conductivity, Orthotropic Thermal Conductivity, Specific Heat
Electromagnetics B-H Curve, Isotropic Relative Permeability, Orthotropic Relative Permeability, Isotropic Resistivity, Orthotropic Resistivity

Working with material data

Exporting

You can export the complete material data to an external XML file. The following format is supported for export:

  • XML in WELSIM Material (MatML 3.1) schema.
  • JSON in WELSIM Material schema.
  • OpenRadioss input script
WelSim/docs

Overview

Material Module serves as a database for material properties used in analysis projects. The module not only provides a material library but allow you to create a material using the given properties. The properties view of a Material object is the primary user interface designed to let you create, save, and retrieve material models. The well-defined material object can be saved and used in the subsequent projects.

finite_element_analysis_material_suppression

Note

The WELSIM Material module and MatEditor share the same features. For the completed and latest content, you can refer to the manual of MatEditor.

Graphical user interface

The ease-of-use Material Module contains the following graphical user interface components:

  • Toolbox: provdies two options (Library and Build tabs) for you to edit material data.
  • Library outline pane: lists predefined materials for you to quickly add material data.
  • Property outline pane: shows an outline of the contents of the togglable material properties. You can add a property data entry to the material by toggling on the property entry or remove property by toggling off the property entry.
  • Properties view pane: displays all properties that are going to be added to the Material Object. You can tune the property values at this pane.
  • Table pane: allows you to define and review tabular data for material properies.
  • Chart pane: displays the property tabular data in vivid.

Predefined materials

WELSIM also provide predefined materials, which covers most of commonly used materials. Users can choose these materials and apply to the successive finite element analysis.

Category Materials
General Materials Structural Steel, Stainless Steel, Aluminum Alloy, Concrete, Copper Alloy, Gray Cast Iron, Titanium Alloy
Nonlinear Materials Aluminum Alloy NL, Concrete NL, Copper Alloy NL, Stainless Steel NL, Structural Steel NL, Titanium Alloy NL
Hyperelastic Materials Elastomer Mooney-Rivlin, Elastomer Neo-Hookean, Elastomer Ogden, Elastomer Yeoh, Neoprene Rubber
Thermal Materials Brass, Bronze, Copper, Diamond, Ferrite, Nodular Cast Iron, Solder, Teflon, Tungsten, Wood
Electromagnetic Materials SS416, Supermendure
Other Materials Water Liquid, Argon, Ash

Material properties

The supported material properties are listed in the table below.

Category Materials
Basic Density, Isotropic Thermal Expansion, Isotropic Instantaneous Thermal Expansion, Orthotropic Thermal Expansion, Orthotropic Instantaneous Thermal Expansion, Constant Damping Coefficient
Linear Elastic Isotropic Elasticity, Orthotropic Elasticity, Viscoelastic
Hyperelastic Test Data Uniaxial Test Data, Biaxial Test Data, Shear Test Data, Volumetric Test Data, SimpleShear Test Data, Uniaxial Tension Test Data, Uniaxial Compression Test Data
Hyperelastic Arruda-Boyce, Blatz-Ko, Gent, Mooney-Rivlin 2, Mooney-Rivlin 3, Mooney-Rivlin 5, Mooney-Rivlin 9, Neo-Hookean, Ogden 1st Order, Ogden 2nd Order, Ogden 3rd Order, Polynomial 1st Order, Polynomial 2nd Order, Polynomial 3rd Order, Yeoh 1st Order, Yeoh 2nd Order, Yeoh 3rd Order
Plasticity Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening, Anand Viscoplasticity
Creep Strain Hardening, Time Hardening, Generalized Exponential, Generalized Graham, Generalized Blackburn, Modified Time Hardening, Modified Strain Hardening, Generalized Garofalo, Exponential Form, Norton, Combined Time Hardening, Rational Polynomial, Generalized Time Hardening
Visco-elastic Prony Shear Relaxation, Prony Volumetric Relaxation
Other Mechanical Strain Life Parameters, Compressive Ultimate Strength, Compressive Yield Strength, LaRc0304 Constants, Orthotropic Strain Limits, Orthotropic Stress Limits, Puck Constants, Tensile Ultimate Strength, Tensile Yield Strength, Tsai-Wu Constants, Shape Memory Effect, Drucker-Prager Strength Piecewise, Drucker-Prager Strength Linear, Ideal Gas EOS, Crushable Foam, Nonlinear Elastic Model Damage, Plakin Special Hardening, Tensile Pressure Failure, Crack Softening Failure
Thermal Enthalpy, Isotropic Thermal Conductivity, Orthotropic Thermal Conductivity, Specific Heat
Electromagnetics B-H Curve, Isotropic Relative Permeability, Orthotropic Relative Permeability, Isotropic Resistivity, Orthotropic Resistivity

Working with material data

Exporting

You can export the complete material data to an external XML file. The following format is supported for export:

  • XML in WELSIM Material (MatML 3.1) schema.
  • JSON in WELSIM Material schema.
  • OpenRadioss input script
\ No newline at end of file +* Right-click the **Material Project** and select the **Export Materials** item from the context menu. -->
\ No newline at end of file diff --git a/mateditor/mat_properties/index.html b/mateditor/mat_properties/index.html index 1d8ff1f..50ad15a 100755 --- a/mateditor/mat_properties/index.html +++ b/mateditor/mat_properties/index.html @@ -1 +1 @@ - Libraries and properties - WelSim Documentation
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Libraries and properties

Definitions

We make use of the following terminology for materials:

Term Definition
Material An identifier that contains a property or multiple properties
Property An identifier the singular information (for example, Density)
Property data An identifier for tabular data (for example, Thermal Conductivity)

Sample libraries

MatEditor provides sample material data categorized into several libraries. However, you still need to validate that the data is consistent with the material you are using in your analysis.

The following materials are included:

  • General Materials: A library of general use materials and consists mostly of metals.
  • General Nonlinear Materials: A library of general use nonlinear materials for performing nonlinear analyses.
  • Hyperelastic Materials: A library of materials containing test data which can be used to represent hyperelastic materails. The data doesn't correspond to any particular material.
  • Thermal Materials: A library of materials containing thermal data.
  • Electromagnetic Materials: A library of materials containing electromagnetic data, specific for use in an electromagnetic analysis.

Supported properties

The supported material properties are listed by category here.

Basics

  • Density
  • Isotropic Thermal Expansion
  • Isotropic Instantaneous Thermal Expansion
  • Orthotropic Thermal Expansion
  • Orthotopic Instantaneous Thermal Expansion
  • Constant Damping Coefficient

Linear Elastic

  • Isotropic Elasticity
  • Orthotropic Elasticity
  • Viscoelastic

Hyperelastic Test Data

  • Uniaxial Test Data
  • Biaxial Test Data
  • Shear Test Data
  • Volumetric Test Data
  • Simple Shear Test Data
  • Uniaxial Tension Test Data
  • Uniaxial Compression Test Data

Hyperelastic

  • Arruda-Boyce
  • Blatz-Ko
  • Gent
  • Mooney-Rivlin 2
  • Mooney-Rivlin 3
  • Mooney-Rivlin 5
  • Mooney-Rivlin 9
  • Neo-Hookean
  • Ogden 1st Order
  • Ogden 2nd Order
  • Ogden 3rd Order
  • Polynomial 1st Order
  • Polynomial 2nd Order
  • Polynomial 3rd Order
  • Yeoh 1st Order
  • Yeoh 2nd Order
  • Yeoh 3rd Order

Plasticity

  • Bilinear Isotropic Hardening
  • Multilinear Isotropic Hardening
  • Bilinear Kinematic Hardening
  • Multilinear Kinematic Hardening
  • Anand Viscoplasticity

Creep

  • Strain Hardening
  • Time Hardening
  • Generalized Exponential
  • Generalized Graham
  • Generalized Blackburn
  • Modified Time Hardening
  • Modified Strain Hardening
  • Generalized Garofalo
  • Exponential Form
  • Norton
  • Combined Time Hardening
  • Rational Polynomial
  • Generalized Time Hardening

Visco-elastic

  • Prony Shear Relaxation
  • Prony Volumetric Relaxation

Thermal

  • Enthalpy
  • Isotropic Thermal Conductivity
  • Orthotropic Thermal Conductivity
  • Specific Heat

Electromagnetics

  • B-H Curve
  • Isotropic Relative Permeability
  • Orthotropic Relative Permeability
  • Isotropic Resistivity
  • Orthotropic Resistivity
  • Isotropic Relative Permittivity
  • Orthotropic Relative Permittivity
  • Isotropic Dielectric Loss Tangent
  • Isotropic Magnetic Loss Tangent
  • Isotropic Relative Imaginary Permeability
  • Orthotropic Dielectric Loss Tangent
  • Orthotropic Magnetic Loss Tangent
\ No newline at end of file + Libraries and properties - WelSim Documentation
Skip to content

Libraries and properties

Definitions

We make use of the following terminology for materials:

Term Definition
Material An identifier that contains a property or multiple properties
Property An identifier the singular information (for example, Density)
Property data An identifier for tabular data (for example, Thermal Conductivity)

Sample libraries

MatEditor provides sample material data categorized into several libraries. However, you still need to validate that the data is consistent with the material you are using in your analysis.

The following materials are included:

  • General Materials: A library of general use materials and consists mostly of metals.
  • General Nonlinear Materials: A library of general use nonlinear materials for performing nonlinear analyses.
  • Hyperelastic Materials: A library of materials containing test data which can be used to represent hyperelastic materails. The data doesn't correspond to any particular material.
  • Thermal Materials: A library of materials containing thermal data.
  • Electromagnetic Materials: A library of materials containing electromagnetic data, specific for use in an electromagnetic analysis.

Supported properties

The supported material properties are listed by category here.

Basics

  • Density
  • Isotropic Thermal Expansion
  • Isotropic Instantaneous Thermal Expansion
  • Orthotropic Thermal Expansion
  • Orthotopic Instantaneous Thermal Expansion
  • Constant Damping Coefficient

Linear Elastic

  • Isotropic Elasticity
  • Orthotropic Elasticity
  • Viscoelastic

Hyperelastic Test Data

  • Uniaxial Test Data
  • Biaxial Test Data
  • Shear Test Data
  • Volumetric Test Data
  • Simple Shear Test Data
  • Uniaxial Tension Test Data
  • Uniaxial Compression Test Data

Hyperelastic

  • Arruda-Boyce
  • Blatz-Ko
  • Gent
  • Mooney-Rivlin 2
  • Mooney-Rivlin 3
  • Mooney-Rivlin 5
  • Mooney-Rivlin 9
  • Neo-Hookean
  • Ogden 1st Order
  • Ogden 2nd Order
  • Ogden 3rd Order
  • Polynomial 1st Order
  • Polynomial 2nd Order
  • Polynomial 3rd Order
  • Yeoh 1st Order
  • Yeoh 2nd Order
  • Yeoh 3rd Order

Plasticity

  • Bilinear Isotropic Hardening
  • Multilinear Isotropic Hardening
  • Bilinear Kinematic Hardening
  • Multilinear Kinematic Hardening
  • Anand Viscoplasticity

Creep

  • Strain Hardening
  • Time Hardening
  • Generalized Exponential
  • Generalized Graham
  • Generalized Blackburn
  • Modified Time Hardening
  • Modified Strain Hardening
  • Generalized Garofalo
  • Exponential Form
  • Norton
  • Combined Time Hardening
  • Rational Polynomial
  • Generalized Time Hardening

Visco-elastic

  • Prony Shear Relaxation
  • Prony Volumetric Relaxation

Thermal

  • Enthalpy
  • Isotropic Thermal Conductivity
  • Orthotropic Thermal Conductivity
  • Specific Heat

Electromagnetics

  • B-H Curve
  • Isotropic Relative Permeability
  • Orthotropic Relative Permeability
  • Isotropic Resistivity
  • Orthotropic Resistivity
  • Isotropic Relative Permittivity
  • Orthotropic Relative Permittivity
  • Isotropic Dielectric Loss Tangent
  • Isotropic Magnetic Loss Tangent
  • Isotropic Relative Imaginary Permeability
  • Orthotropic Dielectric Loss Tangent
  • Orthotropic Magnetic Loss Tangent
\ No newline at end of file diff --git a/mateditor/mat_table_data/index.html b/mateditor/mat_table_data/index.html index 64830fd..3e2e0d1 100755 --- a/mateditor/mat_table_data/index.html +++ b/mateditor/mat_table_data/index.html @@ -1 +1 @@ - Import/Export tabular data - WelSim Documentation
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Import/Export Tabular Data

Import and export tabular data is supported in MatEditor, CurveFitter and WELSIM, this feature facilitates you to input and output massive tabular data with no need to manually input and output data, specifically test data for the hyperelastic and magnetic core loss materials.

The import and export buttons are allocated on the top of the Tabular Data Window, as shown in the figure below:
finite_element_analysis_mateditor_test_data_in_plain_text

Default file format

The default file format used in MatEditor/CurveFitter/WELSIM contains a header block that gives the quantity name, unit, and dependency. This header data allows you to define the units from the external file. The latest version supports both plain text and Excel formats. Both formats share a similar schema. The details of each format are discussed below.

  • The comment line starts with ### symbol and will be ignored by the reader.
  • The first row lists the quantity names.
  • The second row shows the units. For the dimensionless quantity, dash symbol - is used.
  • The third row gives the dependency of the quantity, which could be independent, dependent, subindependent, or subdependent.
  • The kernel test data start from the fourth row.

Note

The number of columns of import data must match the pre-defined headers.

The plain text data file looks like below:
finite_element_analysis_mateditor_test_data_in_plain_text

An example of Excel file is shown below:
finite_element_analysis_mateditor_test_data_in_excel

Format with no header data

MatEditor/CurveFitter/WELSIM also supports the external data that contains no header information (pure value data). You need to ensure unit consistency when importing such data files. Both plain text and Excel file formats are supported.

The plain text file with no header dat looks like below:
finite_element_analysis_mateditor_test_data_in_excel

Note

Due to the lack of the header information, the units of the imported data is determined by the current units of the Table. In addition, the pivoting column may not be set if the file does not contain such data. The number of columns must be identicial to that of the pre-defined table quantities.

Examples

The examples of the import/export tabular data are available at our GitHub page.

\ No newline at end of file + Import/Export tabular data - WelSim Documentation
Skip to content

Import/Export Tabular Data

Import and export tabular data is supported in MatEditor, CurveFitter and WELSIM, this feature facilitates you to input and output massive tabular data with no need to manually input and output data, specifically test data for the hyperelastic and magnetic core loss materials.

The import and export buttons are allocated on the top of the Tabular Data Window, as shown in the figure below:
finite_element_analysis_mateditor_test_data_in_plain_text

Default file format

The default file format used in MatEditor/CurveFitter/WELSIM contains a header block that gives the quantity name, unit, and dependency. This header data allows you to define the units from the external file. The latest version supports both plain text and Excel formats. Both formats share a similar schema. The details of each format are discussed below.

  • The comment line starts with ### symbol and will be ignored by the reader.
  • The first row lists the quantity names.
  • The second row shows the units. For the dimensionless quantity, dash symbol - is used.
  • The third row gives the dependency of the quantity, which could be independent, dependent, subindependent, or subdependent.
  • The kernel test data start from the fourth row.

Note

The number of columns of import data must match the pre-defined headers.

The plain text data file looks like below:
finite_element_analysis_mateditor_test_data_in_plain_text

An example of Excel file is shown below:
finite_element_analysis_mateditor_test_data_in_excel

Format with no header data

MatEditor/CurveFitter/WELSIM also supports the external data that contains no header information (pure value data). You need to ensure unit consistency when importing such data files. Both plain text and Excel file formats are supported.

The plain text file with no header dat looks like below:
finite_element_analysis_mateditor_test_data_in_excel

Note

Due to the lack of the header information, the units of the imported data is determined by the current units of the Table. In addition, the pivoting column may not be set if the file does not contain such data. The number of columns must be identicial to that of the pre-defined table quantities.

Examples

The examples of the import/export tabular data are available at our GitHub page.

\ No newline at end of file diff --git a/mateditor/mat_theory/index.html b/mateditor/mat_theory/index.html index 30f1ba3..729cbee 100644 --- a/mateditor/mat_theory/index.html +++ b/mateditor/mat_theory/index.html @@ -1 +1 @@ - Material Theory - WelSim Documentation
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Material Theory

Some properties are mutually exclusive of each other and require that only one property in the mutually exclusive set be unsuppressed. The addition or removing of the suppression for one of these properties automatically suppresses the other mutually exclusive properties.

For example, defining Isotropic Elasticity and Orthotropic Elasticity for the same material represents redundant elasticity behavior. Only one behavior can be active for the material. When such a conflict occurs, the property defined last is used and the previously defined, conflicting property is automatically suppressed.

The properties that are mutually exclusive are grouped in the following table.

Group Material Property
Elastic properties Isotropic Elasticity, Orthotropic Elasticity, Anisotropic Elasticity, Mooney-Rivlin, Neo-Hookean, Polynomial, Yeoh, Ogden, Arruda-Boyce, Gent, Blatz-Ko, Ogden Foam, Extended Tube, Mullins Effect
Plastic properties Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening
Thermal conductivity properties Thermal Conductivity Isotropic, Thermal Conductivity Orthotropic
Resistivity properties Isotropic Resistivity, Orthotropic Resistivity
Electric permittivity properties Isotropic Relative Permittivity, Orthotropic Relative Permittivity
Dielectric loss properties Isotropic Dielectric Loss Tangent, Orthotropic Dielectric Loss Tangent
Magnetic permeability properties Isotropic Relative Permeability, Orthotropic Relative Permeability
Magnetic loss properties Isotropic Relative Imaginary Permeability, Isotropic Magnetic Loss Tangent, Orthotropic Magnetic Loss Tangent
\ No newline at end of file + Material Theory - WelSim Documentation
Skip to content

Material Theory

Some properties are mutually exclusive of each other and require that only one property in the mutually exclusive set be unsuppressed. The addition or removing of the suppression for one of these properties automatically suppresses the other mutually exclusive properties.

For example, defining Isotropic Elasticity and Orthotropic Elasticity for the same material represents redundant elasticity behavior. Only one behavior can be active for the material. When such a conflict occurs, the property defined last is used and the previously defined, conflicting property is automatically suppressed.

The properties that are mutually exclusive are grouped in the following table.

Group Material Property
Elastic properties Isotropic Elasticity, Orthotropic Elasticity, Anisotropic Elasticity, Mooney-Rivlin, Neo-Hookean, Polynomial, Yeoh, Ogden, Arruda-Boyce, Gent, Blatz-Ko, Ogden Foam, Extended Tube, Mullins Effect
Plastic properties Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening
Thermal conductivity properties Thermal Conductivity Isotropic, Thermal Conductivity Orthotropic
Resistivity properties Isotropic Resistivity, Orthotropic Resistivity
Electric permittivity properties Isotropic Relative Permittivity, Orthotropic Relative Permittivity
Dielectric loss properties Isotropic Dielectric Loss Tangent, Orthotropic Dielectric Loss Tangent
Magnetic permeability properties Isotropic Relative Permeability, Orthotropic Relative Permeability
Magnetic loss properties Isotropic Relative Imaginary Permeability, Isotropic Magnetic Loss Tangent, Orthotropic Magnetic Loss Tangent
\ No newline at end of file diff --git a/mateditor/mat_theory_eos/index.html b/mateditor/mat_theory_eos/index.html index e531332..fea81f6 100644 --- a/mateditor/mat_theory_eos/index.html +++ b/mateditor/mat_theory_eos/index.html @@ -1 +1 @@ - Equations of state (EOS) - WelSim Documentation
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Equations of State (EOS)

MatEditor allows you to define the EOS material properties. The supported properties are listed below.

  • Compaction
  • Gruneisen
  • Ideal Gas
  • Linear
  • LSZK (Landau-Stanyukovich-Zeldovich-Kompaneets)
  • Murnaghan
  • NASG (Noble-Abel Stiffened Gas)
  • Noble-Abel
  • Osborne
  • Polynomial
  • Puff
  • Stiff Gas
  • Tillotson

Compaction EOS

Plastic compaction is along path defined by equation:

\[ p=C_0 + C_1 \mu +C_2 \mu^2 + C_3 \mu^3 \]

where \(P\) is the hydrodynamic pressure in material. \(\mu\) is the volumetric strain that can be obtained by \(\mu=\dfrac{\rho}{\rho_0}-1\).

Unloading bulk modulus \(B\) is the bulk modules for the unloading process.

Pressure Shift \(P_{sh}\) is used to model the relative pressure formulation.

Gruneisen EOS

In the Gruneisen EOS model, the hydrodynamic pressure is described by the following equations:

For the compressed material, \(\mu\)>0

\[ p = \dfrac{\rho_0C^2\mu[1+(1-\dfrac{\gamma_0}{2})\mu-\dfrac{\alpha}{2}\mu^2]}{[1-(S_1-1)\mu-S_2\dfrac{\mu^2}{\mu+1}-S_3\dfrac{\mu^3}{(\mu+1)^2}]^2} + (\gamma_0+\alpha\mu)E \]

For the expanding material, \(\mu\)<0 $$ p = \rho_0C^2\mu + (\gamma_0+\alpha\mu)E $$

where the \(\mu=\dfrac{\rho}{\rho_0}-1\).

Ideal Gas EOS

The pressure in the Ideal Gas model can be represented by the function:

\[ p = (\gamma-1)(1+\mu)E \]

where unitless parameter \(\gamma\) is determined by the heat capacity \(C_v\) and \(C_p\), \(\gamma=\dfrac{C_p}{C_v}\). The initial heat capacity \(C_v\) is calculated from the initial conditions:

\[ C_v=\dfrac{E_0}{\rho_0T_0} \]

Linear EOS

The pressure in linear EOS is given by

\[ p = p_0 + B\mu \]

where \(p_0\) i initial pressure and \(B\) is the initial bulk modulus. Linear EOS is a simplified form of polynomial EOS:

\[ p=C_0+C_1\mu + C_2\mu + C_3\mu + (C_4+C_5)E_0 \]

where, \(C_0=p_0\), \(C_1=B\), \(C_2=C_3 = C_4 = C_5 = 0\).

Bulk modulus is usually treated as \(B=\rho_0c_0^2\), where \(c_0\) is the initial sound speed.

LSZK (Landau-Stanyukovich-Zeldovich-Kompaneets) EOS

This EOS model is the short for the Landau-Stanyukovich-Zeldovich-Kompaneets EOS, used for the detonation modeling. The pressure is given by

\[ p = (\gamma-1)\rho e + a \rho^b \]

where \(\rho\) is the mass density, \(e\) is the internal energy density by mass, \(b\) is the material parameter.

Murnaghan EOS

This EOS is also known as Tait EOS. The pressure is defined by

\[ p = \dfrac{K_0}{K_1}[(\dfrac{V}{V_0})^{-K_1}-1] \]

where \(K_0\), \(K_1\) are material parameters, \(V\) is the volume.

This model is also expressed in terms of the compressibility \(\mu\):

\[ p = p_0 + \dfrac{K_0}{K_1}[(1+\mu)^{K_1}-1] \]

Note

Murnaghan EOS is independent to the energy.

NASG (Noble-Abel Stiffened Gas) EOS

The pressure can be computing by

\[ p = \dfrac{(\gamma-1)(1+\mu)(E-\rho_0q)}{1-b\rho_0(1+\mu)} - \gamma p_{\infty} \]

where \(p_{\infty}\) is the stiffness parameter.

Noble-Abel EOS

This EOS can apply to dense gases at high pressure, as the volume occupied by the moledules is no longer negligible.

\[ p = \dfrac{(\gamma-1)(1+\mu)E}{1-b\rho_0(1+\mu)} \]

where \(\gamma=\dfrac{C_p}{C_v}\)

Note

Covolume parameter b is usually in the range between [0.9e-3, 1.1e-3] \(m^3/kg\).

Osborne EOS

This EOS is also called quadratic EOS.

$$ p = \dfrac{A_1\mu+A_2\mu |\mu| + (B_0+B_1\mu+B_2\mu^2)E + (C_0 + C_1\mu)E^2 }{E+D_0} $$ where \(E\) is the internal energy by initial volume.

Polynomial EOS

The pressure for the linear polynomial EOS can be calculated by

\[ p=C_0+C_1\mu + C_2\mu + C_3\mu + (C_4+C_5)E \]

where \(E\) is the internal energy density by volume.

Note

For the expanding status (\(\mu\)<0), the term \(C_2\mu^2\)=0.

Puff EOS

This EOS model describes pressure accroding to the compressibility \(\mu\) and sublimation energy density by volume \(E_s\).

When \(\mu\geq\) 0:

\[ p = (C_1\mu+C_2\mu^2+C_3\mu^3)(1-\dfrac{\gamma\mu}{2})+\gamma(1+\mu)E \]

when \(\mu\)<0 and \(E\geq E_s\):

\[ p = (T_1\mu+T_2\mu^2)(1-\dfrac{\gamma\mu}{2})+\gamma(1+\mu)E \]

when \(\mu\)<0 and \(E<E_s\):

\[ p = \eta[H+(\gamma_0-H)\sqrt{\eta}][E-E_s(1-exp(\dfrac{N(\eta-1)}{\eta^2}))] \]

with \(N=\dfrac{C_1\eta}{\gamma_0E_s}\).

Stiffened Gas EOS

This EOS was originally designed to simulate water for underwater explosions.

The pressure can be calculated by $$ p = (\gamma-1)(1+\mu)E - \gamma p_{\star} $$

where \(E=\dfrac{E_{int}}{V_0}\), \(\mu=\dfrac{\rho}{\rho_0}-1\). The additional pressure term \(p^{\star}\) is introduced here.

This EOS can be derived from the Polynomial EOS: $$ p=C_0+C_1\mu + C_2\mu + C_3\mu + (C_4+C_5)E $$ when \(C_0 = -\gamma p^{\star}\), \(C_1=C_2=C3=0\), \(C_4=C_5=\gamma-1\), \(E_0=\dfrac{P_0-C_0}{C_4}\).

Tillotson EOS

The pressure is defined by

$$ p = C_1\mu + C_2\mu^2 +(a+\dfrac{b}{\omega})\eta E $$ with \(\omega=1+\dfrac{E}{E_r}\eta^2\) for the region \(\mu \geq\) 0.

$$ p = C_1\mu+(a+\dfrac{b}{\omega})\eta E $$ for the region \(\mu<0\), \(\dfrac{V}{V_0}<V_s\), and \(E<E_s\).

and $$ p = C_1 e^{\beta x} e^{-\alpha x^2}\mu + (a + \dfrac{be^{-\alpha x^2}}{\omega}) \eta E $$

\ No newline at end of file + Equations of state (EOS) - WelSim Documentation
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Equations of State (EOS)

MatEditor allows you to define the EOS material properties. The supported properties are listed below.

  • Compaction
  • Gruneisen
  • Ideal Gas
  • Linear
  • LSZK (Landau-Stanyukovich-Zeldovich-Kompaneets)
  • Murnaghan
  • NASG (Noble-Abel Stiffened Gas)
  • Noble-Abel
  • Osborne
  • Polynomial
  • Puff
  • Stiff Gas
  • Tillotson

Compaction EOS

Plastic compaction is along path defined by equation:

\[ p=C_0 + C_1 \mu +C_2 \mu^2 + C_3 \mu^3 \]

where \(P\) is the hydrodynamic pressure in material. \(\mu\) is the volumetric strain that can be obtained by \(\mu=\dfrac{\rho}{\rho_0}-1\).

Unloading bulk modulus \(B\) is the bulk modules for the unloading process.

Pressure Shift \(P_{sh}\) is used to model the relative pressure formulation.

Gruneisen EOS

In the Gruneisen EOS model, the hydrodynamic pressure is described by the following equations:

For the compressed material, \(\mu\)>0

\[ p = \dfrac{\rho_0C^2\mu[1+(1-\dfrac{\gamma_0}{2})\mu-\dfrac{\alpha}{2}\mu^2]}{[1-(S_1-1)\mu-S_2\dfrac{\mu^2}{\mu+1}-S_3\dfrac{\mu^3}{(\mu+1)^2}]^2} + (\gamma_0+\alpha\mu)E \]

For the expanding material, \(\mu\)<0 $$ p = \rho_0C^2\mu + (\gamma_0+\alpha\mu)E $$

where the \(\mu=\dfrac{\rho}{\rho_0}-1\).

Ideal Gas EOS

The pressure in the Ideal Gas model can be represented by the function:

\[ p = (\gamma-1)(1+\mu)E \]

where unitless parameter \(\gamma\) is determined by the heat capacity \(C_v\) and \(C_p\), \(\gamma=\dfrac{C_p}{C_v}\). The initial heat capacity \(C_v\) is calculated from the initial conditions:

\[ C_v=\dfrac{E_0}{\rho_0T_0} \]

Linear EOS

The pressure in linear EOS is given by

\[ p = p_0 + B\mu \]

where \(p_0\) i initial pressure and \(B\) is the initial bulk modulus. Linear EOS is a simplified form of polynomial EOS:

\[ p=C_0+C_1\mu + C_2\mu + C_3\mu + (C_4+C_5)E_0 \]

where, \(C_0=p_0\), \(C_1=B\), \(C_2=C_3 = C_4 = C_5 = 0\).

Bulk modulus is usually treated as \(B=\rho_0c_0^2\), where \(c_0\) is the initial sound speed.

LSZK (Landau-Stanyukovich-Zeldovich-Kompaneets) EOS

This EOS model is the short for the Landau-Stanyukovich-Zeldovich-Kompaneets EOS, used for the detonation modeling. The pressure is given by

\[ p = (\gamma-1)\rho e + a \rho^b \]

where \(\rho\) is the mass density, \(e\) is the internal energy density by mass, \(b\) is the material parameter.

Murnaghan EOS

This EOS is also known as Tait EOS. The pressure is defined by

\[ p = \dfrac{K_0}{K_1}[(\dfrac{V}{V_0})^{-K_1}-1] \]

where \(K_0\), \(K_1\) are material parameters, \(V\) is the volume.

This model is also expressed in terms of the compressibility \(\mu\):

\[ p = p_0 + \dfrac{K_0}{K_1}[(1+\mu)^{K_1}-1] \]

Note

Murnaghan EOS is independent to the energy.

NASG (Noble-Abel Stiffened Gas) EOS

The pressure can be computing by

\[ p = \dfrac{(\gamma-1)(1+\mu)(E-\rho_0q)}{1-b\rho_0(1+\mu)} - \gamma p_{\infty} \]

where \(p_{\infty}\) is the stiffness parameter.

Noble-Abel EOS

This EOS can apply to dense gases at high pressure, as the volume occupied by the moledules is no longer negligible.

\[ p = \dfrac{(\gamma-1)(1+\mu)E}{1-b\rho_0(1+\mu)} \]

where \(\gamma=\dfrac{C_p}{C_v}\)

Note

Covolume parameter b is usually in the range between [0.9e-3, 1.1e-3] \(m^3/kg\).

Osborne EOS

This EOS is also called quadratic EOS.

$$ p = \dfrac{A_1\mu+A_2\mu |\mu| + (B_0+B_1\mu+B_2\mu^2)E + (C_0 + C_1\mu)E^2 }{E+D_0} $$ where \(E\) is the internal energy by initial volume.

Polynomial EOS

The pressure for the linear polynomial EOS can be calculated by

\[ p=C_0+C_1\mu + C_2\mu + C_3\mu + (C_4+C_5)E \]

where \(E\) is the internal energy density by volume.

Note

For the expanding status (\(\mu\)<0), the term \(C_2\mu^2\)=0.

Puff EOS

This EOS model describes pressure accroding to the compressibility \(\mu\) and sublimation energy density by volume \(E_s\).

When \(\mu\geq\) 0:

\[ p = (C_1\mu+C_2\mu^2+C_3\mu^3)(1-\dfrac{\gamma\mu}{2})+\gamma(1+\mu)E \]

when \(\mu\)<0 and \(E\geq E_s\):

\[ p = (T_1\mu+T_2\mu^2)(1-\dfrac{\gamma\mu}{2})+\gamma(1+\mu)E \]

when \(\mu\)<0 and \(E<E_s\):

\[ p = \eta[H+(\gamma_0-H)\sqrt{\eta}][E-E_s(1-exp(\dfrac{N(\eta-1)}{\eta^2}))] \]

with \(N=\dfrac{C_1\eta}{\gamma_0E_s}\).

Stiffened Gas EOS

This EOS was originally designed to simulate water for underwater explosions.

The pressure can be calculated by $$ p = (\gamma-1)(1+\mu)E - \gamma p_{\star} $$

where \(E=\dfrac{E_{int}}{V_0}\), \(\mu=\dfrac{\rho}{\rho_0}-1\). The additional pressure term \(p^{\star}\) is introduced here.

This EOS can be derived from the Polynomial EOS: $$ p=C_0+C_1\mu + C_2\mu + C_3\mu + (C_4+C_5)E $$ when \(C_0 = -\gamma p^{\star}\), \(C_1=C_2=C3=0\), \(C_4=C_5=\gamma-1\), \(E_0=\dfrac{P_0-C_0}{C_4}\).

Tillotson EOS

The pressure is defined by

$$ p = C_1\mu + C_2\mu^2 +(a+\dfrac{b}{\omega})\eta E $$ with \(\omega=1+\dfrac{E}{E_r}\eta^2\) for the region \(\mu \geq\) 0.

$$ p = C_1\mu+(a+\dfrac{b}{\omega})\eta E $$ for the region \(\mu<0\), \(\dfrac{V}{V_0}<V_s\), and \(E<E_s\).

and $$ p = C_1 e^{\beta x} e^{-\alpha x^2}\mu + (a + \dfrac{be^{-\alpha x^2}}{\omega}) \eta E $$

\ No newline at end of file diff --git a/mateditor/mat_theory_failure/index.html b/mateditor/mat_theory_failure/index.html index f2971f1..2cf61de 100644 --- a/mateditor/mat_theory_failure/index.html +++ b/mateditor/mat_theory_failure/index.html @@ -1 +1 @@ - Failure models - WelSim Documentation
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Failure Models

MatEditor allows you to define the failure material properties. The supported properties are listed below.

  • Glass
  • Bi-Quadratic
  • Cockcroft
  • Connect
  • Extended Mohr-Coulomb
  • Energy
  • Fabric
  • Forming Limit Diagram
  • Hashin
  • Hosford-Coulomb
  • Johnson-Cook
  • Ladeveze delamination
  • Mullins Effect
  • NXT
  • Orthotropic Bi-Quadratic
  • Orthotropic Strain
  • Puck
  • Tuler-Butcher
  • Tensile Strain
  • Wierzbicki
  • Wilkins

Bi-Quadratic

The failure strain is described by two parabolic functions that user input.

Cockcroft

A nonlinear stress-strain based failure criterion with linear damage accumulation.

\[ C_0 = \int _0 ^{\bar{\epsilon}_f} max(\sigma_1, 0) \cdot d\bar{\epsilon} \]

where \(\epsilon_1\) is the first principal tension stress, \(\bar{\epsilon}\) is the equivalent strain.

Extended Mohr-Coulomb

The failure criteria is calculated as:

\[ D = \sum \dfrac{\Delta \bar{\epsilon}_p}{\bar{\epsilon}_{p,fail}} \]

where effective failure strain is

\[ \bar{\epsilon}_{p,fail} = b \cdot (1+c)^{\frac{1}{n}} \cdot \{[\dfrac{1}{2}((f_1-f_2)^a + (f_2-f_3)^a + (f_1 - f_3)^a )]^{\frac{1}{a}} + c(2\eta+f_1+f_3) \}^{-\frac{1}{n}} \]

the coefficient b is computed as

\[ b = b_0[1+\gamma ln(\dfrac{\dot{\bar{\epsilon}}_p}{\dot{\bar{\epsilon}}_0})] \quad if\, \dot{\bar{\epsilon}}_p > \dot{\bar{\epsilon}}_0 \]

or

\[ b = b_0 \quad if\, \dot{\bar{\epsilon}}_p \le \dot{\bar{\epsilon}}_0 \]

Energy

The damage is defined as

\[ D = \dfrac{E-E_1}{E_2 - E_1} \]

where the energy density is the current internal energy of the element divided by the current element volume.

Fabric

The failure and damage is defined independently in each direction (\(i\)=1,2)

\[ D_i = \dfrac{\epsilon_i - \epsilon_{fi}}{\epsilon_{ri} - \epsilon_{fi}} \]

where \(\epsilon_i \ge \epsilon_{fi}\).

Hashin

This model can be used for the composite materials.

The damage factor is calculated as

\[ D = Max(F_1,F_2,F_3, F_4, F_5) \quad for\quad uni-directional\, lamina\, model \]
\[ D = Max(F_1,F_2,F_3, F_4, F_5, F_6, F_7) \quad for\quad fabric\, lamina\, model \]

For the uni-directional lamina model:

Tensile/shear fiber mode:

\[ F_1 = (\dfrac{\langle\sigma_{11}\rangle}{\sigma_1^t})^2 + (\dfrac{\sigma_{12}^2 + \sigma_{13}^2}{{\sigma_{12}^f}^2}) \]

Compression fiber mode:

\[ F_2 = (\dfrac{\langle \sigma_a \rangle}{ \sigma_1^c})^2 \]

with \(\sigma_{\alpha} = -\sigma_{11}+\langle -\dfrac{\sigma_{22}+\sigma_{33}}{2} \rangle\).

Crush mode:

\[ F_3 = (\dfrac{\langle p \rangle}{\sigma_c})^2 \]

with \(p=-\dfrac{\sigma_{11}+\sigma_{22}+\sigma_{33}}{3}\).

Failure matrix mode:

\[ F_4 = (\dfrac{\langle \sigma_{22} \rangle}{\sigma_2^t})^2 + (\dfrac{\sigma_{23}}{S_{23}})^2 + (\dfrac{\sigma_{12}}{S_{12}})^2 \]

Delamination mode:

\[ F_5 = S^2_{del}[(\dfrac{\langle \sigma_{33} \rangle}{\sigma^t_2})^2 + (\dfrac{\sigma_{23}}{\tilde{S}_{23}})^2 + (\dfrac{\sigma_{12}}{S_{12}})^2 ] \]

For the fabirc lamina model:

Tensile/shear fiber mode

\[ F_1 = (\dfrac{\langle\sigma_{11}\rangle}{\sigma_1^t})^2 + (\dfrac{\sigma_{12}^2 + \sigma_{13}^2}{{\sigma_{a}^f}^2}) \]
\[ F_2 = (\dfrac{\langle\sigma_{22}\rangle}{\sigma_2^t})^2 + (\dfrac{\sigma_{12}^2 + \sigma_{23}^2}{{\sigma_{b}^f}^2}) \]

Compression fiber mode:

\[ F_3 = (\dfrac{\langle \sigma_a \rangle}{ \sigma_1^c})^2 \]
\[ F_4 = (\dfrac{\langle \sigma_b \rangle}{ \sigma_2^c})^2 \]

Crush mode:

\[ F_5 = (\dfrac{\langle p \rangle}{\sigma_c})^2 \]

Shear failure matrix mode:

\[ F_6 = (\dfrac{\sigma_12}{\sigma_12^m})^2 \]

Matrix failure mode:

\[ F_7 = S^2_{del}[(\dfrac{\langle \sigma_{33} \rangle}{\sigma^t_3})^2 + (\dfrac{\sigma_{23}}{\tilde{S}_{23}})^2 + (\dfrac{\sigma_{12}}{S_{12}})^2 ] \]

Hosford-Coulomb

The failure strain is described y the Hosford-Coulomb function.

The damage is defined as

\[ D = \sum \dfrac{\Delta \bar{\epsilon}_p} {\bar{\epsilon}^{pr}_{HC}(\eta) } \]

where the strain is calcualted as

\[ \bar{\epsilon}^{pr}_{HC}(\eta, \theta) = b(1+c)^{\frac{1}{n_f}} \{[\dfrac{1}{2}((f_1-f_2)^a + (f_2-f_3)^a + (f_1-f_3)^a)]^{\frac{1}{a}} + c(a\eta + f_1 +f_2) \}^{\frac{1}{n_f}} \]

Johnson-Cook

The failure strain is calculated by the constutitive relation:

\[ \epsilon_f = [D_1+D_2exp(D_3\sigma^*)] [1+D_4 ln(\dot{\epsilon}^*)] (1 + D_5 T^*) \]

The damage factor is defined as

\[ D = \sum \dfrac{\Delta \epsilon_p}{\epsilon_f} \]

Ladeveze Delamination

This is the Ladeveze failure model for delamination (interlaminar fracture). The damage parameters are defined as

\[ Y_{d_3} = \dfrac{\partial E_D}{\partial d_3} \vert _{\sigma=cst}=\dfrac{1}{2} \dfrac{\langle\sigma_{33}\rangle^2}{K_3(1-d_3)^2} \quad Mode\,I \]
\[ Y_{d_2} = \dfrac{\partial E_D}{\partial d_2} \vert _{\sigma=cst}=\dfrac{1}{2} \dfrac{\langle\sigma_{32}\rangle^2}{K_2(1-d_2)^2} \quad Mode\,II \]
\[ Y_{d_1} = \dfrac{\partial E_D}{\partial d_1} \vert _{\sigma=cst}=\dfrac{1}{2} \dfrac{\langle\sigma_{31}\rangle^2}{K_1(1-d_1)^2} \quad Mode\,III \]

The damage value can be

\[ D = \dfrac{k}{a}[1- exp(-a\langle w(Y)-d\rangle)] \]

Mullins Effect

This failure model is used with the hyperelastic materials. The stress during the first loading process is equal to the undamaged stress. Upon unloading and reloading the strss is multiplied by a positive softening factor as

\[ \sigma = \eta dev(\sigma) - pI \]

where dev(\(\sigma\)) is the deviatoric part of the stress, \(p\) is the hydrostatic pressure. The damage factor \(\eta\) is given as

\[ \eta = 1 - \dfrac{1}{R} erf(\dfrac{W_{max}-W}{m+\beta W_{max}}) \]

where \(erf\) is the Gauss error function.

NXT

This model describes the forming limit baed on stresses. This failure is used for shell elements only.

An instability factor is defined as:

\[ \lambda_f=\dfrac{\sigma/h - (\sigma/h)_{SR}}{(\sigma/h)_{3D}-(\sigma/h)_{SR}} + 1 \]

The material is defined as free if \(0<\lambda_f<1\), warning if \(1<\lambda_f<2\), failure if \(\lambda_f \ge 2\).

Orthotropic Bi-Quadratic

The failure strain is described by two parabolicfunctions calculated using curve fitting from user input failure strains.

Orthotropic Strain

A damage factor is the maximum over time and is calculated for each direction and stress state via:

\[ d_ijl = \dfrac{\epsilon_{ijf\_l}}{\epsilon_{ijl}} \cdot \dfrac{\epsilon_{ijl}-\alpha\cdot\epsilon_{ijd\_l}}{\epsilon_{ijf\_l}-\epsilon_{ijd\_l}} \]

where the direction is indicated by using the common \(ij\) notation and loading state is either compression (\(l=c\)) or tension (\(l=t\)). The parameter \(\alpha=factor_{el}\cdot factor_{rate}\).

The element size correction factor is :

\[ factor_{el} = Fscale_{el} \cdot f_{el} \dfrac{Size_{el}}{El_ref} \]

where \(f_{el}\) is the element size correction factor function, \(Size_{el}\) is the characteristic element size.

The strain rate factor is

\[ factor_{rate} = f_{ijl}(\dfrac{\dot{\epsilon}_{ijl}}{\dot{\epsilon}_0}) \]

where \(f_ijl\) is strain rate factor function, \(\dot{\epsilon}_{ijl}\) is the current strain rate in direction ij and load case l, and \(\dot\epsilon_0\) is the reference strate rate.

Generally, the damange for this model is

\[ D = Max(d_{ijl}) = Max(\dfrac{\epsilon_{ijf\_l}}{\epsilon_{ijl}} \cdot \dfrac{\epsilon_{ijl}-\alpha\cdot\epsilon_{ijd\_l}}{\epsilon_{ijf\_l}-\epsilon_{ijd\_l}}) \]

Puck

This failure model can be applied for both solid and shell elements.

For the fiber fraction failure, the damage parameter \(e_f\) is defined by

\[ e_f=\dfrac{\sigma_{11}}{\sigma_{1}^t} \quad for\, tensile \]

or

\[ e_f=\dfrac{|\sigma_{11}|}{\sigma_{1}^c} \quad for\, compression \]

For the inter fiber failure: the damage parameter \(e_f\) is

\[ e_f=\dfrac{1}{\bar{\sigma}_{12}} [ \sqrt{(\dfrac{\bar{\sigma}_{12}}{\sigma_2^t} -p^+_{12})^2\sigma_{22}^2 + \sigma_{12}^2}+p^+_{12}\sigma_{22}] \quad for\, Mode\, A \]

or

\[ e_f=[(\dfrac{\sigma_{12}}{2(1+p^-_{22})\bar{\sigma}_{12}})^2 + (\dfrac{\sigma_{22}}{\sigma_2^c})^2](\dfrac{\sigma^c_2}{-\sigma_{22}}) \quad for\, Mode\, C \]

or

\[ e_f=\dfrac{1}{\bar{\sigma}_{12}} ( \sqrt{\sigma_{12}^2+(p^-_{12}\sigma_{22})^2}+p^-_{12}\sigma_{22}) \quad for\, Mode\, B \]

when the damage parameter \(e_f \ge 1.0\), the stresses are decreased by using an exponential function to avoid numerical instabilities.

The damage is defined by

\[ D = Max(e_f(tensile),e_f(compression), e_f(ModaA), e_f(ModeB), e_f(ModeC) ) \]

Tuler-Butcher

An element fails once the damage is greater than specified critical damage value K. For ductile materials, the cumulative damage parameter is:

\[ D=\int_0^t{max(0, \sigma-\sigma_r)^{\lambda})dt}>K \]

where \(\sigma_r\) is initial fracture stress, \(\sigma\) maximum principal stress, \(\lambda\) is material constant, \(t\) is the time when the element cracks, \(D\) is the damage integral, \(K\) is the critical value of the damage integral.

For brittle materials (shells only), the damage parameter is: $$ \dot{D} = \dfrac{1}{K}(\sigma - \sigma_r)^a $$ $$ \sigma_r=\sigma_0(1-D)^b $$ $$ D=D+\dot{D}\Delta t $$

Tensile Strain

This is a strain-based failure model that is compatible with both solid and shell elements. The damage is calculated by:

\[ D = \dfrac{\epsilon - \epsilon_{t1}}{\epsilon_{t2} - \epsilon_{t1}} \]

where \(\epsilon\) is either the quivlent strain or maximum principal tensile strain.

Wierzbicki model

This model describes the Bao-Xue-Wierzbicki failure model. The damage is defined by

\[ D=\sum{\dfrac{\Delta\epsilon_{p}}{\bar{\epsilon}_f}} \]

where the effective failure strain is

\[ \bar{\epsilon}_f =\{ \bar{\epsilon}_{max}n-[\bar{\epsilon}_{max}n - \bar{\epsilon}_{min}n](1-\bar{\xi}^m)^{\dfrac{1}{m}} \}^{\dfrac{1}{n}} \]

where \(\bar{\epsilon}_{max} = C_1 e^{-1C_{2}\eta}\), and \(\bar{\epsilon}_{min} = C_{3} e^{-1C_{4}\eta}\).

For solid element, the parameters \(\bar{\xi}\) and \(\bar{\eta}\) are defined by the two options.

The option 1 (default) is : $$ \bar{\xi}=\dfrac{\sigma_m}{\sigma_{VM}} \quad \bar{\eta}=\dfrac{27J_3}{2\sigma^3_{VM}} $$

The option 2 is: $$ \bar{\xi}=\dfrac{\int_0^{\epsilon_p}\dfrac{\sigma_m}{\sigma_{VM}}d\epsilon_p}{\epsilon_p} \quad \bar{\eta}=\dfrac{\int_0^{\epsilon_p} \dfrac{27J_3}{2\sigma^3_{VM}} d\epsilon_p}{\epsilon_p} $$

For shell element, the parameters \(\bar{\xi}\) and \(\bar{\eta}\) are $$ \bar{\xi}=\dfrac{\sigma_m}{\sigma_{VM}} \quad \bar{\eta}=-\dfrac{27}{2}\bar{\eta}(\bar{\eta}^2-\dfrac{1}{3}) $$

where \(\sigma_m\) is Hydrostatic stress, \(\sigma_{VM}\) is von Mises stress, and \(J_3\) is the third invariant deviatoric stress.

Wilkins model

The cumulative damage is given by:

\[ D_c = \int W_1 W_2 d \bar{\epsilon_p} \]

where \(W_1=(\dfrac{1}{1-\dfrac{P}{P_{lim}}})^{\alpha}\), \(W_2=(2-A)^{\beta}\), and hydro-pressure \(P=-\dfrac{1}{3}\sum_{j=1}^{3}\sigma_{jj}\), \(A=max(\dfrac{s_2}{s_1}, \dfrac{s_2}{s_3})\). \(s_1\), \(s_2\), \(s_3\) are the deviatoric stresses, and \(s_1 \ge s_2 \ge s_3\).

\ No newline at end of file + Failure models - WelSim Documentation
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Failure Models

MatEditor allows you to define the failure material properties. The supported properties are listed below.

  • Glass
  • Bi-Quadratic
  • Cockcroft
  • Connect
  • Extended Mohr-Coulomb
  • Energy
  • Fabric
  • Forming Limit Diagram
  • Hashin
  • Hosford-Coulomb
  • Johnson-Cook
  • Ladeveze delamination
  • Mullins Effect
  • NXT
  • Orthotropic Bi-Quadratic
  • Orthotropic Strain
  • Puck
  • Tuler-Butcher
  • Tensile Strain
  • Wierzbicki
  • Wilkins

Bi-Quadratic

The failure strain is described by two parabolic functions that user input.

Cockcroft

A nonlinear stress-strain based failure criterion with linear damage accumulation.

\[ C_0 = \int _0 ^{\bar{\epsilon}_f} max(\sigma_1, 0) \cdot d\bar{\epsilon} \]

where \(\epsilon_1\) is the first principal tension stress, \(\bar{\epsilon}\) is the equivalent strain.

Extended Mohr-Coulomb

The failure criteria is calculated as:

\[ D = \sum \dfrac{\Delta \bar{\epsilon}_p}{\bar{\epsilon}_{p,fail}} \]

where effective failure strain is

\[ \bar{\epsilon}_{p,fail} = b \cdot (1+c)^{\frac{1}{n}} \cdot \{[\dfrac{1}{2}((f_1-f_2)^a + (f_2-f_3)^a + (f_1 - f_3)^a )]^{\frac{1}{a}} + c(2\eta+f_1+f_3) \}^{-\frac{1}{n}} \]

the coefficient b is computed as

\[ b = b_0[1+\gamma ln(\dfrac{\dot{\bar{\epsilon}}_p}{\dot{\bar{\epsilon}}_0})] \quad if\, \dot{\bar{\epsilon}}_p > \dot{\bar{\epsilon}}_0 \]

or

\[ b = b_0 \quad if\, \dot{\bar{\epsilon}}_p \le \dot{\bar{\epsilon}}_0 \]

Energy

The damage is defined as

\[ D = \dfrac{E-E_1}{E_2 - E_1} \]

where the energy density is the current internal energy of the element divided by the current element volume.

Fabric

The failure and damage is defined independently in each direction (\(i\)=1,2)

\[ D_i = \dfrac{\epsilon_i - \epsilon_{fi}}{\epsilon_{ri} - \epsilon_{fi}} \]

where \(\epsilon_i \ge \epsilon_{fi}\).

Hashin

This model can be used for the composite materials.

The damage factor is calculated as

\[ D = Max(F_1,F_2,F_3, F_4, F_5) \quad for\quad uni-directional\, lamina\, model \]
\[ D = Max(F_1,F_2,F_3, F_4, F_5, F_6, F_7) \quad for\quad fabric\, lamina\, model \]

For the uni-directional lamina model:

Tensile/shear fiber mode:

\[ F_1 = (\dfrac{\langle\sigma_{11}\rangle}{\sigma_1^t})^2 + (\dfrac{\sigma_{12}^2 + \sigma_{13}^2}{{\sigma_{12}^f}^2}) \]

Compression fiber mode:

\[ F_2 = (\dfrac{\langle \sigma_a \rangle}{ \sigma_1^c})^2 \]

with \(\sigma_{\alpha} = -\sigma_{11}+\langle -\dfrac{\sigma_{22}+\sigma_{33}}{2} \rangle\).

Crush mode:

\[ F_3 = (\dfrac{\langle p \rangle}{\sigma_c})^2 \]

with \(p=-\dfrac{\sigma_{11}+\sigma_{22}+\sigma_{33}}{3}\).

Failure matrix mode:

\[ F_4 = (\dfrac{\langle \sigma_{22} \rangle}{\sigma_2^t})^2 + (\dfrac{\sigma_{23}}{S_{23}})^2 + (\dfrac{\sigma_{12}}{S_{12}})^2 \]

Delamination mode:

\[ F_5 = S^2_{del}[(\dfrac{\langle \sigma_{33} \rangle}{\sigma^t_2})^2 + (\dfrac{\sigma_{23}}{\tilde{S}_{23}})^2 + (\dfrac{\sigma_{12}}{S_{12}})^2 ] \]

For the fabirc lamina model:

Tensile/shear fiber mode

\[ F_1 = (\dfrac{\langle\sigma_{11}\rangle}{\sigma_1^t})^2 + (\dfrac{\sigma_{12}^2 + \sigma_{13}^2}{{\sigma_{a}^f}^2}) \]
\[ F_2 = (\dfrac{\langle\sigma_{22}\rangle}{\sigma_2^t})^2 + (\dfrac{\sigma_{12}^2 + \sigma_{23}^2}{{\sigma_{b}^f}^2}) \]

Compression fiber mode:

\[ F_3 = (\dfrac{\langle \sigma_a \rangle}{ \sigma_1^c})^2 \]
\[ F_4 = (\dfrac{\langle \sigma_b \rangle}{ \sigma_2^c})^2 \]

Crush mode:

\[ F_5 = (\dfrac{\langle p \rangle}{\sigma_c})^2 \]

Shear failure matrix mode:

\[ F_6 = (\dfrac{\sigma_12}{\sigma_12^m})^2 \]

Matrix failure mode:

\[ F_7 = S^2_{del}[(\dfrac{\langle \sigma_{33} \rangle}{\sigma^t_3})^2 + (\dfrac{\sigma_{23}}{\tilde{S}_{23}})^2 + (\dfrac{\sigma_{12}}{S_{12}})^2 ] \]

Hosford-Coulomb

The failure strain is described y the Hosford-Coulomb function.

The damage is defined as

\[ D = \sum \dfrac{\Delta \bar{\epsilon}_p} {\bar{\epsilon}^{pr}_{HC}(\eta) } \]

where the strain is calcualted as

\[ \bar{\epsilon}^{pr}_{HC}(\eta, \theta) = b(1+c)^{\frac{1}{n_f}} \{[\dfrac{1}{2}((f_1-f_2)^a + (f_2-f_3)^a + (f_1-f_3)^a)]^{\frac{1}{a}} + c(a\eta + f_1 +f_2) \}^{\frac{1}{n_f}} \]

Johnson-Cook

The failure strain is calculated by the constutitive relation:

\[ \epsilon_f = [D_1+D_2exp(D_3\sigma^*)] [1+D_4 ln(\dot{\epsilon}^*)] (1 + D_5 T^*) \]

The damage factor is defined as

\[ D = \sum \dfrac{\Delta \epsilon_p}{\epsilon_f} \]

Ladeveze Delamination

This is the Ladeveze failure model for delamination (interlaminar fracture). The damage parameters are defined as

\[ Y_{d_3} = \dfrac{\partial E_D}{\partial d_3} \vert _{\sigma=cst}=\dfrac{1}{2} \dfrac{\langle\sigma_{33}\rangle^2}{K_3(1-d_3)^2} \quad Mode\,I \]
\[ Y_{d_2} = \dfrac{\partial E_D}{\partial d_2} \vert _{\sigma=cst}=\dfrac{1}{2} \dfrac{\langle\sigma_{32}\rangle^2}{K_2(1-d_2)^2} \quad Mode\,II \]
\[ Y_{d_1} = \dfrac{\partial E_D}{\partial d_1} \vert _{\sigma=cst}=\dfrac{1}{2} \dfrac{\langle\sigma_{31}\rangle^2}{K_1(1-d_1)^2} \quad Mode\,III \]

The damage value can be

\[ D = \dfrac{k}{a}[1- exp(-a\langle w(Y)-d\rangle)] \]

Mullins Effect

This failure model is used with the hyperelastic materials. The stress during the first loading process is equal to the undamaged stress. Upon unloading and reloading the strss is multiplied by a positive softening factor as

\[ \sigma = \eta dev(\sigma) - pI \]

where dev(\(\sigma\)) is the deviatoric part of the stress, \(p\) is the hydrostatic pressure. The damage factor \(\eta\) is given as

\[ \eta = 1 - \dfrac{1}{R} erf(\dfrac{W_{max}-W}{m+\beta W_{max}}) \]

where \(erf\) is the Gauss error function.

NXT

This model describes the forming limit baed on stresses. This failure is used for shell elements only.

An instability factor is defined as:

\[ \lambda_f=\dfrac{\sigma/h - (\sigma/h)_{SR}}{(\sigma/h)_{3D}-(\sigma/h)_{SR}} + 1 \]

The material is defined as free if \(0<\lambda_f<1\), warning if \(1<\lambda_f<2\), failure if \(\lambda_f \ge 2\).

Orthotropic Bi-Quadratic

The failure strain is described by two parabolicfunctions calculated using curve fitting from user input failure strains.

Orthotropic Strain

A damage factor is the maximum over time and is calculated for each direction and stress state via:

\[ d_ijl = \dfrac{\epsilon_{ijf\_l}}{\epsilon_{ijl}} \cdot \dfrac{\epsilon_{ijl}-\alpha\cdot\epsilon_{ijd\_l}}{\epsilon_{ijf\_l}-\epsilon_{ijd\_l}} \]

where the direction is indicated by using the common \(ij\) notation and loading state is either compression (\(l=c\)) or tension (\(l=t\)). The parameter \(\alpha=factor_{el}\cdot factor_{rate}\).

The element size correction factor is :

\[ factor_{el} = Fscale_{el} \cdot f_{el} \dfrac{Size_{el}}{El_ref} \]

where \(f_{el}\) is the element size correction factor function, \(Size_{el}\) is the characteristic element size.

The strain rate factor is

\[ factor_{rate} = f_{ijl}(\dfrac{\dot{\epsilon}_{ijl}}{\dot{\epsilon}_0}) \]

where \(f_ijl\) is strain rate factor function, \(\dot{\epsilon}_{ijl}\) is the current strain rate in direction ij and load case l, and \(\dot\epsilon_0\) is the reference strate rate.

Generally, the damange for this model is

\[ D = Max(d_{ijl}) = Max(\dfrac{\epsilon_{ijf\_l}}{\epsilon_{ijl}} \cdot \dfrac{\epsilon_{ijl}-\alpha\cdot\epsilon_{ijd\_l}}{\epsilon_{ijf\_l}-\epsilon_{ijd\_l}}) \]

Puck

This failure model can be applied for both solid and shell elements.

For the fiber fraction failure, the damage parameter \(e_f\) is defined by

\[ e_f=\dfrac{\sigma_{11}}{\sigma_{1}^t} \quad for\, tensile \]

or

\[ e_f=\dfrac{|\sigma_{11}|}{\sigma_{1}^c} \quad for\, compression \]

For the inter fiber failure: the damage parameter \(e_f\) is

\[ e_f=\dfrac{1}{\bar{\sigma}_{12}} [ \sqrt{(\dfrac{\bar{\sigma}_{12}}{\sigma_2^t} -p^+_{12})^2\sigma_{22}^2 + \sigma_{12}^2}+p^+_{12}\sigma_{22}] \quad for\, Mode\, A \]

or

\[ e_f=[(\dfrac{\sigma_{12}}{2(1+p^-_{22})\bar{\sigma}_{12}})^2 + (\dfrac{\sigma_{22}}{\sigma_2^c})^2](\dfrac{\sigma^c_2}{-\sigma_{22}}) \quad for\, Mode\, C \]

or

\[ e_f=\dfrac{1}{\bar{\sigma}_{12}} ( \sqrt{\sigma_{12}^2+(p^-_{12}\sigma_{22})^2}+p^-_{12}\sigma_{22}) \quad for\, Mode\, B \]

when the damage parameter \(e_f \ge 1.0\), the stresses are decreased by using an exponential function to avoid numerical instabilities.

The damage is defined by

\[ D = Max(e_f(tensile),e_f(compression), e_f(ModaA), e_f(ModeB), e_f(ModeC) ) \]

Tuler-Butcher

An element fails once the damage is greater than specified critical damage value K. For ductile materials, the cumulative damage parameter is:

\[ D=\int_0^t{max(0, \sigma-\sigma_r)^{\lambda})dt}>K \]

where \(\sigma_r\) is initial fracture stress, \(\sigma\) maximum principal stress, \(\lambda\) is material constant, \(t\) is the time when the element cracks, \(D\) is the damage integral, \(K\) is the critical value of the damage integral.

For brittle materials (shells only), the damage parameter is: $$ \dot{D} = \dfrac{1}{K}(\sigma - \sigma_r)^a $$ $$ \sigma_r=\sigma_0(1-D)^b $$ $$ D=D+\dot{D}\Delta t $$

Tensile Strain

This is a strain-based failure model that is compatible with both solid and shell elements. The damage is calculated by:

\[ D = \dfrac{\epsilon - \epsilon_{t1}}{\epsilon_{t2} - \epsilon_{t1}} \]

where \(\epsilon\) is either the quivlent strain or maximum principal tensile strain.

Wierzbicki model

This model describes the Bao-Xue-Wierzbicki failure model. The damage is defined by

\[ D=\sum{\dfrac{\Delta\epsilon_{p}}{\bar{\epsilon}_f}} \]

where the effective failure strain is

\[ \bar{\epsilon}_f =\{ \bar{\epsilon}_{max}n-[\bar{\epsilon}_{max}n - \bar{\epsilon}_{min}n](1-\bar{\xi}^m)^{\dfrac{1}{m}} \}^{\dfrac{1}{n}} \]

where \(\bar{\epsilon}_{max} = C_1 e^{-1C_{2}\eta}\), and \(\bar{\epsilon}_{min} = C_{3} e^{-1C_{4}\eta}\).

For solid element, the parameters \(\bar{\xi}\) and \(\bar{\eta}\) are defined by the two options.

The option 1 (default) is : $$ \bar{\xi}=\dfrac{\sigma_m}{\sigma_{VM}} \quad \bar{\eta}=\dfrac{27J_3}{2\sigma^3_{VM}} $$

The option 2 is: $$ \bar{\xi}=\dfrac{\int_0^{\epsilon_p}\dfrac{\sigma_m}{\sigma_{VM}}d\epsilon_p}{\epsilon_p} \quad \bar{\eta}=\dfrac{\int_0^{\epsilon_p} \dfrac{27J_3}{2\sigma^3_{VM}} d\epsilon_p}{\epsilon_p} $$

For shell element, the parameters \(\bar{\xi}\) and \(\bar{\eta}\) are $$ \bar{\xi}=\dfrac{\sigma_m}{\sigma_{VM}} \quad \bar{\eta}=-\dfrac{27}{2}\bar{\eta}(\bar{\eta}^2-\dfrac{1}{3}) $$

where \(\sigma_m\) is Hydrostatic stress, \(\sigma_{VM}\) is von Mises stress, and \(J_3\) is the third invariant deviatoric stress.

Wilkins model

The cumulative damage is given by:

\[ D_c = \int W_1 W_2 d \bar{\epsilon_p} \]

where \(W_1=(\dfrac{1}{1-\dfrac{P}{P_{lim}}})^{\alpha}\), \(W_2=(2-A)^{\beta}\), and hydro-pressure \(P=-\dfrac{1}{3}\sum_{j=1}^{3}\sigma_{jj}\), \(A=max(\dfrac{s_2}{s_1}, \dfrac{s_2}{s_3})\). \(s_1\), \(s_2\), \(s_3\) are the deviatoric stresses, and \(s_1 \ge s_2 \ge s_3\).

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Hyperelasticity and Curve Fitting

Isotropic hyperelasticity

The elastic potential energy in hyperelastic material can be obtained from the initial state with no stress activation. Therefore, we have the main invariable terms of the right Cauchy-Green deformation tensor C(\(I_{1}\), \(I_{2}\), \(I_{3}\)), or the main invariable of the deformation tensor excluding the volume changes (\(\bar{I}_{1}\), \(\bar{I}_{2}\), \(\bar{I}_{3}\)). The potential can be expressed as \(\mathbf{W}=\mathbf{W}(I_{1},I_{2},I_{3})\), or \(\mathbf{W}=\mathbf{W}(\bar{I}_{1},\bar{I}_{2},\bar{I}_{3})\).

The nonlinear constitutive relation of a hyperelastic material is defined by the relation between the second-order Piola-Kirchhoff stress and the Green-Lagrange strain, the total Lagrange method is more efficient in solving such models.

When the elastic potential energy \(W\) of the hyperelasticity is known, the second Piola-Kirchhoff stress and strain-stress relationship can be calculated as follows

\[ S=2\dfrac{\partial W}{\partial C} \]
\[ C=4\dfrac{\partial^{2}W}{\partial C\partial C} \]

The following are several forms of strain-energy potential (W) provided for the modeling of incompressible or nearly incompressible hyperelastic materials.

Arruda-Boyce model

The form of the strain-energy potential for Arruda-Boyce model is

\[ \begin{array}{ccl} W & = & \mu[\dfrac{1}{2}(\bar{I}_{1}-3)+\dfrac{1}{20\lambda_{m}^{2}}(\bar{I_{1}^{2}}-9)+\dfrac{11}{1050\lambda_{m}^{4}}(\bar{I_{1}^{3}}-27)\\ & + & \dfrac{19}{7000\lambda_{m}^{6}}(\bar{I_{1}^{4}}-81) + \dfrac{519}{673750\lambda_{m}^{8}}(\bar{I_{1}^{5}}-243)]\\ & + & \dfrac{1}{D_1}(\dfrac{J^{2}-1}{2}-\mathrm{ln}J) \end{array} \]

where \(\mu\) is the initial shear modulus of the material, \(\lambda_{m}\) is limiting network stretch, and \(D_1\) is the material incompressibility parameter.

The initial shear modulus is

\[ \mu=\dfrac{\mu_{0}}{1+\dfrac{3}{5\lambda_{m}^{2}}+\dfrac{99}{175\lambda_{m}^{4}}+\dfrac{513}{875\lambda_{m}^{6}}+\dfrac{42039}{67375\lambda_{m}^{8}}} \]

The initial bulk modulus is

\[ K=\dfrac{2}{D_1} \]

As the parameter \(\lambda_L\) goes to infinity, the model is equivalent to neo-Hookean form.

WelSim/docs

Hyperelasticity and Curve Fitting

Isotropic hyperelasticity

The elastic potential energy in hyperelastic material can be obtained from the initial state with no stress activation. Therefore, we have the main invariable terms of the right Cauchy-Green deformation tensor C(\(I_{1}\), \(I_{2}\), \(I_{3}\)), or the main invariable of the deformation tensor excluding the volume changes (\(\bar{I}_{1}\), \(\bar{I}_{2}\), \(\bar{I}_{3}\)). The potential can be expressed as \(\mathbf{W}=\mathbf{W}(I_{1},I_{2},I_{3})\), or \(\mathbf{W}=\mathbf{W}(\bar{I}_{1},\bar{I}_{2},\bar{I}_{3})\).

The nonlinear constitutive relation of a hyperelastic material is defined by the relation between the second-order Piola-Kirchhoff stress and the Green-Lagrange strain, the total Lagrange method is more efficient in solving such models.

When the elastic potential energy \(W\) of the hyperelasticity is known, the second Piola-Kirchhoff stress and strain-stress relationship can be calculated as follows

\[ S=2\dfrac{\partial W}{\partial C} \]
\[ C=4\dfrac{\partial^{2}W}{\partial C\partial C} \]

The following are several forms of strain-energy potential (W) provided for the modeling of incompressible or nearly incompressible hyperelastic materials.

Arruda-Boyce model

The form of the strain-energy potential for Arruda-Boyce model is

\[ \begin{array}{ccl} W & = & \mu[\dfrac{1}{2}(\bar{I}_{1}-3)+\dfrac{1}{20\lambda_{m}^{2}}(\bar{I_{1}^{2}}-9)+\dfrac{11}{1050\lambda_{m}^{4}}(\bar{I_{1}^{3}}-27)\\ & + & \dfrac{19}{7000\lambda_{m}^{6}}(\bar{I_{1}^{4}}-81) + \dfrac{519}{673750\lambda_{m}^{8}}(\bar{I_{1}^{5}}-243)]\\ & + & \dfrac{1}{D_1}(\dfrac{J^{2}-1}{2}-\mathrm{ln}J) \end{array} \]

where \(\mu\) is the initial shear modulus of the material, \(\lambda_{m}\) is limiting network stretch, and \(D_1\) is the material incompressibility parameter.

The initial shear modulus is

\[ \mu=\dfrac{\mu_{0}}{1+\dfrac{3}{5\lambda_{m}^{2}}+\dfrac{99}{175\lambda_{m}^{4}}+\dfrac{513}{875\lambda_{m}^{6}}+\dfrac{42039}{67375\lambda_{m}^{8}}} \]

The initial bulk modulus is

\[ K=\dfrac{2}{D_1} \]

As the parameter \(\lambda_L\) goes to infinity, the model is equivalent to neo-Hookean form.

Neo-Hookean model

The Neo-Hookean model is a well-known hyperelastic model with an expanded linear rule (Hooke rule) having isotropy so that it can respond to finite deformation problems. The elastic potential is as follows.

\[ W=\frac{\mu}{2}(\bar{I}_{1}-3)+\dfrac{1}{D_{1}}(J-1)^{2} \]

where \(\mu\) is initial shear modulus of materials, \(D_{1}\) is the material constant.

The initial bulk modulus is given by:

\[ K=\dfrac{2}{D_1} \]

Ogden compressible foam model

The strain-energy potential of the Ogden compressible foam model is based on the principal stretches of left Cauchy strain tensor, which has the form:

\[ W=\sum_{i=1}^{N}\frac{\mu_{i}}{\alpha_{i}}\left(J^{\alpha_{i}/3}\left(\bar{\lambda}_{1}^{\alpha_{i}}+\bar{\lambda}_{2}^{\alpha_{i}}+\bar{\lambda}_{3}^{\alpha_{i}}\right)-3\right)+\sum_{i=1}^{N}\frac{\mu_{i}}{\alpha_{i}\beta_{i}}\left(J^{-\alpha_{i}\beta_{i}}-1\right) \]

where N determines the order of the polynomial, \(\mu_i\), \(\alpha_i\) are material constants, \(D_k\) is incompressiblity parameter. The reduced principal strench is defined by:

\[ \bar{\lambda}_{p}=J^{-\frac{1}{3}}\lambda_p,\; J=(\lambda_{1}\lambda_{2}\lambda_{3})^{\frac{1}{2}} \]

The initial shear modulus is given by:

\[ \mu=\dfrac{\sum_{i=1}^{N}\mu_{i}\alpha_{i}}{2} \]

The initial bulk modulus K is defined by

\[ K = \sum_{i=1}^{N}\mu_{i}\alpha_{i}\left(\dfrac{1}{3}+\beta_{i}\right) \]

When parameters N=1, \(\alpha_1\)=-2, \(\mu_1\)=-\(\mu\), and \(\beta\)=0.5, the Ogden compressible model is converted to the Blatz-Ko model.

Ogden model

The strain-energy potential of the Ogden compressible foam model is based on the principal stretches of left Cauchy strain tensor, which has the form:

\[ W=\sum_{i=1}^{N}\frac{\mu_{i}}{\alpha_{i}}\left(\bar{\lambda}_{1}^{\alpha_{i}}+\bar{\lambda}_{2}^{\alpha_{i}}+\bar{\lambda}_{3}^{\alpha_{i}}-3\right)+\sum_{k=1}^{N}\frac{1}{D_{k}}\left(J-1\right)^{2k} \]

where N determines the order of the polynomial, \(\mu_i\), \(\alpha_i\) are material constants, \(D_k\) is incompressiblity parameter. The reduced principal strench is defined by:

\[ \bar{\lambda}_{p}=J^{-\frac{1}{3}}\lambda_p,\; J=(\lambda_{1}\lambda_{2}\lambda_{3})^{\frac{1}{2}} \]

The initial shear modulus is given by:

\[ \mu=\dfrac{\sum_{i=1}^{N}\mu_{i}\alpha_{i}}{2} \]

The initial bulk modulus K is defined by

\[ K = \dfrac{2}{D_1} \]

When parameters N=1, \(\alpha_1\)=2, the Ogden model is converted to the neo-Hookean model. When parameters N=2, \(\alpha_1\)=2 and \(\alpha_2\)=-2, the Ogden model is converted to the 2-parameter Mooney-Rivlin model.

Polynomial form

The polynomial form of strain-energy potential is:

\[ W=\sum_{i+j=1}^{N}c_{ij}\left(\bar{I}_{1}-3\right)^{i}\left(\bar{I_{2}}-3\right)^{j}+\sum_{k=1}^{N}\frac{1}{D_{k}}\left(J-1\right)^{2k} \]

where \(N\) determines the order of polynomial, \(c_{ij}\), \(D_k\) are material constants.

The initial shear modulus is given by:

\[ \mu=2\left(C_{10}+C_{01}\right) \]

The initial bulk modulus K is defined by

\[ K = \dfrac{2}{D_1} \]

The Polynomial model is converted to following models with specific parameters:

Parameters of Polynomial model Equivalent model
N=1, \(C_{01}\)=0 neo-Hookean
N=1 2-parameter Mooney-Rivlin
N=2 5-parameter Mooney-Rivlin
N=3 9-parameter Mooney-Rivlin

Yeoh model

The Yeoh model is also called the reduced polynomial form. The strain-energy potential is

\[ W=\sum_{i=1}^{N}c_{i0}\left(\bar{I}_{1}-3\right)^{i}+\sum_{k=1}^{N}\frac{1}{D_{k}}\left(J-1\right)^{2k} \]

where N denotes the order of the polynomial, \(C_{i0}\) and \(D_k\) are material constants. When N=1, Yeoh becomes neo-Hookean model.

The initial shear modulus is defined:

\[ \mu=2c_{10} \]

The initial bulk modulus is:

\[ K=\frac{2}{D_1} \]

Hyperelasticity Material Curve Fitting

The mechanical response of hyperelastic materials is determined by the hyperelastic constants in the strain energy density function of a model. To get correct results during a hyperelastic analysis, it is required to precisely assess the material constants of the materials being tested. These constants are usually derived for a material based on the experimental strain-stress data. The test data are generally taken from several modes of deformation over a wide range of strain values. The material constants could be fit using test data in at least as many deformation states as will be experienced in the finite element analysis.

For hyperelastic materials, simple deformation tests can be used to characterize the material constants. The six different deformation modes are graphically illustrated in the figure below. Combinations of data from multiple tests will enhance the characterization of the hyperelastic behavior of a material.

finite_element_analysis_mateditor_deformation_modes

Although these six different deformation states are accepted, we find that upon the addition of hydrostatic stresses, the following modes of deformation are the same:

  1. Uniaxial Tension and Equibiaxial Compression.
  2. Uniaxial Compression and Equibiaxial Tension.
  3. Planar Tension and Planar Compression.

With these equivalent modes of testing, we now have only three independent deformation modes for which one can get experimental data.

In the analysis, when the coordinate system is chosen to consistent with the principal directions of deformation, the right Cauchy-Green strain tensor can be written in matrix form by:

\[ [C] = \begin{bmatrix} \lambda_1^2 & 0 & 0\\ 0 & \lambda_2^2 & 0\\ 0 & 0 & \lambda_3^2 \end{bmatrix} \]

where \(\lambda_i\)=1+\(\epsilon_i\) is principal stretch ratio in the i-th direction, \(epsilon_i\) is principal value of the engineering strain tensor in the i-th direction. The principal invariants of right Cauchy-Green strain tensor \(C_{ij}\) are:

\[ I_1 = \lambda_1^2+\lambda_2^2+\lambda_3^2 \]
\[ I_2 = \lambda_1^2\lambda_2^2 + \lambda_1^2\lambda_3^2 + \lambda_2^2\lambda_3^2 \]
\[ I_3 = \lambda_1^2\lambda_2^2\lambda_3^2 \]

For the fully incompressible material, the principal invariant \(I_3\) is one:

\[ \lambda_1^2\lambda_2^2\lambda_3^2=1 \]

Uniaxial tension (Equibiaxial compression)

For the uniaxial tension deformation, the principal stretch ratios in the directions orthogonal to the 'pulling' axis is identical. Thus, the principal stretches during uniaxial tension \(\lambda_i\) are given by:

  • \(\lambda_1=\)stretch in direction being loaded
  • \(\lambda_2=\lambda_3=\)stretch in directions not being loaded

Due to incompressibility:

\[ \lambda_2\lambda_3=\lambda^{-1} \]

and with

\[ \lambda_2=\lambda_3=\lambda_1^{-1/2} \]

For uniaxial tension, the first and second strain invariants then become:

\[ I_1= \lambda_1^2+2\lambda_1^{-1}\\ I_2=2\lambda_1+\lambda_1^{-2} \]

The corresponding engineering stress can be expressed using principal stretch ratio:

\[ T_1=2(\lambda_1-\lambda_1^{-2})[\dfrac{\partial W}{\partial I_1}+\lambda_1^{-1}\dfrac{\partial W}{\partial I_2}] \]

Equibiaxial tension (Uniaxial compression)

During an equibiaxial tension test, the principal stretch ratios in the directions being loaded are identical. Therefore, for quibiaxial tension, the principal stretches, \(\lambda_i\) are given by:

  • \(\lambda_1=\lambda_2=\)stretch ratio in direction being loaded
  • \(\lambda_3=\)stretch in directions not being loaded

According to incompressibility, we have

\[ \lambda_3=\lambda_1^{-2} \]

For equibiaxial tension, the first and second strain invariants then become:

\[ I_1=2\lambda_1^2+\lambda_1^{-4} \\ I_2=\lambda_1^4+2\lambda_1^{-2} \]

The corresponding engineering stress can be expressed using principal stretch ratio:

\[ T_1=2(\lambda_1-\lambda_1^{-5})[\dfrac{\partial W}{\partial I_1} + \lambda_1^2\dfrac{\partial W}{\partial I_2}] \]

Pure Shear (Uniaxial tension and uniaxial compression in orthogonal directions)

For pure shear deformation mode, plane strain is generally assumed so that there is no deformation in the 'wide' direction of the specimen. Including the incompressibility, we have

\[ \lambda_2=1 \\ \lambda_3 = \lambda_1^{-1} \]

For pure shear, the first and second strain invariants are:

\[ I_1=I_2=\lambda_1^2+\lambda_1^{-2}+1 \]

The corresponding engineering stress can be expressed using principal stretch ratio:

\[ T_1=2(\lambda_1 - \lambda_1^{-3})[\dfrac{\partial W}{\partial I_1} + \dfrac{\partial W}{\partial I_2}] \]

Volumetric Deformation

The volumetric deformation is given as:

\[ \lambda_1=\lambda_2=\lambda_3=\lambda\\ J=\lambda^3 \]

As nearly incompressible is assumed, we have:

\[ \lambda \approx 1 \]

The pressure P is directly related to the volume ratio J:

\[ P=\dfrac{\partial W}{\partial J} \]

Deformations for principal stretches based models

For the models based on the principal stretches, such Ogden model, the strain-stress relation can be obtained by deriving the strain energy with respect to the stretch.

\[ \sigma(\lambda)=\dfrac{\partial W(\lambda)}{\partial \lambda} \]

The corresponding engineering stress is:

\[ T_1 = \dfrac{\partial W(\lambda_1)}{\partial \lambda_1} \lambda_1^{-1} \]

Material stability check

Stability checks are critical for the following analysis. A nonlinear material is stable if the secondary work required for an arbitrary change in the deformation is always positive. We usually use the Drucker stability criterion to determine the stability of the hyperelastic materials. Mathematically, this is:

\[ d\sigma_{ij}d\epsilon_{ij}>0 \]

where \(d\sigma\) is the change in the Cauchy stress tensor corresponding to a change in the logarithmic strain.

The material stability checks can be done at the end of preprocessing but before an analysis actually begins. Checking for the stability of a material can be more conveniently accomplished by checking for the positive definiteness of the material stiffness. The program checks for the loss of stability of six typical stress paths including uniaxial tension and compression, equibiaxial tension and compression, and planar tension and compression. the range of the stretch ratio over which the stability is checked is chosen from 0.1 to 10.

\ No newline at end of file +$$ -->

Neo-Hookean model

The Neo-Hookean model is a well-known hyperelastic model with an expanded linear rule (Hooke rule) having isotropy so that it can respond to finite deformation problems. The elastic potential is as follows.

\[ W=\frac{\mu}{2}(\bar{I}_{1}-3)+\dfrac{1}{D_{1}}(J-1)^{2} \]

where \(\mu\) is initial shear modulus of materials, \(D_{1}\) is the material constant.

The initial bulk modulus is given by:

\[ K=\dfrac{2}{D_1} \]

Ogden compressible foam model

The strain-energy potential of the Ogden compressible foam model is based on the principal stretches of left Cauchy strain tensor, which has the form:

\[ W=\sum_{i=1}^{N}\frac{\mu_{i}}{\alpha_{i}}\left(J^{\alpha_{i}/3}\left(\bar{\lambda}_{1}^{\alpha_{i}}+\bar{\lambda}_{2}^{\alpha_{i}}+\bar{\lambda}_{3}^{\alpha_{i}}\right)-3\right)+\sum_{i=1}^{N}\frac{\mu_{i}}{\alpha_{i}\beta_{i}}\left(J^{-\alpha_{i}\beta_{i}}-1\right) \]

where N determines the order of the polynomial, \(\mu_i\), \(\alpha_i\) are material constants, \(D_k\) is incompressiblity parameter. The reduced principal strench is defined by:

\[ \bar{\lambda}_{p}=J^{-\frac{1}{3}}\lambda_p,\; J=(\lambda_{1}\lambda_{2}\lambda_{3})^{\frac{1}{2}} \]

The initial shear modulus is given by:

\[ \mu=\dfrac{\sum_{i=1}^{N}\mu_{i}\alpha_{i}}{2} \]

The initial bulk modulus K is defined by

\[ K = \sum_{i=1}^{N}\mu_{i}\alpha_{i}\left(\dfrac{1}{3}+\beta_{i}\right) \]

When parameters N=1, \(\alpha_1\)=-2, \(\mu_1\)=-\(\mu\), and \(\beta\)=0.5, the Ogden compressible model is converted to the Blatz-Ko model.

Ogden model

The strain-energy potential of the Ogden compressible foam model is based on the principal stretches of left Cauchy strain tensor, which has the form:

\[ W=\sum_{i=1}^{N}\frac{\mu_{i}}{\alpha_{i}}\left(\bar{\lambda}_{1}^{\alpha_{i}}+\bar{\lambda}_{2}^{\alpha_{i}}+\bar{\lambda}_{3}^{\alpha_{i}}-3\right)+\sum_{k=1}^{N}\frac{1}{D_{k}}\left(J-1\right)^{2k} \]

where N determines the order of the polynomial, \(\mu_i\), \(\alpha_i\) are material constants, \(D_k\) is incompressiblity parameter. The reduced principal strench is defined by:

\[ \bar{\lambda}_{p}=J^{-\frac{1}{3}}\lambda_p,\; J=(\lambda_{1}\lambda_{2}\lambda_{3})^{\frac{1}{2}} \]

The initial shear modulus is given by:

\[ \mu=\dfrac{\sum_{i=1}^{N}\mu_{i}\alpha_{i}}{2} \]

The initial bulk modulus K is defined by

\[ K = \dfrac{2}{D_1} \]

When parameters N=1, \(\alpha_1\)=2, the Ogden model is converted to the neo-Hookean model. When parameters N=2, \(\alpha_1\)=2 and \(\alpha_2\)=-2, the Ogden model is converted to the 2-parameter Mooney-Rivlin model.

Polynomial form

The polynomial form of strain-energy potential is:

\[ W=\sum_{i+j=1}^{N}c_{ij}\left(\bar{I}_{1}-3\right)^{i}\left(\bar{I_{2}}-3\right)^{j}+\sum_{k=1}^{N}\frac{1}{D_{k}}\left(J-1\right)^{2k} \]

where \(N\) determines the order of polynomial, \(c_{ij}\), \(D_k\) are material constants.

The initial shear modulus is given by:

\[ \mu=2\left(C_{10}+C_{01}\right) \]

The initial bulk modulus K is defined by

\[ K = \dfrac{2}{D_1} \]

The Polynomial model is converted to following models with specific parameters:

Parameters of Polynomial model Equivalent model
N=1, \(C_{01}\)=0 neo-Hookean
N=1 2-parameter Mooney-Rivlin
N=2 5-parameter Mooney-Rivlin
N=3 9-parameter Mooney-Rivlin

Yeoh model

The Yeoh model is also called the reduced polynomial form. The strain-energy potential is

\[ W=\sum_{i=1}^{N}c_{i0}\left(\bar{I}_{1}-3\right)^{i}+\sum_{k=1}^{N}\frac{1}{D_{k}}\left(J-1\right)^{2k} \]

where N denotes the order of the polynomial, \(C_{i0}\) and \(D_k\) are material constants. When N=1, Yeoh becomes neo-Hookean model.

The initial shear modulus is defined:

\[ \mu=2c_{10} \]

The initial bulk modulus is:

\[ K=\frac{2}{D_1} \]

Hyperelasticity Material Curve Fitting

The mechanical response of hyperelastic materials is determined by the hyperelastic constants in the strain energy density function of a model. To get correct results during a hyperelastic analysis, it is required to precisely assess the material constants of the materials being tested. These constants are usually derived for a material based on the experimental strain-stress data. The test data are generally taken from several modes of deformation over a wide range of strain values. The material constants could be fit using test data in at least as many deformation states as will be experienced in the finite element analysis.

For hyperelastic materials, simple deformation tests can be used to characterize the material constants. The six different deformation modes are graphically illustrated in the figure below. Combinations of data from multiple tests will enhance the characterization of the hyperelastic behavior of a material.

finite_element_analysis_mateditor_deformation_modes

Although these six different deformation states are accepted, we find that upon the addition of hydrostatic stresses, the following modes of deformation are the same:

  1. Uniaxial Tension and Equibiaxial Compression.
  2. Uniaxial Compression and Equibiaxial Tension.
  3. Planar Tension and Planar Compression.

With these equivalent modes of testing, we now have only three independent deformation modes for which one can get experimental data.

In the analysis, when the coordinate system is chosen to consistent with the principal directions of deformation, the right Cauchy-Green strain tensor can be written in matrix form by:

\[ [C] = \begin{bmatrix} \lambda_1^2 & 0 & 0\\ 0 & \lambda_2^2 & 0\\ 0 & 0 & \lambda_3^2 \end{bmatrix} \]

where \(\lambda_i\)=1+\(\epsilon_i\) is principal stretch ratio in the i-th direction, \(epsilon_i\) is principal value of the engineering strain tensor in the i-th direction. The principal invariants of right Cauchy-Green strain tensor \(C_{ij}\) are:

\[ I_1 = \lambda_1^2+\lambda_2^2+\lambda_3^2 \]
\[ I_2 = \lambda_1^2\lambda_2^2 + \lambda_1^2\lambda_3^2 + \lambda_2^2\lambda_3^2 \]
\[ I_3 = \lambda_1^2\lambda_2^2\lambda_3^2 \]

For the fully incompressible material, the principal invariant \(I_3\) is one:

\[ \lambda_1^2\lambda_2^2\lambda_3^2=1 \]

Uniaxial tension (Equibiaxial compression)

For the uniaxial tension deformation, the principal stretch ratios in the directions orthogonal to the 'pulling' axis is identical. Thus, the principal stretches during uniaxial tension \(\lambda_i\) are given by:

Due to incompressibility:

\[ \lambda_2\lambda_3=\lambda^{-1} \]

and with

\[ \lambda_2=\lambda_3=\lambda_1^{-1/2} \]

For uniaxial tension, the first and second strain invariants then become:

\[ I_1= \lambda_1^2+2\lambda_1^{-1}\\ I_2=2\lambda_1+\lambda_1^{-2} \]

The corresponding engineering stress can be expressed using principal stretch ratio:

\[ T_1=2(\lambda_1-\lambda_1^{-2})[\dfrac{\partial W}{\partial I_1}+\lambda_1^{-1}\dfrac{\partial W}{\partial I_2}] \]

Equibiaxial tension (Uniaxial compression)

During an equibiaxial tension test, the principal stretch ratios in the directions being loaded are identical. Therefore, for quibiaxial tension, the principal stretches, \(\lambda_i\) are given by:

According to incompressibility, we have

\[ \lambda_3=\lambda_1^{-2} \]

For equibiaxial tension, the first and second strain invariants then become:

\[ I_1=2\lambda_1^2+\lambda_1^{-4} \\ I_2=\lambda_1^4+2\lambda_1^{-2} \]

The corresponding engineering stress can be expressed using principal stretch ratio:

\[ T_1=2(\lambda_1-\lambda_1^{-5})[\dfrac{\partial W}{\partial I_1} + \lambda_1^2\dfrac{\partial W}{\partial I_2}] \]

Pure Shear (Uniaxial tension and uniaxial compression in orthogonal directions)

For pure shear deformation mode, plane strain is generally assumed so that there is no deformation in the 'wide' direction of the specimen. Including the incompressibility, we have

\[ \lambda_2=1 \\ \lambda_3 = \lambda_1^{-1} \]

For pure shear, the first and second strain invariants are:

\[ I_1=I_2=\lambda_1^2+\lambda_1^{-2}+1 \]

The corresponding engineering stress can be expressed using principal stretch ratio:

\[ T_1=2(\lambda_1 - \lambda_1^{-3})[\dfrac{\partial W}{\partial I_1} + \dfrac{\partial W}{\partial I_2}] \]

Volumetric Deformation

The volumetric deformation is given as:

\[ \lambda_1=\lambda_2=\lambda_3=\lambda\\ J=\lambda^3 \]

As nearly incompressible is assumed, we have:

\[ \lambda \approx 1 \]

The pressure P is directly related to the volume ratio J:

\[ P=\dfrac{\partial W}{\partial J} \]

Deformations for principal stretches based models

For the models based on the principal stretches, such Ogden model, the strain-stress relation can be obtained by deriving the strain energy with respect to the stretch.

\[ \sigma(\lambda)=\dfrac{\partial W(\lambda)}{\partial \lambda} \]

The corresponding engineering stress is:

\[ T_1 = \dfrac{\partial W(\lambda_1)}{\partial \lambda_1} \lambda_1^{-1} \]

Material stability check

Stability checks are critical for the following analysis. A nonlinear material is stable if the secondary work required for an arbitrary change in the deformation is always positive. We usually use the Drucker stability criterion to determine the stability of the hyperelastic materials. Mathematically, this is:

\[ d\sigma_{ij}d\epsilon_{ij}>0 \]

where \(d\sigma\) is the change in the Cauchy stress tensor corresponding to a change in the logarithmic strain.

The material stability checks can be done at the end of preprocessing but before an analysis actually begins. Checking for the stability of a material can be more conveniently accomplished by checking for the positive definiteness of the material stiffness. The program checks for the loss of stability of six typical stress paths including uniaxial tension and compression, equibiaxial tension and compression, and planar tension and compression. the range of the stretch ratio over which the stability is checked is chosen from 0.1 to 10.

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Theory IO

Some properties are mutually exclusive of each other and require that only one property in the mutually exclusive set be unsuppressed. The addition or removing of the suppression for one of these properties automatically suppresses the other mutually exclusive properties.

For example, defining Isotropic Elasticity and Orthotropic Elasticity for the same material represents redundant elasticity behavior. Only one behavior can be active for the material. When such a conflict occurs, the property defined last is used and the previously defined, conflicting property is automatically suppressed.

The properties that are mutually exclusive are grouped in the following table.

Group Material Property
Elastic properties Isotropic Elasticity, Orthotropic Elasticity, Anisotropic Elasticity, Mooney-Rivlin, Neo-Hookean, Polynomial, Yeoh, Ogden, Arruda-Boyce, Gent, Blatz-Ko, Ogden Foam, Extended Tube, Mullins Effect
Plastic properties Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening
Thermal conductivity properties Thermal Conductivity Isotropic, Thermal Conductivity Orthotropic
Resistivity properties Isotropic Resistivity, Orthotropic Resistivity
Electric permittivity properties Isotropic Relative Permittivity, Orthotropic Relative Permittivity
Dielectric loss properties Isotropic Dielectric Loss Tangent, Orthotropic Dielectric Loss Tangent
Magnetic permeability properties Isotropic Relative Permeability, Orthotropic Relative Permeability
Magnetic loss properties Isotropic Relative Imaginary Permeability, Isotropic Magnetic Loss Tangent, Orthotropic Magnetic Loss Tangent
\ No newline at end of file + Theory IO - WelSim Documentation
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Theory IO

Some properties are mutually exclusive of each other and require that only one property in the mutually exclusive set be unsuppressed. The addition or removing of the suppression for one of these properties automatically suppresses the other mutually exclusive properties.

For example, defining Isotropic Elasticity and Orthotropic Elasticity for the same material represents redundant elasticity behavior. Only one behavior can be active for the material. When such a conflict occurs, the property defined last is used and the previously defined, conflicting property is automatically suppressed.

The properties that are mutually exclusive are grouped in the following table.

Group Material Property
Elastic properties Isotropic Elasticity, Orthotropic Elasticity, Anisotropic Elasticity, Mooney-Rivlin, Neo-Hookean, Polynomial, Yeoh, Ogden, Arruda-Boyce, Gent, Blatz-Ko, Ogden Foam, Extended Tube, Mullins Effect
Plastic properties Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening
Thermal conductivity properties Thermal Conductivity Isotropic, Thermal Conductivity Orthotropic
Resistivity properties Isotropic Resistivity, Orthotropic Resistivity
Electric permittivity properties Isotropic Relative Permittivity, Orthotropic Relative Permittivity
Dielectric loss properties Isotropic Dielectric Loss Tangent, Orthotropic Dielectric Loss Tangent
Magnetic permeability properties Isotropic Relative Permeability, Orthotropic Relative Permeability
Magnetic loss properties Isotropic Relative Imaginary Permeability, Isotropic Magnetic Loss Tangent, Orthotropic Magnetic Loss Tangent
\ No newline at end of file diff --git a/mateditor/mat_theory_plasticity/index.html b/mateditor/mat_theory_plasticity/index.html index e971f5a..bc4df1e 100644 --- a/mateditor/mat_theory_plasticity/index.html +++ b/mateditor/mat_theory_plasticity/index.html @@ -1 +1 @@ - Plasticity - WelSim Documentation
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Plasticity

This section describes the plastic laws in details.

Johnson-Cook Model

In this model the material behaves as a linear-elastic material when the quivalent stress is lower than the plastic yield stress. For higher stress values, the material behavior is plastic, and the true stress is calculated as:

\[ \sigma = (a+b\epsilon_p^n)(1+c\cdot ln\dfrac{\dot{\epsilon}}{\dot{\epsilon}_0})(1-(\dfrac{T-T_r}{T_{melt}-T_r})^m) \]

where \(\epsilon_p\) is the plastic strain, \(\dot{\epsilon}\) is strain rate, \(T\) is the temperature, \(T_r\) is the ambient temperature, \(T_{melt}\) is the melting temperature. The plastic yield stress \(a\) should always be greater than zero. The plastic hardening exponent \(n\) must be less than or equal to 1.

Zerilli-Armstrong Model

The stress during plastic deformation is defined by

\[ \sigma = C_0 + C_1 exp(-C_3 T + C_4 T ln \dfrac{\dot{\epsilon}}{\dot{\epsilon}_0} ) + C_5 \epsilon_p ^n \]

where the yield stress \(C_0\) should be positive, plastic hardening exponent \(n\) must be less than 1.

Hill Model

The Hill model describes the orthotropic plastic material. The yield stress can be input by parameters or tabular data. The yield stress is defined as:

\[ \sigma_y = a(\epsilon_0+\epsilon_p)^n \mathrm{max}(\dot{\epsilon}, \dot{\epsilon}_0)^m \]

The maximum elastic stress is given by

\[ \sigma_0 = a(\epsilon_0)^n (\dot{\epsilon}_0)^m \]

The yield stress is compresed to the equivalent stress: $$ \sigma_{eq} = \sqrt{A_1 \sigma_1^2 + A_2 \sigma_2^2 -A_3 \sigma_1 \sigma_2 +A_{12} \sigma_{12}^2} $$

where parameters \(A_1\), \(A_2\), \(A_3\), and \(A_{12}\) are defined by the Lankford constants.

Orthotropic Hill Model

This model describes the orthotropic elastic behavior material with Hill plasticity. The yield stress is compared to an equivalent stress for the orthotropic materials. The equivalent stress for solid elements is defined as:

\[ \sigma_{eq} = \sqrt{F(\sigma_{22}^2 - \sigma_{33}^2) + G(\sigma_{33}^2 - \sigma_{11}^2) + H(\sigma_{11} - \sigma_{22}^2) + 2L\sigma_{23}^2 + 2M\sigma_{31}^2 + 2N\sigma_{12}^2} \]

For the shell element, the equivalent yield stress is :

\[ \sigma_{eq} = \sqrt{(G+H)\sigma_{11}^2 +(F+H) \sigma_{22}^2 - 2H \sigma_{11} \sigma_{22} + 2N\sigma_{12}^2} \]

Rate-Dependent MultiLinear Hardening

This model describes an isotropic elasto-plastic material using user-input funcitons for the strain-stress curves at the different strain rates. No yield stress equations are needed because constitutive relations are given by the tabular data.

Cowper-Symonds Model

Similar to the Johnson-Cook model, Cowper-Symonds law models isotropic elasto-plastic materials. The yield stress is defined by the stress constants, tabular data, or a combination of both. The pure constant formulation is given here:

\[ \sigma = (a+b\epsilon_p^n)(1+(\dfrac{\dot{\epsilon}}{c})^{\frac{1}{p}}) \]

where the yield stress \(a\) should be positive, plastic hardening exponent \(n\) must be less than 1.

Zhao Model

Zhao model describes the isotropic plastic strain rate-dependent materials. The strain-stress relation is based on the formula below:

\[ \sigma = (A + B \epsilon_p^n) + (C-D\epsilon_p^m)\cdot \mathrm{ln}\dfrac{\dot{\epsilon}}{\dot{\epsilon}_0}+E_1 \dot{\epsilon}^k \]

where the yield stress \(A\) should be positive, plastic hardening exponent \(n\) must be less than 1. If \(\dot{\epsilon} \le \dot{\epsilon}_0\), the term \((C-D\epsilon_p^m)\cdot \mathrm{ln}\dfrac{\dot{\epsilon}}{\dot{\epsilon}_0}=0\), the stress becomes:

\[ \sigma = (A + B \epsilon_p^n) + E_1 \dot{\epsilon}^k \]

Steinberg-Guinan Model

This model defines an isotropic elasto-plastic mateial with thermal softening. When the material approaches melting temperature, the yield strength and shear modulus decrease to zeero. The melting energy is given as

\[ E_m = E_c + \rho_0 C_p T_m \]

where \(E_c\) is the cold compression energy.

When the internal energy \(E\) is less than \(Em\), the shear modulus and the yield stress are :

\[ G = G_0 [1 + b_1 p V^{\frac{1}{3}} - h(T-T_0)] e^{-\frac{fE}{E-E_m}} \]
\[ \sigma_y = \sigma_0(1+\beta \epsilon_p^{\mathrm{(max)}})^n [1 + b_2 p V^{\frac{1}{3}} -h(T-T_0)]e^{-\frac{fE}{E-E_m}} \]

where initial shear modulus \(G_0 = \dfrac{E_0}{2(1+\nu)}\).

Gurson Model

The Gurson law can be used to model visco-elasto-plastic strain rate-depdent porous materials. The yield stress can be obtained from the tabular data or the Cowper-Symond's law, the latter formulation is defined as:

\[ \sigma_M = (A + B \epsilon_M^n) (1 + (\dfrac{\dot{\epsilon}}{c})^{\frac{1}{p}}) \]

The von Mises critera for the viscoplastic flow are given as

\[ \Omega_{vm} = \sigma_{qt} - \sigma_{M}\sqrt{1 + q_3 f^{*2} - 2q_1 f^{*2} \mathrm{cosh}(\dfrac{3q_2\sigma_m}{2\sigma_M})} \]

or

\[ \Omega_{vm} =\dfrac{\sigma^2_{qe}}{\sigma^2_M} + 2q_1 f^* \mathrm{cosh}(\dfrac{3}{2}q_2 \dfrac{\sigma_m}{\sigma_M}) - (1 + q_3 f^{*2}) \]

where \(\sigma_M\) is the admissible stress, \(\sigma_m\) is the trace, \(\sigma_eq\) is the von Mises stress, \(q_1\), \(q_2\), and \(q_3\) are the Gurson material constants. The specific coalescence function \(f*\) is defined as

\[ f^* = f_c + \dfrac{f_u - f_c}{f_F - f_c}(f - f_c) \quad \mathrm{if}\, f \gt f_c \]

Barlat3 Model

This is an orthotropic elastoplastic law for modeling anisotropic materials in metal forming process. Thus it is widely applied in the shell elements. The plastic hardening is described by the input parameters or user-defined tabular data. The anisotropic yield criteria F for plane stress is given by:

\[ F = a |K_1 + K_2|^m + a |K_1 - K_2|^m + c |2K_2|^m - 2\sigma_y^m = 0 \]

where coefficient \(K_1 = \frac{\sigma_{xx} + h \sigma_{yy}}{2}\) and \(K_2 = \sqrt{(\frac{\sigma_{xx} - h \sigma_{yy}}{2})^2 + p^2 \sigma_{xy}^2}\). The constants \(a\), \(c\), and \(h\) can be obtained from the Lankford constants.

When the Young's modulus is based on the input parameters. The expression is

\[ E(t) = E - (E_0-E_{inf})[1-\mathrm{exp}(-C_E \bar{\epsilon}_p)] \]

where \(E_0\) is the initial Youngs' modulus, \(E_{inf}\) is the asymptotic Young's modulus, and \(\bar{\epsilon}_p\) is the accumulated equivalent plastic strain.

Yoshida-Uemori Model

This model can describe the large strain cyclic plasticity of metals. The law is based on the yielding and bounding surfaces.

For solid elements, von Mises yield criterion is used as:

\[ f = \dfrac{3}{2} (\mathbf{s} - \mathbf{\alpha}) \colon (\mathbf{s} - \mathbf{\alpha}) - Y^2 \]

For shell elements, Hill or Barlat3 yield criterion is used. The Hill law is expressed as:

\[ f_{Hill} = \varphi(\mathbf{\sigma} - \mathbf{\alpha})- Y^2 \]

where \(Y\) is yield stress, and \(\mathbf{\alpha}\) is total back stress. Let \(\mathbf{A}=\mathbf{\sigma}-\mathbf{\alpha}\), the function \(\varphi\) becomes

\[ \varphi(A) = A_{xx}^2 - \dfrac{2r_0}{1+r_0}A_{xx}A_{yy} + \dfrac{r_0(1+r_{90})}{r_{90}(1+r_0)}A_{yy}^2 + \frac{r_0 + r_{90}}{r_{90}(1+r_0)}(2r_{45}+1)A_{xy}^2 \]

The Barlat law is defined as:

\[ f_{Barlat} = \phi(\sigma - \alpha) - 2Y^M \]

where \(M\) is the exponent in Barlat's yield criterion.

Hohnson-Holmquist Model

This law describes the behaivor of brittle materials, such as glass and ceramics.

\[ \sigma^* = (1-D)\sigma^*_i + D \sigma_f^* \]

where the equivalent stress of the intact materials \(\sigma_i^*\) can be expressed as

\[ \sigma_i^* = a (P^* + T^*)^n (1 + c\mathrm{ln}\dfrac{\dot{\epsilon}}{\dot{\epsilon}_0}) \]

and the equivalent stress of the failed materials \(\sigma_f^*\) is

\[ \sigma_f^* = b(P^*)^m (1+c\mathrm{ln}\dfrac{\dot{\epsilon}}{\dot{\epsilon}_0}) \]

Swift-Voce Model

Swift-Voce elastoplastic model can combine the Johnson-Cook strain rate hardening and temperature softening. This model can be applied for the orthotropic materials and allows a quadratic non-assoicated flow rule. The yield stress can be calculated using a combination of Swift and Voce models as shown below.

\(\sigma_y = \{ \alpha [A(\bar{\epsilon}_p + \epsilon_0)^n] + (1+\alpha)[K_0 + Q(1-\mathrm{exp}(-B\bar{\epsilon }_p))]\} (1+C \mathrm{ln}\dfrac{\dot{\bar{\epsilon}}_p}{\dot{\epsilon}_0}) [1 - (\dfrac{T-T_{ref}}{T_{melt} - T_{ref}})^m]\)

The plastic non-associated flow rule is computed as:

\[ \Delta \epsilon_p = \Delta \bar{\epsilon}_p \dfrac{\partial g(\sigma)}{\partial \sigma} \]

where \(g(\sigma) = \sqrt{\sigma^TG\sigma}\).

Hensel-Spittel Model

The hensel-Spittel yield stress is a function of strain, strain rate, and temperature. This model is often used in hot forging simulations. The yield stress is defined as :

\[ \sigma_y = A_0 e^{m_1 T} \epsilon^{m_2} \dot{\epsilon}^{m_3} e^{\frac{m_4}{\epsilon}} (1+\epsilon)^{m_5T} e^{m_7\epsilon} \]

where true strain \(\epsilon = \epsilon_0 + \bar{\epsilon}_p\), \(\dot{\epsilon}\) is the true strain rate.

Vegter Model

The yield function is defined as

\[ \phi = \bar{\sigma} - \sigma_Y \]

where \(\bar{\sigma}\) is the interpolated Vegter equivalent stress.

\ No newline at end of file + Plasticity - WelSim Documentation
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Plasticity

This section describes the plastic laws in details.

Johnson-Cook Model

In this model the material behaves as a linear-elastic material when the quivalent stress is lower than the plastic yield stress. For higher stress values, the material behavior is plastic, and the true stress is calculated as:

\[ \sigma = (a+b\epsilon_p^n)(1+c\cdot ln\dfrac{\dot{\epsilon}}{\dot{\epsilon}_0})(1-(\dfrac{T-T_r}{T_{melt}-T_r})^m) \]

where \(\epsilon_p\) is the plastic strain, \(\dot{\epsilon}\) is strain rate, \(T\) is the temperature, \(T_r\) is the ambient temperature, \(T_{melt}\) is the melting temperature. The plastic yield stress \(a\) should always be greater than zero. The plastic hardening exponent \(n\) must be less than or equal to 1.

Zerilli-Armstrong Model

The stress during plastic deformation is defined by

\[ \sigma = C_0 + C_1 exp(-C_3 T + C_4 T ln \dfrac{\dot{\epsilon}}{\dot{\epsilon}_0} ) + C_5 \epsilon_p ^n \]

where the yield stress \(C_0\) should be positive, plastic hardening exponent \(n\) must be less than 1.

Hill Model

The Hill model describes the orthotropic plastic material. The yield stress can be input by parameters or tabular data. The yield stress is defined as:

\[ \sigma_y = a(\epsilon_0+\epsilon_p)^n \mathrm{max}(\dot{\epsilon}, \dot{\epsilon}_0)^m \]

The maximum elastic stress is given by

\[ \sigma_0 = a(\epsilon_0)^n (\dot{\epsilon}_0)^m \]

The yield stress is compresed to the equivalent stress: $$ \sigma_{eq} = \sqrt{A_1 \sigma_1^2 + A_2 \sigma_2^2 -A_3 \sigma_1 \sigma_2 +A_{12} \sigma_{12}^2} $$

where parameters \(A_1\), \(A_2\), \(A_3\), and \(A_{12}\) are defined by the Lankford constants.

Orthotropic Hill Model

This model describes the orthotropic elastic behavior material with Hill plasticity. The yield stress is compared to an equivalent stress for the orthotropic materials. The equivalent stress for solid elements is defined as:

\[ \sigma_{eq} = \sqrt{F(\sigma_{22}^2 - \sigma_{33}^2) + G(\sigma_{33}^2 - \sigma_{11}^2) + H(\sigma_{11} - \sigma_{22}^2) + 2L\sigma_{23}^2 + 2M\sigma_{31}^2 + 2N\sigma_{12}^2} \]

For the shell element, the equivalent yield stress is :

\[ \sigma_{eq} = \sqrt{(G+H)\sigma_{11}^2 +(F+H) \sigma_{22}^2 - 2H \sigma_{11} \sigma_{22} + 2N\sigma_{12}^2} \]

Rate-Dependent MultiLinear Hardening

This model describes an isotropic elasto-plastic material using user-input funcitons for the strain-stress curves at the different strain rates. No yield stress equations are needed because constitutive relations are given by the tabular data.

Cowper-Symonds Model

Similar to the Johnson-Cook model, Cowper-Symonds law models isotropic elasto-plastic materials. The yield stress is defined by the stress constants, tabular data, or a combination of both. The pure constant formulation is given here:

\[ \sigma = (a+b\epsilon_p^n)(1+(\dfrac{\dot{\epsilon}}{c})^{\frac{1}{p}}) \]

where the yield stress \(a\) should be positive, plastic hardening exponent \(n\) must be less than 1.

Zhao Model

Zhao model describes the isotropic plastic strain rate-dependent materials. The strain-stress relation is based on the formula below:

\[ \sigma = (A + B \epsilon_p^n) + (C-D\epsilon_p^m)\cdot \mathrm{ln}\dfrac{\dot{\epsilon}}{\dot{\epsilon}_0}+E_1 \dot{\epsilon}^k \]

where the yield stress \(A\) should be positive, plastic hardening exponent \(n\) must be less than 1. If \(\dot{\epsilon} \le \dot{\epsilon}_0\), the term \((C-D\epsilon_p^m)\cdot \mathrm{ln}\dfrac{\dot{\epsilon}}{\dot{\epsilon}_0}=0\), the stress becomes:

\[ \sigma = (A + B \epsilon_p^n) + E_1 \dot{\epsilon}^k \]

Steinberg-Guinan Model

This model defines an isotropic elasto-plastic mateial with thermal softening. When the material approaches melting temperature, the yield strength and shear modulus decrease to zeero. The melting energy is given as

\[ E_m = E_c + \rho_0 C_p T_m \]

where \(E_c\) is the cold compression energy.

When the internal energy \(E\) is less than \(Em\), the shear modulus and the yield stress are :

\[ G = G_0 [1 + b_1 p V^{\frac{1}{3}} - h(T-T_0)] e^{-\frac{fE}{E-E_m}} \]
\[ \sigma_y = \sigma_0(1+\beta \epsilon_p^{\mathrm{(max)}})^n [1 + b_2 p V^{\frac{1}{3}} -h(T-T_0)]e^{-\frac{fE}{E-E_m}} \]

where initial shear modulus \(G_0 = \dfrac{E_0}{2(1+\nu)}\).

Gurson Model

The Gurson law can be used to model visco-elasto-plastic strain rate-depdent porous materials. The yield stress can be obtained from the tabular data or the Cowper-Symond's law, the latter formulation is defined as:

\[ \sigma_M = (A + B \epsilon_M^n) (1 + (\dfrac{\dot{\epsilon}}{c})^{\frac{1}{p}}) \]

The von Mises critera for the viscoplastic flow are given as

\[ \Omega_{vm} = \sigma_{qt} - \sigma_{M}\sqrt{1 + q_3 f^{*2} - 2q_1 f^{*2} \mathrm{cosh}(\dfrac{3q_2\sigma_m}{2\sigma_M})} \]

or

\[ \Omega_{vm} =\dfrac{\sigma^2_{qe}}{\sigma^2_M} + 2q_1 f^* \mathrm{cosh}(\dfrac{3}{2}q_2 \dfrac{\sigma_m}{\sigma_M}) - (1 + q_3 f^{*2}) \]

where \(\sigma_M\) is the admissible stress, \(\sigma_m\) is the trace, \(\sigma_eq\) is the von Mises stress, \(q_1\), \(q_2\), and \(q_3\) are the Gurson material constants. The specific coalescence function \(f*\) is defined as

\[ f^* = f_c + \dfrac{f_u - f_c}{f_F - f_c}(f - f_c) \quad \mathrm{if}\, f \gt f_c \]

Barlat3 Model

This is an orthotropic elastoplastic law for modeling anisotropic materials in metal forming process. Thus it is widely applied in the shell elements. The plastic hardening is described by the input parameters or user-defined tabular data. The anisotropic yield criteria F for plane stress is given by:

\[ F = a |K_1 + K_2|^m + a |K_1 - K_2|^m + c |2K_2|^m - 2\sigma_y^m = 0 \]

where coefficient \(K_1 = \frac{\sigma_{xx} + h \sigma_{yy}}{2}\) and \(K_2 = \sqrt{(\frac{\sigma_{xx} - h \sigma_{yy}}{2})^2 + p^2 \sigma_{xy}^2}\). The constants \(a\), \(c\), and \(h\) can be obtained from the Lankford constants.

When the Young's modulus is based on the input parameters. The expression is

\[ E(t) = E - (E_0-E_{inf})[1-\mathrm{exp}(-C_E \bar{\epsilon}_p)] \]

where \(E_0\) is the initial Youngs' modulus, \(E_{inf}\) is the asymptotic Young's modulus, and \(\bar{\epsilon}_p\) is the accumulated equivalent plastic strain.

Yoshida-Uemori Model

This model can describe the large strain cyclic plasticity of metals. The law is based on the yielding and bounding surfaces.

For solid elements, von Mises yield criterion is used as:

\[ f = \dfrac{3}{2} (\mathbf{s} - \mathbf{\alpha}) \colon (\mathbf{s} - \mathbf{\alpha}) - Y^2 \]

For shell elements, Hill or Barlat3 yield criterion is used. The Hill law is expressed as:

\[ f_{Hill} = \varphi(\mathbf{\sigma} - \mathbf{\alpha})- Y^2 \]

where \(Y\) is yield stress, and \(\mathbf{\alpha}\) is total back stress. Let \(\mathbf{A}=\mathbf{\sigma}-\mathbf{\alpha}\), the function \(\varphi\) becomes

\[ \varphi(A) = A_{xx}^2 - \dfrac{2r_0}{1+r_0}A_{xx}A_{yy} + \dfrac{r_0(1+r_{90})}{r_{90}(1+r_0)}A_{yy}^2 + \frac{r_0 + r_{90}}{r_{90}(1+r_0)}(2r_{45}+1)A_{xy}^2 \]

The Barlat law is defined as:

\[ f_{Barlat} = \phi(\sigma - \alpha) - 2Y^M \]

where \(M\) is the exponent in Barlat's yield criterion.

Hohnson-Holmquist Model

This law describes the behaivor of brittle materials, such as glass and ceramics.

\[ \sigma^* = (1-D)\sigma^*_i + D \sigma_f^* \]

where the equivalent stress of the intact materials \(\sigma_i^*\) can be expressed as

\[ \sigma_i^* = a (P^* + T^*)^n (1 + c\mathrm{ln}\dfrac{\dot{\epsilon}}{\dot{\epsilon}_0}) \]

and the equivalent stress of the failed materials \(\sigma_f^*\) is

\[ \sigma_f^* = b(P^*)^m (1+c\mathrm{ln}\dfrac{\dot{\epsilon}}{\dot{\epsilon}_0}) \]

Swift-Voce Model

Swift-Voce elastoplastic model can combine the Johnson-Cook strain rate hardening and temperature softening. This model can be applied for the orthotropic materials and allows a quadratic non-assoicated flow rule. The yield stress can be calculated using a combination of Swift and Voce models as shown below.

\(\sigma_y = \{ \alpha [A(\bar{\epsilon}_p + \epsilon_0)^n] + (1+\alpha)[K_0 + Q(1-\mathrm{exp}(-B\bar{\epsilon }_p))]\} (1+C \mathrm{ln}\dfrac{\dot{\bar{\epsilon}}_p}{\dot{\epsilon}_0}) [1 - (\dfrac{T-T_{ref}}{T_{melt} - T_{ref}})^m]\)

The plastic non-associated flow rule is computed as:

\[ \Delta \epsilon_p = \Delta \bar{\epsilon}_p \dfrac{\partial g(\sigma)}{\partial \sigma} \]

where \(g(\sigma) = \sqrt{\sigma^TG\sigma}\).

Hensel-Spittel Model

The hensel-Spittel yield stress is a function of strain, strain rate, and temperature. This model is often used in hot forging simulations. The yield stress is defined as :

\[ \sigma_y = A_0 e^{m_1 T} \epsilon^{m_2} \dot{\epsilon}^{m_3} e^{\frac{m_4}{\epsilon}} (1+\epsilon)^{m_5T} e^{m_7\epsilon} \]

where true strain \(\epsilon = \epsilon_0 + \bar{\epsilon}_p\), \(\dot{\epsilon}\) is the true strain rate.

Vegter Model

The yield function is defined as

\[ \phi = \bar{\sigma} - \sigma_Y \]

where \(\bar{\sigma}\) is the interpolated Vegter equivalent stress.

\ No newline at end of file diff --git a/mateditor/mat_workflow/index.html b/mateditor/mat_workflow/index.html index 797ca20..d1aa7a4 100755 --- a/mateditor/mat_workflow/index.html +++ b/mateditor/mat_workflow/index.html @@ -1 +1 @@ - Workflow - WelSim Documentation
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Material workflow

This section discusses about the material data, and precedures for working with MatEditor.

Material data

Material data is the source of the material information that is used for the analysis of the system it is contained in. The information in a material data component system is used if shared to an analysis system. MatEditor allows you to view, edit, and add data for use in your analysis system.

Importing

You can import data into an system as a new material. The following types of files are supported for import:

  • WELSIM material data format
  • Material(s) file following the MatML 3.1 schema

Note

When you import material data, the materials contained in that source will be added to the material outline.

Editing

Property and Table panes provide constant and tabular data input. You can edit both constant and tabular data.

Constant data

You edit constant data by changing the value and/or unit of that data in the Properties pane. The value is modified by clicking the cell in the Value column and typing in the new value. If available, changing the unit will convert the value to correspond to the new unit. If the value entered is invalid or not acceptable it will be indicated in yellow or red to gain users' attention.

Tabular data

If Value cell shows a tabular format indication. This data is edited in the Table pane and each datum is a value and unit as one integral piece. If the value entered is invalid or not acceptable it will be indicated in yellow or red to gain users' attention. The unit is shown in the header, and you can change unit if necessary. The units between table header and Property pane column are connnected. Modifying either one of them changes units on both areas.

Suppression

A material property may be defined but suppressed to prevent it from being sent to analysis process in the system. A data item may be suppressed by selecting the dropdown in the suppression column. Suppressed items and its children are shown by a strike through the name (for example, ) and the dropdown being set to True in the suppression column.

finite_element_analysis_mateditor_suppression

Perform material tasks in MatEditor

All material related tasks require that you perform the following basic tasks:

Task Procedure
Create new material. In the Menu or Toolbar, click New Material to add a new material.
Add material properties.
  1. Activate the material in the Material Outline pane that is to receive the additional property.
  2. Toggle the property in the Property Outline pane that you want to add.
Delete material properties.
  1. Activate the material in the Material Outline pane whose property is to be deleted.
  2. Select the material property in the Properties pane.
  3. Right-click and choose Delete or on the menu bar, choose Delete.
Modify material properties.
  1. Activate the material in the Material Outline pane that contains the property you want to modify.
  2. In the Properties pane change the value or unit for constant data.
  3. Perform one of the following:
    • For constant data, change the value or unit in the Properties pane.
    • For tabular data, change the value or unit(s) in the Table pane.
Suppress material properties.
  1. Activate the material in the Material Outline pane that contains the property you want to suppress.
  2. Select the dropdown in the suppression column for the property you want to suppress.
\ No newline at end of file + Workflow - WelSim Documentation
Skip to content

Material workflow

This section discusses about the material data, and precedures for working with MatEditor.

Material data

Material data is the source of the material information that is used for the analysis of the system it is contained in. The information in a material data component system is used if shared to an analysis system. MatEditor allows you to view, edit, and add data for use in your analysis system.

Importing

You can import data into an system as a new material. The following types of files are supported for import:

  • WELSIM material data format
  • Material(s) file following the MatML 3.1 schema

Note

When you import material data, the materials contained in that source will be added to the material outline.

Editing

Property and Table panes provide constant and tabular data input. You can edit both constant and tabular data.

Constant data

You edit constant data by changing the value and/or unit of that data in the Properties pane. The value is modified by clicking the cell in the Value column and typing in the new value. If available, changing the unit will convert the value to correspond to the new unit. If the value entered is invalid or not acceptable it will be indicated in yellow or red to gain users' attention.

Tabular data

If Value cell shows a tabular format indication. This data is edited in the Table pane and each datum is a value and unit as one integral piece. If the value entered is invalid or not acceptable it will be indicated in yellow or red to gain users' attention. The unit is shown in the header, and you can change unit if necessary. The units between table header and Property pane column are connnected. Modifying either one of them changes units on both areas.

Suppression

A material property may be defined but suppressed to prevent it from being sent to analysis process in the system. A data item may be suppressed by selecting the dropdown in the suppression column. Suppressed items and its children are shown by a strike through the name (for example, ) and the dropdown being set to True in the suppression column.

finite_element_analysis_mateditor_suppression

Perform material tasks in MatEditor

All material related tasks require that you perform the following basic tasks:

Task Procedure
Create new material. In the Menu or Toolbar, click New Material to add a new material.
Add material properties.
  1. Activate the material in the Material Outline pane that is to receive the additional property.
  2. Toggle the property in the Property Outline pane that you want to add.
Delete material properties.
  1. Activate the material in the Material Outline pane whose property is to be deleted.
  2. Select the material property in the Properties pane.
  3. Right-click and choose Delete or on the menu bar, choose Delete.
Modify material properties.
  1. Activate the material in the Material Outline pane that contains the property you want to modify.
  2. In the Properties pane change the value or unit for constant data.
  3. Perform one of the following:
    • For constant data, change the value or unit in the Properties pane.
    • For tabular data, change the value or unit(s) in the Table pane.
Suppress material properties.
  1. Activate the material in the Material Outline pane that contains the property you want to suppress.
  2. Select the dropdown in the suppression column for the property you want to suppress.
\ No newline at end of file diff --git a/mateditor/mateditor_overview/index.html b/mateditor/mateditor_overview/index.html index 2259c5c..32e90be 100755 --- a/mateditor/mateditor_overview/index.html +++ b/mateditor/mateditor_overview/index.html @@ -1,4 +1,4 @@ - Overview - WelSim Documentation
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Overview

MatEditor is a free material editor software program for engineers. This tool provides you comprehensive material properties those are often used in engineering simulation and finite element analysis.

finite_element_analysis_mateditor_gui

Specification

Specification Description
Operation system Microsoft Windows 7 to 10; 64-bit
Physical memory At least 4 GB

Supported unit systems :

  • SI: (kg, m, s, K, A, N, V)
  • MKS Standard: (kg, m, s, °C, A, N, V)
  • NMMTON Standard: (tonne, mm, s, °C, A, N, mV)
  • BIN Standard: (lbm, in, s, °F, A, lbf, V)
  • US Engineering: (lb, in, s, R, A, lbf, V)
  • CGS Standard: (g, cm, s, °C, A, dyne, V)
  • NMM Standard: (kg, mm, s, °C, mA, N, mV)
  • UMKS Standard: (kg, µm, s, °C, mA, µN, V)
  • NMMDAT Standard: (decatonne, mm, s, °C, mA, N, mV)
  • BFT Standard: (lbm, ft, s, °F, A, lbf, V)
  • CGS Consistent: (g, m, s, °C, A, dyne, V)
  • NMM Consistent: (tonne, m, s, °C, mA, t⋅mm/s2, mV)
  • UMKS Consistent: (kg, m, s, °C, pA, µN, pV)
  • BIN Consistent: (slinch, in, s, °C, A, slinch⋅in/s2, V)
  • BFT Consistent: (slug, ft, s, °C, A, slug⋅ft/s2, V)
  • CGuS Standard: (g, cm, \(\mu\)s, °C, A, dyne, V)

Material properties

The supported material properties are listed in the table below.

Category Materials
Basic Density, Isotropic Thermal Expansion, Isotropic Instantaneous Thermal Expansion, Orthotropic Thermal Expansion, Orthotropic Instantaneous Thermal Expansion, Constant Damping Coefficient
Linear Elastic Isotropic Elasticity, Orthotropic Elasticity, Viscoelastic
Hyperelastic Test Data Uniaxial Test Data, Biaxial Test Data, Shear Test Data, Volumetric Test Data, SimpleShear Test Data, Uniaxial Tension Test Data, Uniaxial Compression Test Data
Hyperelastic Arruda-Boyce, Blatz-Ko, Gent, Mooney-Rivlin 2, Mooney-Rivlin 3, Mooney-Rivlin 5, Mooney-Rivlin 9, Neo-Hookean, Ogden 1st Order, Ogden 2nd Order, Ogden 3rd Order, Polynomial 1st Order, Polynomial 2nd Order, Polynomial 3rd Order, Yeoh 1st Order, Yeoh 2nd Order, Yeoh 3rd Order
Plasticity Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening, Anand Viscoplasticity, Johnson-Cook, Zerilli-Armstrong
Creep Strain Hardening, Time Hardening, Generalized Exponential, Generalized Graham, Generalized Blackburn, Modified Time Hardening, Modified Strain Hardening, Generalized Garofalo, Exponential Form, Norton, Combined Time Hardening, Rational Polynomial, Generalized Time Hardening
Visco-elastic Prony Shear Relaxation, Prony Volumetric Relaxation
Equations of State (EOS) Compaction, Gruneisen, Ideal Gas, Linear, LSZK, Murnaghan, NASG, Noble-Abel, Osborne, Polynomial, Puff, Stiff Gas, Tillotson
Failure Johnson
Other Mechanical Strain Life Parameters, Compressive Ultimate Strength, Compressive Yield Strength, LaRc0304 Constants, Orthotropic Strain Limits, Orthotropic Stress Limits, Puck Constants, Tensile Ultimate Strength, Tensile Yield Strength, Tsai-Wu Constants, Shape Memory Effect, Drucker-Prager Strength Piecewise, Drucker-Prager Strength Linear, Ideal Gas EOS, Crushable Foam, Nonlinear Elastic Model Damage, Plakin Special Hardening, Tensile Pressure Failure, Crack Softening Failure
Thermal Enthalpy, Isotropic Thermal Conductivity, Orthotropic Thermal Conductivity, Specific Heat
Electromagnetics B-H Curve, Isotropic Relative Permeability, Orthotropic Relative Permeability, Isotropic Resistivity, Orthotropic Resistivity, Isotropic Relative Permittivity, Orthotropic Relative Permittivity, Isotropic Dielectric Loss Tangent, Isotropic Magnetic Loss Tangent, Isotropic Relative Imaginary Permeability, Orthotropic Dielectric Loss Tangent, Orthotropic Magnetic Loss Tangent
Fluid Dynamic Viscosity, Kinematic Viscosity, Lemalar Prandtl Number, Turbulent Prandtl Number, ALE
WelSim/docs

Overview

MatEditor is a free material editor software program for engineers. This tool provides you comprehensive material properties those are often used in engineering simulation and finite element analysis.

finite_element_analysis_mateditor_gui

Specification

Specification Description
Operation system Microsoft Windows 7 to 10; 64-bit
Physical memory At least 4 GB

Supported unit systems :

  • SI: (kg, m, s, K, A, N, V)
  • MKS Standard: (kg, m, s, °C, A, N, V)
  • NMMTON Standard: (tonne, mm, s, °C, A, N, mV)
  • BIN Standard: (lbm, in, s, °F, A, lbf, V)
  • US Engineering: (lb, in, s, R, A, lbf, V)
  • CGS Standard: (g, cm, s, °C, A, dyne, V)
  • NMM Standard: (kg, mm, s, °C, mA, N, mV)
  • UMKS Standard: (kg, µm, s, °C, mA, µN, V)
  • NMMDAT Standard: (decatonne, mm, s, °C, mA, N, mV)
  • BFT Standard: (lbm, ft, s, °F, A, lbf, V)
  • CGS Consistent: (g, m, s, °C, A, dyne, V)
  • NMM Consistent: (tonne, m, s, °C, mA, t⋅mm/s2, mV)
  • UMKS Consistent: (kg, m, s, °C, pA, µN, pV)
  • BIN Consistent: (slinch, in, s, °C, A, slinch⋅in/s2, V)
  • BFT Consistent: (slug, ft, s, °C, A, slug⋅ft/s2, V)
  • CGuS Standard: (g, cm, \(\mu\)s, °C, A, dyne, V)

Material properties

The supported material properties are listed in the table below.

Category Materials
Basic Density, Isotropic Thermal Expansion, Isotropic Instantaneous Thermal Expansion, Orthotropic Thermal Expansion, Orthotropic Instantaneous Thermal Expansion, Constant Damping Coefficient
Linear Elastic Isotropic Elasticity, Orthotropic Elasticity, Viscoelastic
Hyperelastic Test Data Uniaxial Test Data, Biaxial Test Data, Shear Test Data, Volumetric Test Data, SimpleShear Test Data, Uniaxial Tension Test Data, Uniaxial Compression Test Data
Hyperelastic Arruda-Boyce, Blatz-Ko, Gent, Mooney-Rivlin 2, Mooney-Rivlin 3, Mooney-Rivlin 5, Mooney-Rivlin 9, Neo-Hookean, Ogden 1st Order, Ogden 2nd Order, Ogden 3rd Order, Polynomial 1st Order, Polynomial 2nd Order, Polynomial 3rd Order, Yeoh 1st Order, Yeoh 2nd Order, Yeoh 3rd Order
Plasticity Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening, Anand Viscoplasticity, Johnson-Cook, Zerilli-Armstrong
Creep Strain Hardening, Time Hardening, Generalized Exponential, Generalized Graham, Generalized Blackburn, Modified Time Hardening, Modified Strain Hardening, Generalized Garofalo, Exponential Form, Norton, Combined Time Hardening, Rational Polynomial, Generalized Time Hardening
Visco-elastic Prony Shear Relaxation, Prony Volumetric Relaxation
Equations of State (EOS) Compaction, Gruneisen, Ideal Gas, Linear, LSZK, Murnaghan, NASG, Noble-Abel, Osborne, Polynomial, Puff, Stiff Gas, Tillotson
Failure Johnson
Other Mechanical Strain Life Parameters, Compressive Ultimate Strength, Compressive Yield Strength, LaRc0304 Constants, Orthotropic Strain Limits, Orthotropic Stress Limits, Puck Constants, Tensile Ultimate Strength, Tensile Yield Strength, Tsai-Wu Constants, Shape Memory Effect, Drucker-Prager Strength Piecewise, Drucker-Prager Strength Linear, Ideal Gas EOS, Crushable Foam, Nonlinear Elastic Model Damage, Plakin Special Hardening, Tensile Pressure Failure, Crack Softening Failure
Thermal Enthalpy, Isotropic Thermal Conductivity, Orthotropic Thermal Conductivity, Specific Heat
Electromagnetics B-H Curve, Isotropic Relative Permeability, Orthotropic Relative Permeability, Isotropic Resistivity, Orthotropic Resistivity, Isotropic Relative Permittivity, Orthotropic Relative Permittivity, Isotropic Dielectric Loss Tangent, Isotropic Magnetic Loss Tangent, Isotropic Relative Imaginary Permeability, Orthotropic Dielectric Loss Tangent, Orthotropic Magnetic Loss Tangent
Fluid Dynamic Viscosity, Kinematic Viscosity, Lemalar Prandtl Number, Turbulent Prandtl Number, ALE

Predefined materials

WELSIM also provide predefined materials, which covers most of commonly used materials. Users can choose these materials and apply to the successive finite element analysis.

Category Materials
General Materials Structural Steel, Stainless Steel, Aluminum Alloy, Concrete, Copper Alloy, Gray Cast Iron, Titanium Alloy
Nonlinear Materials Aluminum Alloy NL, Concrete NL, Copper Alloy NL, Stainless Steel NL, Structural Steel NL, Titanium Alloy NL
Hyperelastic Materials Elastomer Mooney-Rivlin, Elastomer Neo-Hookean, Elastomer Ogden, Elastomer Yeoh, Neoprene Rubber
Thermal Materials Brass, Bronze, Copper, Diamond, Ferrite, Nodular Cast Iron, Solder, Teflon, Tungsten, Wood
Electromagnetic Materials SS416, Supermendure, TDK-K1, TDK-M33, TDK-N30, TDK-N41, TDK-N45, TDK-N48, TDK-N49, TDK-N87, TDK-N97, TDK-T38, TDK-T66
Other Materials Water Liquid, Argon, Ash

Download

MatEditor software is available at our official website.

\ No newline at end of file +* [x] Orthotropic Resistivity -->

Predefined materials

WELSIM also provide predefined materials, which covers most of commonly used materials. Users can choose these materials and apply to the successive finite element analysis.

Category Materials
General Materials Structural Steel, Stainless Steel, Aluminum Alloy, Concrete, Copper Alloy, Gray Cast Iron, Titanium Alloy
Nonlinear Materials Aluminum Alloy NL, Concrete NL, Copper Alloy NL, Stainless Steel NL, Structural Steel NL, Titanium Alloy NL
Hyperelastic Materials Elastomer Mooney-Rivlin, Elastomer Neo-Hookean, Elastomer Ogden, Elastomer Yeoh, Neoprene Rubber
Thermal Materials Brass, Bronze, Copper, Diamond, Ferrite, Nodular Cast Iron, Solder, Teflon, Tungsten, Wood
Electromagnetic Materials SS416, Supermendure, TDK-K1, TDK-M33, TDK-N30, TDK-N41, TDK-N45, TDK-N48, TDK-N49, TDK-N87, TDK-N97, TDK-T38, TDK-T66
Other Materials Water Liquid, Argon, Ash

Download

MatEditor software is available at our official website.

\ No newline at end of file diff --git a/mateditor/material_data/index.html b/mateditor/material_data/index.html index dff39d9..9e69da0 100755 --- a/mateditor/material_data/index.html +++ b/mateditor/material_data/index.html @@ -1 +1 @@ - Defining materials - WelSim Documentation
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Defining materials

This section describes how to create material objects and define material properties in the WELSIM application.

Overview

Material Module serves as a database for material properties used in a modeling project. The module not only provides a material library but also allow you to create a material using the given properties. The spreadsheet of a Material object is the primary user interface designed to let you create, save, and retrieve material models. The well-defined material object can be saved and used in the subsequent projects.

Material Module is shown as a Material Project and Material Objects in the Project Explorer (tree) window. The solution system contains only one Material Project, which acts as a material repository in the modeling system. The Material Project may include multiple Material Objects, where the properties can be added or edited by users.

To access Material Object properties, you can choose one of the following methods: * Double click on the Material Object. * Right click on a Material Object, and select Edit item from the context menu.

Modes of operation

  • Material for subsequent analysis: You can create a material that can be consumed in the subsequent analysis. For example, a defined material can be assigned to the specific geometry bodies.
  • Material Data for files: You can create a material and export the material data into an external file.

The data included in the Material Module is automatically saved as you save the project.

User interface

The Material Editor spreadsheet is an essential portion of the WELSIM user interface, and it displays material-related components that allow users to edit material data easily.

Editing mode

Presented in this section are two configurations for the material property editing. The first configuration method is based on the library as shown in Figure [fig:ch3_guide_mat_ui_lib], and the second configuration is designed to manually combine the properties for the material object as shown in Figure [fig:ch3_guide_mat_ui_build]. You can click on the Library or Build tab to switch these two editing modes.

Note

  1. You can click on category tabs to browse different materials.
  2. Loading a material dataset from the library removes all pre-existing properties.

Build outline tab

The Build Outline Tab shows an outline of the contents of the togglable material properties. You can add a property data entry to the material by toggling on the property entry or remove property by toggling off the property entry.

Properties pane

The Properties pane displays all properties that are going to be added to the Material Object. You can tune the property values at this pane. The columns in this spreadsheet pane are:

  • Name: A read-only text field to display the property name.
  • Value: A number field to display and input the value.
  • Description: A read-only text field to display the attribute of this property.

You can delete a property by right-clicking on a row and select Remove Rows from the pop-up context menu.

The Material Properties pane provides the following command buttons to the bottom of the window:

  • OK: Save the properties and exit the material editor.
  • Apply: Save the current properties to the material database.
  • Cancel: Exit the material editor without Saving.
  • Clear: Remove all properties.

Working with material data

Exporting

You can export the complete material data to an external file. The following format is supported for export:

  • XML in WELSIM Material (MatML 3.1) schema.
  • JSON in WELSIM Material schema.
  • OpenRadioss input script

To implement the exporting, you can use one of the following methods:

  • Click the Export Materials button from the standard Toolbar.
  • Click the Export Materials item from the Material Menu.
  • Right-click the Material Project and select the Export Materials item from the context menu.

MatEditor applicaiton

MatEditor is a free application allow you to create and edit material data for the computer aided engineering. It is a smaller and concise application but has most of features that material module of WELSIM has. More details about MatEditor, please visit MatEditor page.

\ No newline at end of file + Defining materials - WelSim Documentation
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Defining materials

This section describes how to create material objects and define material properties in the WELSIM application.

Overview

Material Module serves as a database for material properties used in a modeling project. The module not only provides a material library but also allow you to create a material using the given properties. The spreadsheet of a Material object is the primary user interface designed to let you create, save, and retrieve material models. The well-defined material object can be saved and used in the subsequent projects.

Material Module is shown as a Material Project and Material Objects in the Project Explorer (tree) window. The solution system contains only one Material Project, which acts as a material repository in the modeling system. The Material Project may include multiple Material Objects, where the properties can be added or edited by users.

To access Material Object properties, you can choose one of the following methods: * Double click on the Material Object. * Right click on a Material Object, and select Edit item from the context menu.

Modes of operation

  • Material for subsequent analysis: You can create a material that can be consumed in the subsequent analysis. For example, a defined material can be assigned to the specific geometry bodies.
  • Material Data for files: You can create a material and export the material data into an external file.

The data included in the Material Module is automatically saved as you save the project.

User interface

The Material Editor spreadsheet is an essential portion of the WELSIM user interface, and it displays material-related components that allow users to edit material data easily.

Editing mode

Presented in this section are two configurations for the material property editing. The first configuration method is based on the library as shown in Figure [fig:ch3_guide_mat_ui_lib], and the second configuration is designed to manually combine the properties for the material object as shown in Figure [fig:ch3_guide_mat_ui_build]. You can click on the Library or Build tab to switch these two editing modes.

Note

  1. You can click on category tabs to browse different materials.
  2. Loading a material dataset from the library removes all pre-existing properties.

Build outline tab

The Build Outline Tab shows an outline of the contents of the togglable material properties. You can add a property data entry to the material by toggling on the property entry or remove property by toggling off the property entry.

Properties pane

The Properties pane displays all properties that are going to be added to the Material Object. You can tune the property values at this pane. The columns in this spreadsheet pane are:

  • Name: A read-only text field to display the property name.
  • Value: A number field to display and input the value.
  • Description: A read-only text field to display the attribute of this property.

You can delete a property by right-clicking on a row and select Remove Rows from the pop-up context menu.

The Material Properties pane provides the following command buttons to the bottom of the window:

  • OK: Save the properties and exit the material editor.
  • Apply: Save the current properties to the material database.
  • Cancel: Exit the material editor without Saving.
  • Clear: Remove all properties.

Working with material data

Exporting

You can export the complete material data to an external file. The following format is supported for export:

  • XML in WELSIM Material (MatML 3.1) schema.
  • JSON in WELSIM Material schema.
  • OpenRadioss input script

To implement the exporting, you can use one of the following methods:

  • Click the Export Materials button from the standard Toolbar.
  • Click the Export Materials item from the Material Menu.
  • Right-click the Material Project and select the Export Materials item from the context menu.

MatEditor applicaiton

MatEditor is a free application allow you to create and edit material data for the computer aided engineering. It is a smaller and concise application but has most of features that material module of WELSIM has. More details about MatEditor, please visit MatEditor page.

\ No newline at end of file diff --git a/misc/index.html b/misc/index.html index dfec93c..91ccb9a 100755 --- a/misc/index.html +++ b/misc/index.html @@ -1 +1 @@ - MISC - WelSim Documentation
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MISC

Comparison explicit and implicit time integrations

显式算法 隐式算法
适用问题 动力学（动态） 静力学（静态）和动力学（动态）
阻尼 人工阻尼 数值阻尼
时间步求解方法 矩阵乘法 线性方程组
组装刚度矩阵 否 是
数据存储需求 小 大
每步计算速度 快 中
迭代收敛性 无 有
确定性 有确定解 可能是病态无确定解
时间稳定性 有条件 无条件
时间步 小 大
计算精度 低 高
Explicit method Implicit method
Target problems Dynamic(transient) Static and dynamic(transient)
Damping Artificial damping Numerical damping
Time stepping method Matrix multiplication Linear algebra equations
Assemble stiffness matrix No Yes
Data storage requirement Small Large
Solving speed each step Quick Mediate
Iteration convergence No Yes
Solution Certain solution Could be uncertain solution
Stability Conditionally stable Unconditionally stable
Time step Small Large
Accuracy Low High
应力-应变曲线含有 适用的Mooney-Rivlin函数 参数正定性要求
没有拐点(单曲率) 2-或3-参数 C10 + C01 > 0
1个拐点(双曲率) 5-参数

C10 + C01 > 0
C20 > 0
C02 < 0
C20 + C11 + C02 > 0
2个拐点 9-参数

C10 + C01 > 0
C30>0
C03 < 0
C30 + C21 + C12 + C03 > 0
Strain-stress curve Suitable Mooney-Rivlin model Parameter requirement for positive definiteness
No inflection point (single curvature) 2- or 3-parameter C10 + C01 > 0
One inflection point (double curvature) 5-parameter

C10 + C01 > 0
C20 > 0
C02 < 0
C20 + C11 + C02 > 0
Two inflection points 9-parameter

C10 + C01 > 0
C30>0
C03 < 0
C30 + C21 + C12 + C03 > 0
\ No newline at end of file + MISC - WelSim Documentation
Skip to content

MISC

Comparison explicit and implicit time integrations

显式算法 隐式算法
适用问题 动力学（动态） 静力学（静态）和动力学（动态）
阻尼 人工阻尼 数值阻尼
时间步求解方法 矩阵乘法 线性方程组
组装刚度矩阵 否 是
数据存储需求 小 大
每步计算速度 快 中
迭代收敛性 无 有
确定性 有确定解 可能是病态无确定解
时间稳定性 有条件 无条件
时间步 小 大
计算精度 低 高
Explicit method Implicit method
Target problems Dynamic(transient) Static and dynamic(transient)
Damping Artificial damping Numerical damping
Time stepping method Matrix multiplication Linear algebra equations
Assemble stiffness matrix No Yes
Data storage requirement Small Large
Solving speed each step Quick Mediate
Iteration convergence No Yes
Solution Certain solution Could be uncertain solution
Stability Conditionally stable Unconditionally stable
Time step Small Large
Accuracy Low High
应力-应变曲线含有 适用的Mooney-Rivlin函数 参数正定性要求
没有拐点(单曲率) 2-或3-参数 C10 + C01 > 0
1个拐点(双曲率) 5-参数

C10 + C01 > 0
C20 > 0
C02 < 0
C20 + C11 + C02 > 0
2个拐点 9-参数

C10 + C01 > 0
C30>0
C03 < 0
C30 + C21 + C12 + C03 > 0
Strain-stress curve Suitable Mooney-Rivlin model Parameter requirement for positive definiteness
No inflection point (single curvature) 2- or 3-parameter C10 + C01 > 0
One inflection point (double curvature) 5-parameter

C10 + C01 > 0
C20 > 0
C02 < 0
C20 + C11 + C02 > 0
Two inflection points 9-parameter

C10 + C01 > 0
C30>0
C03 < 0
C30 + C21 + C12 + C03 > 0
\ No newline at end of file diff --git a/search/search_index.json b/search/search_index.json index fdb6c9a..a44bc27 100755 --- a/search/search_index.json +++ b/search/search_index.json @@ -1 +1 @@ -{"config":{"lang":["en"],"separator":"[\\s\\-\\.]+","pipeline":["stopWordFilter"]},"docs":[{"location":"","title":"Welcome","text":"

WELSIM was born out of a vision to create a general-purpose simulation utility that could successfully enable a wide range of engineering and science communities to conduct simulation with more confidence. Customers use our software to help ensure the integrity of their innovations. WELSIM comes with an all-in-one user interface and self-integrated features. It is a long-term-support product that aims to accurately model engineering problems using the prestigious open source solvers.

"},{"location":"#why-welsim","title":"Why WELSIM","text":""},{"location":"#where-to-start","title":"Where to start","text":"

Engineers can do a thousand things with the WELSIM simulation solutions. We recommend starting with:

If you already use WELSIM:

If you are interested in our free engineering software:

Last Updated: Jan. 8th, 2024

"},{"location":"features/","title":"Features","text":"

As a general-purpose engineering simulation software program, WELSIM contains tons of features those allow you to conduct various simulation studies.

"},{"location":"features/#specification","title":"Specification","text":"Specification Description Operaton system Microsoft Windows 10/11, 64-bit; Linux: Ubuntu 22.04 LTS and higher versions, 64-bit; 3D rendering driver: OpenGL 3.2 or higher Physical memory At least 4 GB, and 32 GB and higher is recommended Geometry modules Imported geometry formats: STEP, IGES, STL, GDS Built-in geometry generation: Box, Cylinder, Sphere, Plane, Line, Circle, Vertex Boolean operations: Union, Intersection, Cut Supported automatic mesh Tet10, Tet4, Tri6, Tri3 "},{"location":"features/#structural","title":"Structural","text":"Structural analysis Description Types Static, transient, and modal Materials Isotropic elastic, hyper-elastic, plastic, visco-elastic, and creep Deformation types Small, and finite Contact types bonded, frictionless, and frictional; small and finite sliding Boundary conditions constraints, displacement, force, pressure, velocity, acceleration Body conditions body force, acceleration, standard earth gravity, rotational velocity Results deformations, stresses, strains, velocity, acceleration Probe results reaction force (total, x, y, z) "},{"location":"features/#explicit-structural-dynamics-using-openradioss","title":"Explicit Structural Dynamics (using OpenRadioss)","text":"Structural analysis Description Materials Isotropic elasto-plastic (Johnson-Cook, Zerillii-Armstrong, Gray, Cowper-Symonds, Yoshida-Uemori, Hensel-Spittel, voce), Isotropic linear elastic (Hooke's law, Johnson-Cook), hyper-elastic (Ogden, Neo-Hookean, Mooney\u2013Rivlin), visco-elastic (Boltamann, Generalized Maxwell-Kelvin), creep, explosive (JWL), Rock (Drucker-Prager), Hill orthotropic Equation of state Compaction, Gruneisen, ideal gas, linear, LSZK, Murnaghan, NASG, Noble, Polynomial, Puff, Sesame, Tillotson Failure models Alter, Biquad, Chang, Cockcroft, EMC, Energy, Fabric, forming limit diagram, Gurson, Hashin, Johnson, Ladeveze, Mullins effect with Ogden and Roxburgh criteria, NXT, orthotropic biquad, Puck, Spalling, Wierzbicki Element type Solid, shell Contact types bonded, frictionless, and frictional; small and finite sliding Boundary conditions constraints, displacement, force, pressure, velocity, acceleration, etc. Body conditions rigid body, body force, acceleration, standard earth gravity, rotational velocity, etc. Results deformations, stresses, strains, velocity, acceleration, etc"},{"location":"features/#thermal","title":"Thermal","text":"Thermal analysis Description Types Static, and transient Materials linear and nonlinear Initial conditions Initial temperature Boundary conditions temperature, convection, radiation, heat flux, heat flow, perfectly insulated Body conditions Internal heat generation Results temperature "},{"location":"features/#computational-fluid-dynamics-through-su2","title":"Computational Fluid Dynamics (through SU2)","text":"Fluid analysis Description Types Steady-state, and transient Governing equation Euler, Navier-Stokes, RANS Boundary conditions wall, inlet, outlet, pressure, velocity, temperature, convection, heat flux Results velocity, pressure, mass density, pressure coefficient, mach number, energy "},{"location":"features/#electromangetic","title":"Electromangetic","text":"Electromagnetic analysis Description Types Electrostatic, magnetostatic, eigenmode, driven, full-wave transient Materials linear Boundary conditions ground, voltage, symmetry, zero charge, surface charge density, electric displacement, insulting, magnetic vector potential, magnetic flux density Results voltage, electric field, electric displacement, magnetic vector potential, magnetic flux density, magnetic field, energy density "},{"location":"features/#need-new-features","title":"Need new features?","text":"

Feel free to send questions, comments, requests, bug reports, and success stories. Asking for a new feature usually results in adding the request to the TODO list or, if it already is in the list, in assigning higher priority to it.

"},{"location":"glossary/","title":"Glossary","text":""},{"location":"glossary/#a","title":"A","text":""},{"location":"glossary/#b","title":"B","text":""},{"location":"glossary/#c","title":"C","text":""},{"location":"glossary/#d","title":"D","text":""},{"location":"glossary/#e","title":"E","text":""},{"location":"glossary/#f","title":"F","text":""},{"location":"glossary/#g","title":"G","text":""},{"location":"glossary/#h","title":"H","text":""},{"location":"glossary/#i","title":"I","text":""},{"location":"glossary/#j","title":"J","text":""},{"location":"glossary/#k","title":"K","text":""},{"location":"glossary/#l","title":"L","text":""},{"location":"glossary/#m","title":"M","text":""},{"location":"glossary/#n","title":"N","text":""},{"location":"glossary/#o","title":"O","text":""},{"location":"glossary/#p","title":"P","text":""},{"location":"glossary/#r","title":"R","text":""},{"location":"glossary/#s","title":"S","text":""},{"location":"glossary/#t","title":"T","text":""},{"location":"glossary/#u","title":"U","text":""},{"location":"glossary/#v","title":"V","text":""},{"location":"glossary/#w","title":"W","text":""},{"location":"glossary/#y","title":"Y","text":""},{"location":"glossary/#z","title":"Z","text":""},{"location":"license/","title":"License","text":""},{"location":"license/#welsim-license","title":"WELSIM License","text":"

WELSIM SOFTWARE LICENSE AGREEMENT Copyright (C) 2017-2024 WELSIMULATION LLC Version effective date: August 10, 2017

READ THIS SOFTWARE LICENSE AGREEMENT CAREFULLY BEFORE PROCEEDING. THIS IS A LEGALLY BINDING CONTRACT BETWEEN LICENSEE AND LICENSOR FOR LICENSEE TO USE THE PROGRAM(S), AND IT INCLUDES DISCLAIMERS OF WARRANTY AND LIMITATIONS OF LIABILITY. WELSIMULATION LLC IS WILLING TO LICENSE THE SOFTWARE ONLY UPON THE CONDITION THAT YOU ACCEPT ALL OF THE TERMS CONTAINED IN THIS SOFTWARE LICENSE AGREEMENT. PLEASE READ THE TERMS CAREFULLY. BY CLICKING ON \"I AGREE\" OR BY INSTALLING THE SOFTWARE, YOU WILL INDICATE YOUR AGREEMENT WITH THEM. IF YOU ARE ENTERING INTO THIS AGREEMENT ON BEHALF OF A COMPANY OR OTHER LEGAL ENTITY, YOUR ACCEPTANCE REPRESENTS THAT YOU HAVE THE AUTHORITY TO BIND SUCH ENTITY TO THESE TERMS, IN WHICH CASE \"YOU\" OR \"YOUR\" SHALL REFER TO YOUR ENTITY. IF YOU DO NOT AGREE WITH THESE TERMS, OR IF YOU DO NOT HAVE THE AUTHORITY TO BIND YOUR ENTITY, THEN WELSIMULATION LLC IS UNWILLING TO LICENSE THE SOFTWARE, AND YOU SHOULD NOT INSTALL THE SOFTWARE.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

THE ACCOMPANYING PROGRAM IS PROVIDED UNDER THE TERMS OF THIS COMMON PUBLIC LICENSE (\"AGREEMENT\"). ANY USE, REPRODUCTION OR DISTRIBUTION OF THE PROGRAM CONSTITUTES RECIPIENT'S ACCEPTANCE OF THIS AGREEMENT.

This software is provided 'as-is', without any express or implied warranty. In no event will the authors be held liable for any damages or consequences arising from the use of this software.

  1. Parties. The parties to this Agreement are you, the licensee (\"You\") and WELSIMULATION LLC. If You are not acting on behalf of Yourself as an individual, then \"You\" means Your company or organization. A company or organization shall in either case mean a single business entity, and shall not include its affiliates or wholly owned subsidiaries.

  2. The Software. The accompanying materials including, but not limited to, source code, binary executables, documentation, images, and scripts, which are distributed by WELSIMULATION LLC, and derivatives of that collection and/or those files are referred to herein as the \"Software\".

  3. Restrictions. WELSIMULATION LLC encourages You to promote use of the Software. However this Agreement does not grant permission to use the trade names, trademarks, service marks, or product names of WELSIMULATION LLC, except as required for reasonable and customary use in describing the origin of the Software. In particular, You cannot use any of these marks in any way that might state or imply that WELSIMULATION LLC endorses Your work, or might state or imply that You created the Software covered by this Agreement. Except as expressly provided herein, you may not:

    1. modify or translate the Software;
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  5. Infringement Indemnification. You shall defend or settle, at Your expense, any action brought against WELSIMULATION LLC based upon the claim that any modifications to the Software or combination of the Software with products infringes or violates any third party right; provided, however, that: (i) WELSIMULATION LLC shall notify Licensee promptly in writing of any such claim; (ii) WELSIMULATION LLC shall not enter into any settlement or compromise any such claim without Your prior written consent; (iii) You shall have sole control of any such action and settlement negotiations; and (iv) WELSIMULATION LLC shall provide You with commercially reasonable information and assistance, at Your request and expense, necessary to settle or defend such claim. You agree to pay all damages and costs finally awarded against WELSIMULATION LLC attributable to such claim.

  6. No warranty The program is provided on an 'as is' basis, without warranties or conditions of any kind, either express or implied including, without limitation, any warranties or conditions of title, non-infringement, merchantability or fitness for a particular purpose. Each Recipient is solely responsible for determining the appropriateness of using and distributing the Program and assumes all risks associated with its exercise of rights under this Agreement, including but not limited to the risks and costs of program errors, compliance with applicable laws, damage to or loss of data, programs or equipment, and unavailability or interruption of operations.

  7. Licensee Outside The U.S. If You are located outside the U.S.,then the following provisions shall apply: (i) The parties confirm that this Agreement and all related documentation is and will be in the English language; and (ii) You are responsible for complying with any local laws in your jurisdiction which might impact your right to import, export or use the Software, and You represent that You have complied with any regulations or registration procedures required by applicable law to make this license enforceable.

  8. Assignment. Except as expressly provided herein neither this Agreement nor any rights granted hereunder, nor the use of any of the software may be assigned, or otherwise transferred, in whole or in part, by Licensee, without the prior written consent of WELSIMULATION LLC. WELSIMULATION LLC may assign this Agreement in the event of a merger or sale of all or substantially all of the stock of assets of WELSIMULATION LLC without the consent of Licensee. Any attempted assignment will be void and of no effect unless permitted by the foregoing. This Agreement shall inure to the benefit of the parties permitted successors and assigns.

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"},{"location":"misc/","title":"MISC","text":""},{"location":"misc/#comparison-explicit-and-implicit-time-integrations","title":"Comparison explicit and implicit time integrations","text":"\u663e\u5f0f\u7b97\u6cd5 \u9690\u5f0f\u7b97\u6cd5 \u9002\u7528\u95ee\u9898 \u52a8\u529b\u5b66\uff08\u52a8\u6001\uff09 \u9759\u529b\u5b66\uff08\u9759\u6001\uff09\u548c\u52a8\u529b\u5b66\uff08\u52a8\u6001\uff09 \u963b\u5c3c \u4eba\u5de5\u963b\u5c3c \u6570\u503c\u963b\u5c3c \u65f6\u95f4\u6b65\u6c42\u89e3\u65b9\u6cd5 \u77e9\u9635\u4e58\u6cd5 \u7ebf\u6027\u65b9\u7a0b\u7ec4 \u7ec4\u88c5\u521a\u5ea6\u77e9\u9635 \u5426 \u662f \u6570\u636e\u5b58\u50a8\u9700\u6c42 \u5c0f \u5927 \u6bcf\u6b65\u8ba1\u7b97\u901f\u5ea6 \u5feb \u4e2d \u8fed\u4ee3\u6536\u655b\u6027 \u65e0 \u6709 \u786e\u5b9a\u6027 \u6709\u786e\u5b9a\u89e3 \u53ef\u80fd\u662f\u75c5\u6001\u65e0\u786e\u5b9a\u89e3 \u65f6\u95f4\u7a33\u5b9a\u6027 \u6709\u6761\u4ef6 \u65e0\u6761\u4ef6 \u65f6\u95f4\u6b65 \u5c0f \u5927 \u8ba1\u7b97\u7cbe\u5ea6 \u4f4e \u9ad8 Explicit method Implicit method Target problems Dynamic(transient) Static and dynamic(transient) Damping Artificial damping Numerical damping Time stepping method Matrix multiplication Linear algebra equations Assemble stiffness matrix No Yes Data storage requirement Small Large Solving speed each step Quick Mediate Iteration convergence No Yes Solution Certain solution Could be uncertain solution Stability Conditionally stable Unconditionally stable Time step Small Large Accuracy Low High \u5e94\u529b-\u5e94\u53d8\u66f2\u7ebf\u542b\u6709 \u9002\u7528\u7684Mooney-Rivlin\u51fd\u6570 \u53c2\u6570\u6b63\u5b9a\u6027\u8981\u6c42 \u6ca1\u6709\u62d0\u70b9(\u5355\u66f2\u7387) 2-\u62163-\u53c2\u6570 C10 + C01 > 0 1\u4e2a\u62d0\u70b9(\u53cc\u66f2\u7387) 5-\u53c2\u6570

C10 + C01 > 0C20 > 0C02 < 0C20 + C11 + C02 > 0

2\u4e2a\u62d0\u70b9 9-\u53c2\u6570

C10 + C01 > 0C30>0C03 < 0C30 + C21 + C12 + C03 > 0

Strain-stress curve Suitable Mooney-Rivlin model Parameter requirement for positive definiteness No inflection point (single curvature) 2- or 3-parameter C10 + C01 > 0 One inflection point (double curvature) 5-parameter

C10 + C01 > 0C20 > 0C02 < 0C20 + C11 + C02 > 0

Two inflection points 9-parameter

C10 + C01 > 0C30>0C03 < 0C30 + C21 + C12 + C03 > 0

"},{"location":"support/","title":"Support","text":"

Thanks so much for choosing WELSIM! At WELSIM, we want all engineers and scientists to excel. We believe that given the right tools and guidance, all engineers can be highly productive. We strive to provide tools that give their users super powers and we\u2019re happy to provide any guidance we can to help you use them most effectively. If you have any questions or need any help of any kind, don\u2019t hesitate to contact us in whatever way is most convenient for you.

We exist to help you be as productive you can be. Let us know how we can help you. Happy simulation!

"},{"location":"beamsection/beamsection_getstart/","title":"Getting Started","text":"

Using BeamSection is straightforward, this section shows you how to calculate the beam properties step by step.

"},{"location":"beamsection/beamsection_getstart/#graphical-interface","title":"Graphical Interface","text":"

An overview of the Graphical User Interface (GUI) with notation is shown in the figure below.

"},{"location":"beamsection/beamsection_getstart/#menu","title":"Menu","text":"

This section provides you basic actions in using CurveFitter. The actions include:

"},{"location":"beamsection/beamsection_getstart/#toolbox","title":"Toolbox","text":"

This section lists all available curves for you to choose from. The default curve is the straight line (first-order polynomial). The curves are grouped by the characteristics as follows.

"},{"location":"beamsection/beamsection_getstart/#basic-curves","title":"Basic Curves","text":"

Straight line, Natural logarithm, Exponential, Power, Gaussian

"},{"location":"beamsection/beamsection_getstart/#polynomial-curves","title":"Polynomial Curves","text":"

2nd Order Polynomial, 3rd Order Polynomial, 4th Order Polynomial, 5th Order Polynomial

"},{"location":"beamsection/beamsection_getstart/#nonlinear-curves","title":"Nonlinear Curves","text":"

Symmetrical Sigmoidal, Asymmetrical Sigmoidal, Rectangular Hyperbola, Basic Exponential, Half-Life Exponential, Proportional Rate Growth or Decrease

"},{"location":"beamsection/beamsection_getstart/#hyperelastic-material-model-curves","title":"Hyperelastic Material Model Curves","text":"

Arruda-Boyce, Gent, Mooney-Rivlin 2, 3, 5, and 9 Parameters, Neo-Hookean, Ogden 1st-3rd Orders, Polynomial 1st-3rd Orders, Yeoh 1st-3rd Orders

"},{"location":"beamsection/beamsection_getstart/#electromagnetic-model-curves","title":"Electromagnetic Model Curves","text":"

Electrical Steel, Power Ferrite

"},{"location":"beamsection/beamsection_getstart/#curve-description","title":"Curve Description","text":"

This section contains details about the selected curve, such as the function or energy functional, parameters to fit, variable descriptions.

For the hyperelastic model curves, additional Hyperelastic Test Data checkboxes shows in this seciton. It allows users to set/edit the test data at different deformations.

"},{"location":"beamsection/beamsection_getstart/#fitted-parameters","title":"Fitted Parameters","text":"

This section outputs the fitted parameters for users. You also can edit the constants in the line edit widget and review the curves in the Chart window.

"},{"location":"beamsection/beamsection_getstart/#actions","title":"Actions","text":"

There are three actions provided for users to analyze or fit the test data.

"},{"location":"beamsection/beamsection_getstart/#chart-windows","title":"Chart Windows","text":"

This section displays the test data dots and fitted curves in the same window, these dots and curves can be differentiated by legends and colors. Zoom in and out showing area are supported. You also can set the logarithmic axis for the curve display.

"},{"location":"beamsection/beamsection_getstart/#workflow","title":"Workflow","text":"

This section demonstrates the procedures in applying curve fitting. The steps are followed:

  1. Select the designated curve type from the toolbox.

  2. Edit table data or import data from an external file.

  3. Review the test data in the Chart.

  4. Check the input data (Optional). A pop-up message box indicates the status of the input data.

  5. Solve the curves with the input tabular data. If it succeeded, the Constants line edits are filled with fitted parameters, and the Chart window displays the fitted curves along with the test data. These fitted parameters are the answers that we want.

  6. Adjust parameters to evaluate the similar curves (Optional). You can change the parameters and hit the Update Chart button to see the new curves with modified parameters.

Note

Your test data is critical for your fitted constants, please ensure that the test data cover the entire range of your curve expreience.

"},{"location":"beamsection/beamsection_overview/","title":"Beam Cross-Section Overview","text":"

BeamSection is a free beam cross-section software program for engineers. This tool provides you comprehensive beam property calculations those are often used in engineering simulation and practice.

"},{"location":"beamsection/beamsection_overview/#questions-or-comments","title":"Questions or Comments?","text":"

Feel free to send questions, comments, requests, bug reports, and success stories. Asking for a new feature usually results in adding the request to the TODO list or, if it already is in the list, in assigning higher priority to it.

"},{"location":"curvefitter/curvefit_getstart/","title":"Getting Started","text":"

Using CurveFitter is straightforward, this section shows you how to conduct the curve fitting step by step.

"},{"location":"curvefitter/curvefit_getstart/#graphical-interface","title":"Graphical Interface","text":"

An overview of the Graphical User Interface (GUI) with notation is shown in the figure below.

"},{"location":"curvefitter/curvefit_getstart/#menu","title":"Menu","text":"

This section provides you basic actions in using CurveFitter. The actions include:

"},{"location":"curvefitter/curvefit_getstart/#toolbox","title":"Toolbox","text":"

This section lists all available curves for you to choose from. The default curve is the straight line (first-order polynomial). The curves are grouped by the characteristics as follows.

"},{"location":"curvefitter/curvefit_getstart/#basic-curves","title":"Basic Curves","text":"

Straight line, Natural logarithm, Exponential, Power, Gaussian

"},{"location":"curvefitter/curvefit_getstart/#polynomial-curves","title":"Polynomial Curves","text":"

2nd Order Polynomial, 3rd Order Polynomial, 4th Order Polynomial, 5th Order Polynomial

"},{"location":"curvefitter/curvefit_getstart/#nonlinear-curves","title":"Nonlinear Curves","text":"

Symmetrical Sigmoidal, Asymmetrical Sigmoidal, Rectangular Hyperbola, Basic Exponential, Half-Life Exponential, Proportional Rate Growth or Decrease

"},{"location":"curvefitter/curvefit_getstart/#hyperelastic-material-model-curves","title":"Hyperelastic Material Model Curves","text":"

Arruda-Boyce, Gent, Mooney-Rivlin 2, 3, 5, and 9 Parameters, Neo-Hookean, Ogden 1st-3rd Orders, Polynomial 1st-3rd Orders, Yeoh 1st-3rd Orders

"},{"location":"curvefitter/curvefit_getstart/#electromagnetic-model-curves","title":"Electromagnetic Model Curves","text":"

Electrical Steel, Power Ferrite

"},{"location":"curvefitter/curvefit_getstart/#curve-description","title":"Curve Description","text":"

This section contains details about the selected curve, such as the function or energy functional, parameters to fit, variable descriptions.

For the hyperelastic model curves, additional Hyperelastic Test Data checkboxes shows in this seciton. It allows users to set/edit the test data at different deformations.

"},{"location":"curvefitter/curvefit_getstart/#fitted-parameters","title":"Fitted Parameters","text":"

This section outputs the fitted parameters for users. You also can edit the constants in the line edit widget and review the curves in the Chart window.

"},{"location":"curvefitter/curvefit_getstart/#actions","title":"Actions","text":"

There are three actions provided for users to analyze or fit the test data.

"},{"location":"curvefitter/curvefit_getstart/#tabular-data-windows","title":"Tabular Data Windows","text":"

This section enables you to edit and review the table data. For most of curves, the tables have two columns. The frequency-dependent curves have a sub-table for each frequency row. You can input tabular values cell by cell, or import a plain text or Excel file to input massive data. The external file formats are depicted here.

You also can export the tabular data to an external file in plain text or Excel format.

"},{"location":"curvefitter/curvefit_getstart/#chart-windows","title":"Chart Windows","text":"

This section displays the test data dots and fitted curves in the same window, these dots and curves can be differentiated by legends and colors. Zoom in and out showing area are supported. You also can set the logarithmic axis for the curve display.

"},{"location":"curvefitter/curvefit_getstart/#workflow","title":"Workflow","text":"

This section demonstrates the procedures in applying curve fitting. The steps are followed:

  1. Select the designated curve type from the toolbox.

  2. Edit table data or import data from an external file.

  3. Review the test data in the Chart.

  4. Check the input data (Optional). A pop-up message box indicates the status of the input data.

  5. Solve the curves with the input tabular data. If it succeeded, the Constants line edits are filled with fitted parameters, and the Chart window displays the fitted curves along with the test data. These fitted parameters are the answers that we want.

  6. Adjust parameters to evaluate the similar curves (Optional). You can change the parameters and hit the Update Chart button to see the new curves with modified parameters.

Note

Your test data is critical for your fitted constants, please ensure that the test data cover the entire range of your curve expreience.

"},{"location":"curvefitter/curvefit_io/","title":"I/O File Format","text":"

The I/O file format is consistent to the Import/Export format in MatEditor module. For more details please refer to the Import/Export Tabular Data

"},{"location":"curvefitter/curvefit_overview/","title":"Curve Fitter Overview","text":"

CurveFitter is a free software program for nonlinear curve fitting of analytical functions to experimental data. It provides tools for linear, polynomial, exponential, power, Schulz-Flory, nonlinear, hyperelastic materials, magnetic core loss curve fitting along with validation, and goodness-of-fit tests. The easy-to-use graphical user interface enables you to start fitting projects with no learning curves. You can summarize and present your results with customized fitting reports. There are many time-saving options such as an import-export feature which allows you to quickly input/output massive tabular data from/to external files.

Curve fitting is one of the most widely used analysis methods in science and technology. Curve fitting examines the relationship between one or more predictors (independent variables) and a response variable (dependent variable), with the goal of defining a \"best fit\" model of the relationship. It is reportedly used in crystallography, chromatography, photoluminescence and photoelectron spectroscopy, infrared, Raman spectroscopy, and finite element analysis.

"},{"location":"curvefitter/curvefit_overview/#specification","title":"Specification","text":"

The system requirements for running CurveFitter are given in the table below.

Specification Description Operation system Microsoft Windows 10 to 11; 64-bit Physical memory At least 4 GB Import/Export file format Plain text, Excel

The supported functions/curves are listed in the table below.

Category Materials Basic Straight line, Natural logarithm, Exponential, Power, Gaussian Polynomial 2nd-5th Order Polynomial Schulz-Flory 1nd-6th Order Schulz-Flory Nonlinear Symmetrical Sigmoidal, Asymmetrical Sigmoidal, Rectangular Hyperbola, Basic Exponential, Half-Life Exponential, Proportional Rate Growth or Decrease Hyperelastic material model Arruda-Boyce, Gent, Mooney-Rivlin 2 3 5 and 9 Parameters, Neo-Hookean, 1st-3rd Order Ogden, 1st-3rd Order Polynomial, 1st-3rd Order Yeoh Electromagnetic Core loss Model Electrical Steel, Power Ferrite (Steinmetz)"},{"location":"curvefitter/curvefit_overview/#linear-polynomial-regression","title":"Linear, Polynomial Regression","text":"

Linear and Polynomial regressions in CurveFitter make use of the least-square method to fit a linear model function or a polynomial model function to data, respectively.

"},{"location":"curvefitter/curvefit_overview/#nonlinear-curve-fitting","title":"Nonlinear Curve Fitting","text":"

CurveFitter's nonlinear fit tool is powerful, flexible, and easy to use. This tool includes more than 10 built-in fitting functions, selected from a wide range of categories and disciplines.

"},{"location":"curvefitter/curvefit_overview/#hyperelastic-material-model-fitting","title":"Hyperelastic Material Model Fitting","text":"

CurveFitter's hyperelastic model fitting tool allows you to obtain material constants from the uniaxial, biaxial, or shear test data. You can choose the available test data type by toggling the corresponding checkbox. The supported hyperelastic models are: Arruda-Boyce, Gent, Mooney-Rivlin, Neo-Hookean, Ogden, Polynomial, and Yeoh. The input test data is engineering strain and engineering stress.

"},{"location":"curvefitter/curvefit_overview/#magnetic-core-loss-model-fitting","title":"Magnetic Core Loss Model Fitting","text":"

Core Loss Model fitting tool enables you to fit the parameters in estimating energy loss analysis. The tabular data window contains both regular tables and sub-tables for you to input multiple frequency-based data. The chart supports the logarithmic axis to better review the frequency-based curves.

"},{"location":"curvefitter/curvefit_overview/#questions-or-comments","title":"Questions or Comments?","text":"

Feel free to send questions, comments, requests, bug reports, and success stories. Asking for a new feature usually results in adding the request to the TODO list or, if it already is in the list, in assigning higher priority to it.

"},{"location":"curvefitter/curvefit_theory/","title":"Curve Fitting Theory","text":"

The section shows you the theoretical details of each curve or function.

"},{"location":"curvefitter/curvefit_theory/#basic-curves","title":"Basic Curves","text":"

The group of Basic contains all commonly used curves.

"},{"location":"curvefitter/curvefit_theory/#straight-line","title":"Straight line","text":"

The function of this curve is given by

\\[ y(x)=a+bx \\]

where \\(a\\) and \\(b\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair. This function is also called 1st order polynomial.

"},{"location":"curvefitter/curvefit_theory/#natural-logarithm","title":"Natural logarithm","text":"

The function of this curve is given by

\\[ y(x)=a+b \\cdot ln(x) \\]

where \\(a\\) and \\(b\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

Note

Independent variable \\(x\\) must be larger than zero.

"},{"location":"curvefitter/curvefit_theory/#exponential","title":"Exponential","text":"

The function of this curve is given by

\\[ y(x)=ae^{bx} \\]

where \\(a\\) and \\(b\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

Note

Dependent variable \\(y\\) must be larger than zero.

"},{"location":"curvefitter/curvefit_theory/#power","title":"Power","text":"

The function of this curve is given by

\\[ y(x)=ax^{b} \\]

where \\(a\\) and \\(b\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

Note

Variables \\(x\\) and \\(y\\) must be larger than zero.

"},{"location":"curvefitter/curvefit_theory/#gaussian","title":"Gaussian","text":"

The function of this curve is given by

\\[ y(x)=a \\exp{(-\\dfrac{(x-b)^2}{2c^2})} \\]

where \\(a\\), \\(b\\), and \\(c\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

Note

Dependent variables \\(y\\) must be larger than zero.

"},{"location":"curvefitter/curvefit_theory/#polynomial-curves","title":"Polynomial Curves","text":"

The group of Polynomial contains polynomial curves. The first-order polynomial is located in the Basic group as Straight Line.

"},{"location":"curvefitter/curvefit_theory/#2nd-order-polynomial","title":"2nd Order Polynomial","text":"

The function of this curve is given by

\\[ y(x)=a+bx+cx^2 \\]

where \\(a\\), \\(b\\), and \\(c\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

"},{"location":"curvefitter/curvefit_theory/#3rd-order-polynomial","title":"3rd Order Polynomial","text":"

The function of this curve is given by

\\[ y(x)=a+bx+cx^2+dx^3 \\]

where \\(a\\), \\(b\\), \\(c\\), and \\(d\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

"},{"location":"curvefitter/curvefit_theory/#4th-order-polynomial","title":"4th Order Polynomial","text":"

The function of this curve is given by

\\[ y(x)=a+bx+cx^2+dx^3+ex^4 \\]

where \\(a\\), \\(b\\), \\(c\\), \\(d\\), and \\(e\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

"},{"location":"curvefitter/curvefit_theory/#5th-order-polynomial","title":"5th Order Polynomial","text":"

The function of this curve is given by

\\[ y(x)=a+bx+cx^2+dx^3+ex^4+ex^5 \\]

where \\(a\\), \\(b\\), \\(c\\), \\(d\\), \\(e\\), and \\(f\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

"},{"location":"curvefitter/curvefit_theory/#schulz-flory-functions","title":"Schulz-Flory functions","text":"

Schulz Flory distribution function to describe relative ratios of polymers after a polymerization process. The function of this curve is given by

\\[ y(x) = \\sum_{i=1}^{n} ln(10) \\dfrac{a_i}{b_i^2} \\exp{(4.6x-\\dfrac{\\exp{(2.3x)}}{b_i})} \\]

where \\(a_i\\) and \\(b_i\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair. The parameter must satisfy the condition: \\(0<a_i<1\\).

"},{"location":"curvefitter/curvefit_theory/#nonlinear-curves","title":"Nonlinear Curves","text":"

The group of Nonlinear curves contains nonlinear curves that do not belong to the polynomial.

"},{"location":"curvefitter/curvefit_theory/#symmetrical-sigmoidal","title":"Symmetrical Sigmoidal","text":"

The function of this curve is given by

\\[ y(x)=d + \\dfrac{a-d}{1+(\\dfrac{x}{c})^b} \\]

where \\(a\\), \\(b\\), \\(c\\), and \\(d\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

"},{"location":"curvefitter/curvefit_theory/#asymmetrical-sigmoidal","title":"Asymmetrical Sigmoidal","text":"

The function of this curve is given by

\\[ y(x)=d + \\dfrac{a-d}{ (1+(\\dfrac{x}{c})^b)^m } \\]

where \\(a\\), \\(b\\), \\(c\\), \\(d\\), and \\(m\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

"},{"location":"curvefitter/curvefit_theory/#rectangular-hyperbola","title":"Rectangular Hyperbola","text":"

The function of this curve is given by

\\[ y(x)=\\dfrac{V_{max}x}{ K_m + x} \\]

where \\(V_{max}\\) and \\(K_m\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

"},{"location":"curvefitter/curvefit_theory/#basic-exponential","title":"Basic Exponential","text":"

The function of this curve is given by

\\[ y(x)=a + be^{-cx} \\]

where \\(a\\), \\(b\\), and \\(c\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

"},{"location":"curvefitter/curvefit_theory/#half-life-exponential","title":"Half-Life Exponential","text":"

The function of this curve is given by

\\[ y(x)=a + \\dfrac{b}{2^{(\\dfrac{x}{c})}} \\]

where \\(a\\), \\(b\\), and \\(c\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

"},{"location":"curvefitter/curvefit_theory/#proportional-rate-growth-or-decrease","title":"Proportional Rate Growth or Decrease","text":"

The function of this curve is given by

\\[ y(x)=Y_0 + \\dfrac{V_0}{K}(1-e^{-Kx}) \\]

where \\(Y_0\\), \\(V_0\\), and \\(K\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

"},{"location":"curvefitter/curvefit_theory/#log-normal-particle-size-distribution","title":"Log-Normal Particle Size Distribution","text":"

The function of this curve is given by

\\[ \\dfrac{dy(x)}{d\\ln{x}}=\\dfrac{C_t}{\\sigma_g\\sqrt{2}\\pi} \\exp{(-\\dfrac{(\\ln{x}-\\ln{D_m})^2}{2\\ln{\\sigma_g}^2})} \\]

where \\(D_m\\), \\(\\sigma_g\\), and \\(C_t\\) are constants to fit, x and y are test data pair. In the computation, the Left-Hand-Side term (\\(dy(x)/d\\ln{x}\\)) is calculated using finite difference scheme.

Note

Independent variables \\(x\\) must be larger than zero. The number of input x-y pairs must be large than 3.

"},{"location":"curvefitter/curvefit_theory/#hyperelastic-material-model-curves","title":"Hyperelastic Material Model Curves","text":"

The group of hyperelastic material models contains the commonly used hyperelastic models in the finite element analysis. The test data pair is engineering strain and stress.

"},{"location":"curvefitter/curvefit_theory/#arruda-boyce","title":"Arruda-Boyce","text":"

The form of the strain-energy potential for Arruda-Boyce model is

\\[ \\begin{array}{ccl} W & = & \\mu[\\dfrac{1}{2}(\\bar{I}_{1}-3)+\\dfrac{1}{20\\lambda_{m}^{2}}(\\bar{I_{1}^{2}}-9)+\\dfrac{11}{1050\\lambda_{m}^{4}}(\\bar{I_{1}^{3}}-27)\\\\ & + & \\dfrac{19}{7000\\lambda_{m}^{6}}(\\bar{I_{1}^{4}}-81) + \\dfrac{519}{673750\\lambda_{m}^{8}}(\\bar{I_{1}^{5}}-243)] \\end{array} \\]

where \\(\\mu\\) is the initial shear modulus of the material, \\(\\lambda_{m}\\) is limiting network stretch.

"},{"location":"curvefitter/curvefit_theory/#gent","title":"Gent","text":"

The form of the strain-energy potential for the Gent model is:

\\[ W=-\\frac{\\mu J_{m}}{2}\\mathrm{ln}\\left(1-\\frac{\\bar{I}_{1}-3}{J_{m}}\\right) \\]

where \\(\\mu\\) is the initial shear modulus of the material, \\(J_m\\) is limiting value of \\(\\bar{I}_1-3\\).

"},{"location":"curvefitter/curvefit_theory/#mooney-rivlin-2-3-5-and-9-parameters","title":"Mooney-Rivlin 2 3 5 and 9 Parameters","text":"

This model includes two-, three-, five-, and nine-terma Mooney-Rivlin models. The form of the strain-energy potential for a two-parameter Mooney-Rivlin model is

\\[ W=C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right) \\]

where \\(C_{10}\\), \\(C_{01}\\), and \\(D_{1}\\) are the material constants.

The form of strain-energy potential for a three-parameter Mooney-Rivlin model is

\\[ W=C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right)+C_{11}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right) \\]

where \\(C_{10}\\), \\(C_{01}\\), and \\(C_{11}\\) are material constants.

The form of strain-energy potential for a five-parameter Mooney-Rivlin model is

\\[ \\begin{array}{ccl} W & = & C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right)+C_{20}\\left(\\bar{I}_{1}-3\\right)^{2}\\\\ & + & C_{11}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right)+C_{02}\\left(\\bar{I}_{2}-3\\right)^{2} \\end{array} \\]

where \\(C_{10}\\), \\(C_{01}\\), \\(C_{20}\\), \\(C_{11}\\), and \\(C_{02}\\) are material constants.

The form of strain-energy potential for a nine-parameter Mooney-Rivlin model is

\\[ \\begin{array}{ccl} W & = & C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right)+C_{20}\\left(\\bar{I}_{1}-3\\right)^{2}\\\\ & + & C_{11}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right)+C_{02}\\left(\\bar{I}_{2}-3\\right)^{2}+C_{30}\\left(\\bar{I}_{1}-3\\right)^{3}\\\\ & + & C_{21}\\left(\\bar{I}_{1}-3\\right)^{2}\\left(\\bar{I}_{2}-3\\right)+C_{12}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right)^{2}+C_{03}\\left(\\bar{I}_{2}-3\\right)^{3} \\end{array} \\]

where \\(C_{10}\\), \\(C_{01}\\), \\(C_{20}\\), \\(C_{11}\\), \\(C_{02}\\), \\(C_{30}\\), \\(C_{21}\\), \\(C_{12}\\), and \\(C_{03}\\) are material constants.

"},{"location":"curvefitter/curvefit_theory/#neo-hookean","title":"Neo-Hookean","text":"

The Neo-Hookean model is a well-known hyperelastic model with an expanded linear rule (Hooke rule) having isotropy so that it can respond to finite deformation problems. The elastic potential is as follows.

\\[ W=\\frac{\\mu}{2}(\\bar{I}_{1}-3) \\]

where \\(\\mu\\) is initial shear modulus of materials.

"},{"location":"curvefitter/curvefit_theory/#ogden","title":"Ogden","text":"

The strain-energy potential of the Ogden compressible foam model is based on the principal stretches of left Cauchy strain tensor, which has the form:

\\[ W=\\sum_{i=1}^{N}\\frac{\\mu_{i}}{\\alpha_{i}}\\left(\\bar{\\lambda}_{1}^{\\alpha_{i}}+\\bar{\\lambda}_{2}^{\\alpha_{i}}+\\bar{\\lambda}_{3}^{\\alpha_{i}}-3\\right)+\\sum_{k=1}^{N}\\frac{1}{D_{k}}\\left(J-1\\right)^{2k} \\]

where N determines the order of the polynomial, \\(\\mu_i\\), \\(\\alpha_i\\) are material constants. The reduced principal strench is defined by:

\\[ \\bar{\\lambda}_{p}=J^{-\\frac{1}{3}}\\lambda_p,\\; J=(\\lambda_{1}\\lambda_{2}\\lambda_{3})^{\\frac{1}{2}} \\]

When parameters N=1, \\(\\alpha_1\\)=2, the Ogden model is converted to the neo-Hookean model. When parameters N=2, \\(\\alpha_1\\)=2 and \\(\\alpha_2\\)=-2, the Ogden model is converted to the 2-parameter Mooney-Rivlin model.

"},{"location":"curvefitter/curvefit_theory/#polynomial","title":"Polynomial","text":"

The polynomial form of strain-energy potential is:

\\[ W=\\sum_{i+j=1}^{N}c_{ij}\\left(\\bar{I}_{1}-3\\right)^{i}\\left(\\bar{I_{2}}-3\\right)^{j} \\]

where \\(N\\) determines the order of the polynomial, \\(c_{ij}\\) are material constants.

The Polynomial model is converted to following models with specific parameters:

Parameters of Polynomial model Equivalent model N=1, \\(C_{01}\\)=0 neo-Hookean N=1 2-parameter Mooney-Rivlin N=2 5-parameter Mooney-Rivlin N=3 9-parameter Mooney-Rivlin"},{"location":"curvefitter/curvefit_theory/#yeoh","title":"Yeoh","text":"

The Yeoh model is also called the reduced polynomial form. The strain-energy potential is

\\[ W=\\sum_{i=1}^{N}c_{i0}\\left(\\bar{I}_{1}-3\\right)^{i} \\]

where N denotes the order of the polynomial, \\(C_{i0}\\) are material constants. When N=1, Yeoh becomes neo-Hookean model.

"},{"location":"curvefitter/curvefit_theory/#electromagnetic-model-curves","title":"Electromagnetic Model Curves","text":"

This group includes the commonly used fitting curves in the electromagnetic analysis.

"},{"location":"curvefitter/curvefit_theory/#electrical-steel","title":"Electrical Steel","text":"

The iron-core loss without DC flux bias is expressed as the following:

\\[ p_v=P_h+P_c+P_e=K_{f} f (B_m)^2 + K_c (fB_m)^2 + K_e(fB_m)^{1.5} \\]

where

"},{"location":"curvefitter/curvefit_theory/#power-ferrite","title":"Power Ferrite","text":"

The iron-core loss is expressed as the Steinmetz approximation

\\[ p_v=C_m f^x B_m^y \\]

where \\(p_v\\) is the average power density, \\(f\\) is the excitation frequency, and \\(B_m\\) is the peak flux density, is commonly used to characterize core loss data for sinusoidal excitation, but can also be applied to square-wave data.

To linearize the equation for curve fitting, we used base-10 logarithms. The equation above can be rewritten to

\\[ log(p_v)=c + x\\cdot log(f) + y \\cdot(B_m) \\]

where \\(c=log(C_m)\\).

"},{"location":"install/licensing/","title":"WELSIM licensing guide","text":""},{"location":"install/licensing/#preface","title":"Preface","text":"

This document contains information for running the WELSIM License Manager with all WelSimulation LLC products.

"},{"location":"install/licensing/#supported-hardware-platforms","title":"Supported hardware platforms","text":"

This document details information about licensing WelSimulation LLC products on the hardware platforms listed below.

For specific operating system requirements, contact the customer support for the product and platform you are running.

"},{"location":"install/licensing/#conventions-used-in-this-document","title":"Conventions used in this document","text":"

Computer prompts and responses and user input are printed using this font:

/welsim_com/shared_files/licensing/welslic_admin\n

Wild card arguments and variables are italicized. Commands appear in bold face.

"},{"location":"install/licensing/#introduction","title":"Introduction","text":"

WelSimulation LLC uses the internal license manager for all of its licensed products. The communication between the WELSIM applications and license manager occurs through an internal process. The communication is nearly transparent; you should not see any noticeable difference in your day-to-day operation of WELSIM products.

You do not need to run the license manager installation. The license manager is installed together with the WELSIM application package.

"},{"location":"install/licensing/#the-licensing-process","title":"The licensing process","text":"

The licensing process for WELSIM is as follows:

  1. Install the software.
  2. Start the software and generate your unique Computer ID, send the Computer ID to info@welsim.com.
  3. After you receive your license file, run the License Manager Wizard from Toolbar of WELSIM application.
  4. Set up the licensing environment and input license. See Activating the WELSIM.
"},{"location":"install/licensing/#explanation-of-licensing-terms","title":"Explanation of licensing terms","text":"

The main components of the licensing are:

These components are explained in more detail in the following sections.

"},{"location":"install/licensing/#the-license-file","title":"The license file","text":"

Licensing data is stored in a text file called the license file. The license file is created by WelSimulation LLC and is installed by the end user. It contains information about the version, signature, and date.

The default and recommended location for the WELSIM license file (wsimkey.dat) is in the %APPDATA%/WELSIM directory. The application can automatically place the license file at this location after activation. End users can manually copy the license file to that directory, although are not suggested.

"},{"location":"install/licensing/#license-file-format","title":"License file format","text":"

License files usually contain eight lines. You cannot modify any these data items in the license files.

Note

Everything in the license key should be entered exactly as supplied. All data in the license file is case sensitive, unless otherwise indicated.

"},{"location":"install/licensing/#application-line","title":"Application line","text":"

The application line specifies the application name. Normally a license file for WELSIM application uses the \u201c[WELSIM]\u201d. The example of the application line is: 

[WELSIM]\n

"},{"location":"install/licensing/#license-version-line","title":"License version line","text":"

The license version line specifies the version of current license file. The example of the this line is shown below: 

license_verion = 100\n

"},{"location":"install/licensing/#license-signature-line","title":"License signature line","text":"

A license signature line describes the password key to use a product. The example of the signature line is: 

license_signature = Tvp919deAq5od+nCUjRF15mgeBIKCLgscLgvR8eFYAlBrqqcjETIyuY0Lu/brYbOKYrIPOXqFzWn8asLqieImA== \n

"},{"location":"install/licensing/#computer-id-line","title":"Computer ID line","text":"

The computer ID line is the string generated from client's computer. The example of the Computer ID line is: 

client_signature = KXfe-uAAA-KXfe-uQAA\n

"},{"location":"install/licensing/#application-version-lines","title":"Application version lines","text":"

The application version lines include two parts, one is the start version number and another is the end version. The example of the application version lines are: 

from_sw_version = 100\nto_sw_version = 100\n

"},{"location":"install/licensing/#effective-date-lines","title":"Effective date lines","text":"

The effective date lines include both start and end date. The example of the effective date lines are: 

from_date = 2017-07-02\nto_date = 2018-08-02\n

"},{"location":"install/licensing/#sample-license-files","title":"Sample license files","text":"

A sample license file is shown here. This file is for WELSIM v1.8 and later tasks. 

[WELSIM]\nlicense_version = 100\nlicense_signature = Tvp919deAq5od+nCUjRF15mgeBIKCLgscLgvR8eFYAlBrqqcjETIyuY0Lu/brYbOKYrIPOXqFzWn8asLqieImA==\nclient_signature = KXfe-uAAA-KXfe-uQAA\nfrom_sw_version = 100\nto_sw_version = 100\nfrom_date = 2023-07-02\nto_date = 2024-07-02\n

"},{"location":"install/licensing/#recognizing-a-welsim-license-file","title":"Recognizing a WELSIM license file","text":"

If you receive a license file and are not sure if it is a WELSIM license file, you can determine if it is by looking at the contents of the license file. If it is a WELSIM license file, then

"},{"location":"install/licensing/#installing-the-welsim-license-manager","title":"Installing the WELSIM license manager","text":"

The WelSim License Manager is included in the WELSIM application installation. As the user installs the application, the license manager is already installed.

"},{"location":"install/licensing/#troubleshooting","title":"Troubleshooting","text":"

This section lists problems and error messages that you may encounter while setting up licensing. The possible error messages are:

An example of the license message error message is shown in Figure\u00a0[fig:ch10_license_not_found].

"},{"location":"install/linux/","title":"Linux installation guide","text":""},{"location":"install/linux/#installation-prerequisites-for-linux","title":"Installation prerequisites for Linux","text":"

This document describes the steps necessary to correctly install and configure WELSIM application on Linux platforms. These products include:

"},{"location":"install/linux/#system-prerequisites","title":"System prerequisites","text":"

WELSIM application is supported on the Linux platforms and operating system levels listed in Table\u00a0below.

Platform Operating system Availability Linux x64 Ubuntu 22.04 LTS or higher Download

Note

  1. If you run WELSIM on Ubuntu, we recommand Ubuntu 22.04 LTS or higher with the latest libstdc++ and libfortran libraries.
"},{"location":"install/linux/#disk-space-and-memory-requirements","title":"Disk space and memory requirements","text":"

You will need the disk space shown in Table\u00a0below for installation and proper functioning.

Product Disk space Memory WELSIM application at least 1 GB at least 4 GB"},{"location":"install/linux/#platform-details","title":"Platform details","text":"

For all 64-bit Linux platforms, the libraries listed below should be installed.

"},{"location":"install/linux/#installing-the-welsim-for-a-linux-system","title":"Installing the WELSIM for a Linux system","text":"

This section explains how to download and install WELSIM.

You can install WELSIM as root, or non-root; however, if you are root user, you can install the application in the system directory. The application can be used by different users.

"},{"location":"install/linux/#product-download-instructions","title":"Product download instructions","text":"

To download the installation files from our website, you will need to agree the US Export Restrictions. You only need to download one installer file.

  1. From the website1, select the Linux version of WELSIM and click the download button on the webpage.
  2. The downloaded installer file has the name like: WelSim%version%SetupUbuntu.run. For example, the installer of 2024R1 is WelSim28SetupUbuntu.run.
  3. Begin the product installation as described in the next section.
"},{"location":"install/linux/#production-installation","title":"Production installation","text":"

1.Navigate to the directory where you placed the installer file. Run the commands below in a terminal window. Note that we take the version of 2024R1 as an example, if you are installing a different version, replace the installer name in the command line below. 

$ chmod +x WelSim28SetupUbuntu.run\n$ ./WelSim28SetupUbuntu.run\n

Note

Running the installer requires the libxcb-xinerama0 library installed in your system.

2.The WELSIM installation Launcher appears as shown below.

3.Click the Next button to start the installation on your computer.

4.The installation folder setting appears as shown below. You can input your designated directory or keep the default one. After specifying the directory, Click Next.

5.The component selection interface appears as shown below. You can select the components that you want to install. The user can keep the default selection, and know the occupied disk space for this installation. Click Next.

6.The license agreement appears as shown below. Read the agreement, and if you agree to the terms and conditions, select I Agree. Click Next.

7.The installation needs your conformation to start as shown below. Click Install.

8.The installation completed as shown below. Click Next.

"},{"location":"install/linux/#starting-the-software-on-linux","title":"Starting the software on Linux","text":"

After installation, starting the WELSIM software application is straightforward. Here are steps:

1.Install the dependencies to your Ubuntu OS 

sudo apt update\nsudo apt upgrade\nsudo apt install openmpi-bin libomp-dev\n

2.Allocate the installed WELSIM application folder, double click the executable file runWelSim.

Note

If the WELSIM does not start, the executable file may have no exectuable attribute on your machine. You could open a terminal window and type commends below. 

$ chmod +x runWelSim.sh\n$ ./runWelSim.sh \n

3.WELSIM application starts, the GUI shows the system information in Figure\u00a0below.

"},{"location":"install/linux/#uninstalling-the-software","title":"Uninstalling the software","text":"

To uninstall WELSIM, you can browse file explorer into the installation folder, and double click on the Uninstaller. Following the instructions on the Uninstaller, you can remove the application from your computer.

You also can simply delete the installation folder to uninstall the WELSIM.

  1. https://welsim.com/download \u21a9

"},{"location":"install/windows/","title":"Windows installation guide","text":""},{"location":"install/windows/#installation-prerequisites-for-windows","title":"Installation prerequisites for Windows","text":"

This document describes the steps essential to correctly install and configure WELSIM on Windows platform.

"},{"location":"install/windows/#system-prerequisites","title":"System prerequisites","text":"

WELSIM is supported on the following Windows platforms and operating system levels.

Platform Operating System Platform Architecture Availability x64 Windows 11 winx64 Download"},{"location":"install/windows/#disk-space-and-memory-requirements","title":"Disk space and memory requirements","text":"

You will need the disk space shown in Table\u00a0[tab:ch11_win_disk_space] for installation and proper functioning. The numbers listed here are the maximum amount of disk space you will need.

Product Disk Space Memory WELSIM 1 GB at least 4GB"},{"location":"install/windows/#software-prerequisites","title":"Software prerequisites","text":"

You need to have the following software installed on your system. These software prerequisites will be installed automatically when you launch the product installation. If you have finished an installation successfully, the prerequisites executable are located under the %Installed Folder%\\Prerequisites directory.

"},{"location":"install/windows/#digital-signatures","title":"Digital signatures","text":"

WELSIM installer and executable files are signed with digital certificates. The signer name is: WelSimulation LLC.

"},{"location":"install/windows/#platform-details","title":"Platform details","text":""},{"location":"install/windows/#compiler-requirements-for-windows-systems","title":"Compiler requirements for Windows systems","text":"

The compiler requirements for Windows systems are listed in Table\u00a0[tab:ch12_win_compiler_req].

No. WELSIM Compilers 1 Visual Studio 2022 (including the Microsoft C++ compiler) 2 Intel Visual Fortran 2022 compiler

Note

Those compilers are not required if you only use WELSIM application.

"},{"location":"install/windows/#installing-the-welsim-for-a-windows-system","title":"Installing the WELSIM for a Windows system","text":"

This section includes the steps required for installing WELSIM and licensing configuration on one Windows machine.

"},{"location":"install/windows/#downloading-the-installation-file","title":"Downloading the installation file","text":"

To download the installation files from our website, you will need to agree the US Export Restrictions.

You only need to download one installer file.

  1. From the website, select the Windows version of WELSIM and click the download button on the webpage.
  2. The downloaded installer file has the name: WelSim28Setup.exe
  3. Begin the product installation as described in the next section.
"},{"location":"install/windows/#installing-welsim","title":"Installing WELSIM","text":"
  1. Navigate to the directory where you placed the installer file. Run the installer by double click.
  2. The WELSIM installation Launcher appears as shown in Figure\u00a0below.
  3. Click the Next button to start the installation on your computer.
  4. The license agreement appears as shown in Figure\u00a0below. Read the agreement, and if you agree to the terms and conditions, select I Agree. Click Next.
  5. The installation folder setting appears as shown in the figure below. You can input your designated directory or keep the default one. After specifying the directory, Click Next.
  6. The prerequesites libraries installation appears as shown in the figure below. Your system requires these libraries to run the WELSIM application. Click Yes.
  7. The installation completed as shown in the figure\u00a0below. Click Finish.

Note

WELSIM relies on the latest version of Microsoft MPI. If the Microsoft MPI redistributable installation conflicts with your pre-existing MS MPI libraries, please uninstall the pre-existing MPI from the Control Panel and reinstall the WELSIM.

"},{"location":"install/windows/#activating-the-welsim","title":"Activating the WELSIM","text":"

In this section, assuming you already received the license file wsimkey.dat. To activate WELSIM on your computer with client licensing, you can follow the steps below:

  1. Start WELSIM application on your computer.
  2. Click the License Manager from the menu: HELP -> License Manager
  3. WELSIM License Manager user interface appears. There are five buttons on the interface:
    1. Generate Computer ID: generate user's unique ID for license key generation.
    2. Evaluate: click to continue using the trial version.
    3. Exit: quit the License Manager with no software activation.
    4. Buy Now: open your default internet browser and direct your visit to the pricing page.
    5. Enter Code: If you have received the license key file, click this button to import the license file.
  4. If the user are running software at the first time, generate the Computer ID by clicking the button of \u201cGenerate Computer ID\u201d, and send this string (format of xxxx-xxxx-xxxx-xxxx) to info@welsim.com. The user will receive the license key within 24 hours.
  5. After receiving the license file (wsimkey.dat), click \u201cEnter Code\u201d button to import the license. In the License Code interface, the user can paste the license content from clipboard, or directly import the license from file.
  6. Click OK button to activate the WELSIM. A successfully activated software is shown in figure\u00a0below.

"},{"location":"install/windows/#starting-the-software","title":"Starting the software","text":"

After installation, starting the WELSIM software is straightforward. Here are three methods:

  1. Double click the shortcut of WELSIM, if you toggle the option \u201cCreate Desktop Shortcut\u201d during the last step of installation.
  2. Click the shortcut of WELSIM from the Start menu. From Start -> WELSIM ->WELSIM v1.8.
  3. Browse the directory of installation, double click the runWelSim.exe file.

As shown in the figure\u00a0below, WESLIM application is started successfully on the Windows operation system.

"},{"location":"install/windows/#uninstalling-the-software","title":"Uninstalling the software","text":"

Uninstalling the software is straightforward. The user can run the unint.exe from one of methods below:

  1. Click the shortcut of WELSIM uninstaller from the Start menu. From Start -> WELSIM ->Uninstall.
  2. Browse the directory of installation, double click the uninst.exe file.
  3. Unstall the WELSIM application from the system Control Panel.
"},{"location":"legal/","title":"Legal notice","text":""},{"location":"legal/#copyright-and-trademark-information","title":"Copyright and trademark information","text":"

\u00a92023 WelSimulation LLC. All rights reserved. Unauthorized use, distribution or duplication is prohibited.

WELSIM and any and all WelSimulation LLC brand, product, service and feature names, logos and slogans are registered trademarks or trademarks of WelSimulation LLC. or its subsidiaries in the United States or other countries. All other brand, product, service and feature names or trademarks are the property of their respective owners.

"},{"location":"legal/#disclaimer-notice","title":"Disclaimer notice","text":"

THIS WELSIM SOFTWARE PRODUCT AND PROGRAM DOCUMENTATION INCLUDE TRADE SECRETS AND ARE CONFIDENTIAL AND PROPRIETARY PRODUCTS OF WELSIMULATION LLC, ITS SUBSIDIARIES, OR LICENSORS. The software products and documentation are furnished by WelSimulation LLC, its subsidiaries, or affiliates under a software license agreement that contains provisions concerning non-disclosure, copying, length and nature of use, compliance with exporting laws, warranties, disclaimers, limitations of liability, and remedies, and other provisions. The software products and documentation may be used, disclosed, transferred, or copied only in accordance with the terms and conditions of that software license agreement.

"},{"location":"legal/#us-government-rights","title":"U.S. government rights","text":"

For U.S. Government users, except as specifically granted by the WelSimulation LLC software license agreement, the use, duplication, or disclosure by the United States Government is subject to restrictions stated in the WelSimulation LLC software license agreement.

"},{"location":"legal/#third-party-software","title":"Third-party software","text":"

This product may contain the following licensed software which requires reproduction of the following notices.

"},{"location":"legal/LGPL/","title":"GNU Lesser Genreal Public License (LGPL)","text":""},{"location":"legal/LGPL/#version-3-gnu-lesser-general-public-license","title":"Version 3 GNU Lesser General Public License","text":"

Version 3, 29 June 2007

Copyright \u00a9 2007 Free Software Foundation, Inc. http://fsf.org/

Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed.

This version of the GNU Lesser General Public License incorporates the terms and conditions of version 3 of the GNU General Public License, supplemented by the additional permissions listed below.

  1. Additional Definitions. As used herein, \u201cthis License\u201d refers to version 3 of the GNU Lesser General Public License, and the \u201cGNU GPL\u201d refers to version 3 of the GNU General Public License.

    \u201cThe Library\u201d refers to a covered work governed by this License, other than an Application or a Combined Work as defined below.

    An \u201cApplication\u201d is any work that makes use of an interface provided by the Library, but which is not otherwise based on the Library. Defining a subclass of a class defined by the Library is deemed a mode of using an interface provided by the Library.

    A \u201cCombined Work\u201d is a work produced by combining or linking an Application with the Library. The particular version of the Library with which the Combined Work was made is also called the \u201cLinked Version\u201d.

    The \u201cMinimal Corresponding Source\u201d for a Combined Work means the Corresponding Source for the Combined Work, excluding any source code for portions of the Combined Work that, considered in isolation, are based on the Application, and not on the Linked Version.

    The \u201cCorresponding Application Code\u201d for a Combined Work means the object code and/or source code for the Application, including any data and utility programs needed for reproducing the Combined Work from the Application, but excluding the System Libraries of the Combined Work.

  2. Exception to Section 3 of the GNU GPL. You may convey a covered work under sections 3 and 4 of this License without being bound by section 3 of the GNU GPL.

  3. Conveying Modified Versions.

    If you modify a copy of the Library, and, in your modifications, a facility refers to a function or data to be supplied by an Application that uses the facility (other than as an argument passed when the facility is invoked), then you may convey a copy of the modified version:

    1. under this License, provided that you make a good faith effort to ensure that, in the event an Application does not supply the function or data, the facility still operates, and performs whatever part of its purpose remains meaningful, or

    2. under the GNU GPL, with none of the additional permissions of this License applicable to that copy.

  4. Object Code Incorporating Material from Library Header Files. The object code form of an Application may incorporate material from a header file that is part of the Library. You may convey such object code under terms of your choice, provided that, if the incorporated material is not limited to numerical parameters, data structure layouts and accessors, or small macros, inline functions and templates (ten or fewer lines in length), you do both of the following:

    1. Give prominent notice with each copy of the object code that the Library is used in it and that the Library and its use are covered by this License.

    2. Accompany the object code with a copy of the GNU GPL and this license document.

  5. Combined Works. You may convey a Combined Work under terms of your choice that, taken together, effectively do not restrict modification of the portions of the Library contained in the Combined Work and reverse engineering for debugging such modifications, if you also do each of the following:

    1. Give prominent notice with each copy of the Combined Work that the Library is used in it and that the Library and its use are covered by this License.
    2. Accompany the Combined Work with a copy of the GNU GPL and this license document.
    3. For a Combined Work that displays copyright notices during execution, include the copyright notice for the Library among these notices, as well as a reference directing the user to the copies of the GNU GPL and this license document.

    4. Do one of the following:

      1. Convey the Minimal Corresponding Source under the terms of this License, and the Corresponding Application Code in a form suitable for, and under terms that permit, the user to recombine or relink the Application with a modified version of the Linked Version to produce a modified Combined Work, in the manner specified by section 6 of the GNU GPL for conveying Corresponding Source.

      2. Use a suitable shared library mechanism for linking with the Library. A suitable mechanism is one that (a) uses at run time a copy of the Library already present on the user's computer system, and (b) will operate properly with a modified version of the Library that is interface-compatible with the Linked Version.

    5. Provide Installation Information, but only if you would otherwise be required to provide such information under section 6 of the GNU GPL, and only to the extent that such information is necessary to install and execute a modified version of the Combined Work produced by recombining or relinking the Application with a modified version of the Linked Version. (If you use option 4d0, the Installation Information must accompany the Minimal Corresponding Source and Corresponding Application Code. If you use option 4d1, you must provide the Installation Information in the manner specified by section 6 of the GNU GPL for conveying Corresponding Source.)

  6. Combined Libraries. You may place library facilities that are a work based on the Library side by side in a single library together with other library facilities that are not Applications and are not covered by this License, and convey such a combined library under terms of your choice, if you do both of the following:

    1. Accompany the combined library with a copy of the same work based on the Library, uncombined with any other library facilities, conveyed under the terms of this License.
    2. Give prominent notice with the combined library that part of it is a work based on the Library, and explaining where to find the accompanying uncombined form of the same work.

  7. Revised Versions of the GNU Lesser General Public License. The Free Software Foundation may publish revised and/or new versions of the GNU Lesser General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns.

    Each version is given a distinguishing version number. If the Library as you received it specifies that a certain numbered version of the GNU Lesser General Public License \u201cor any later version\u201d applies to it, you have the option of following the terms and conditions either of that published version or of any later version published by the Free Software Foundation. If the Library as you received it does not specify a version number of the GNU Lesser General Public License, you may choose any version of the GNU Lesser General Public License ever published by the Free Software Foundation.

    If the Library as you received it specifies that a proxy can decide whether future versions of the GNU Lesser General Public License shall apply, that proxy's public statement of acceptance of any version is permanent authorization for you to choose that version for the Library.

"},{"location":"legal/LGPL/#version-21","title":"Version 2.1","text":"

GNU LESSER GENERAL PUBLIC LICENSE (LGPL) Version 2.1, February 1999 Copyright \u00a9 1991, 1999, Free Software Foundation, Inc. 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA

WelSimulation LLC will provide you with a complete machine-readable copy of the source code, valid for three years. The source code can be obtained by contacting WelSimulation LLC at info@welsim.com.

Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. NO WARRANTY BECAUSE THE LIBRARY IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY FOR THE LIBRARY, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE LIBRARY \"AS IS\" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE LIBRARY IS WITH YOU. SHOULD THE LIBRARY PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.

"},{"location":"legal/LGPL/#gnu-lesser-general-public-license","title":"GNU Lesser General Public License","text":"

Version 2.1

Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed.

Preamble

The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public Licenses are intended to guarantee your freedom to share and change free software--to make sure the software is free for all its users.

This license, the Lesser General Public License, applies to some specially designated software packages--typically libraries--of the Free Software Foundation and other authors who decide to use it. You can use it too, but we suggest you first think carefully about whether this license or the ordinary General Public License is the better strategy to use in any particular case, based on the explanations below.

When we speak of free software, we are referring to freedom of use, not price. Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software (and charge for this service if you wish); that you receive source code or can get it if you want it; that you can change the software and use pieces of it in new free programs; and that you are informed that you can do these things.

To protect your rights, we need to make restrictions that forbid distributors to deny you these rights or to ask you to surrender these rights. These restrictions translate to certain responsibilities for you if you distribute copies of the library or if you modify it.

For example, if you distribute copies of the library, whether gratis or for a fee, you must give the recipients all the rights that we gave you. You must make sure that they, too, receive or can get the source code. If you link other code with the library, you must provide complete object files to the recipients, so that they can relink them with the library after making changes to the library and recompiling it. And you must show them these terms so they know their rights.

We protect your rights with a two-step method: (1) we copyright the library, and (2) we offer you this license, which gives you legal permission to copy, distribute and/or modify the library.

To protect each distributor, we want to make it very clear that there is no warranty for the free library. Also, if the library is modified by someone else and passed on, the recipients should know that what they have is not the original version, so that the original author's reputation will not be affected by problems that might be introduced by others.

Finally, software patents pose a constant threat to the existence of any free program. We wish to make sure that a company cannot effectively restrict the users of a free program by obtaining a restrictive license from a patent holder. Therefore, we insist that any patent license obtained for a version of the library must be consistent with the full freedom of use specified in this license.

Most GNU software, including some libraries, is covered by the ordinary GNU General Public License. This license, the GNU Lesser General Public License, applies to certain designated libraries, and is quite different from the ordinary General Public License. We use this license for certain libraries in order to permit linking those libraries into non-free programs.

When a program is linked with a library, whether statically or using a shared library, the combination of the two is legally speaking a combined work, a derivative of the original library. The ordinary General Public License therefore permits such linking only if the entire combination fits its criteria of freedom. The Lesser General Public License permits more lax criteria for linking other code with the library.

We call this license the \"Lesser\" General Public License because it does Less to protect the user's freedom than the ordinary General Public License. It also provides other free software developers Less of an advantage over competing non-free programs. These disadvantages are the reason we use the ordinary General Public License for many libraries. However, the Lesser license provides advantages in certain special circumstances.

For example, on rare occasions, there may be a special need to encourage the widest possible use of a certain library, so that it becomes a de-facto standard. To achieve this, non-free programs must be allowed to use the library. A more frequent case is that a free library does the same job as widely used non-free libraries. In this case, there is little to gain by limiting the free library to free software only, so we use the Lesser General Public License.

In other cases, permission to use a particular library in non-free programs enables a greater number of people to use a large body of free software. For example, permission to use the GNU C Library in non-free programs enables many more people to use the whole GNU operating system, as well as its variant, the GNU/Linux operating system.

Although the Lesser General Public License is Less protective of the users' freedom, it does ensure that the user of a program that is linked with the Library has the freedom and the wherewithal to run that program using a modified version of the Library.

The precise terms and conditions for copying, distribution and modification follow. Pay close attention to the difference between a \"work based on the library\" and a \"work that uses the library\". The former contains code derived from the library, whereas the latter must be combined with the library in order to run.

GNU LESSER GENERAL PUBLIC LICENSE

TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION

  1. This License Agreement applies to any software library or other program which contains a notice placed by the copyright holder or other authorized party saying it may be distributed under the terms of this Lesser General Public License (also called \"this License\"). Each licensee is addressed as \"you\".

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The \"Library\", below, refers to any such software library or work which has been distributed under these terms. A \"work based on the Library\" means either the Library or any derivative work under copyright law: that is to say, a work containing the Library or a portion of it, either verbatim or with modifications and/or translated straightforwardly into another language. (Hereinafter, translation is included without limitation in the term \"modification\".)

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  1. You may copy and distribute verbatim copies of the Library's complete source code as you receive it, in any medium, provided that you conspicuously and appropriately publish on each copy an appropriate copyright notice and disclaimer of warranty; keep intact all the notices that refer to this License and to the absence of any warranty; and distribute a copy of this License along with the Library.

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  1. You may modify your copy or copies of the Library or any portion of it, thus forming a work based on the Library, and copy and distribute such modifications or work under the terms of Section 1 above, provided that you also meet all of these conditions:

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Once this change is made in a given copy, it is irreversible for that copy, so the ordinary GNU General Public License applies to all subsequent copies and derivative works made from that copy.\\noindent

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END OF TERMS AND CONDITIONS

"},{"location":"legal/contact/","title":"WelSimulation LLC contact information","text":"

WelSimulation LLC

1840 Mayview Rd. Suite 208

Bridgeville, PA 15017

USA

Email: info@welsim.com

Website: https://welsim.com

Phone: +1 724-914-8722

"},{"location":"legal/trademarks/","title":"WELSIM Trademarks List","text":""},{"location":"mateditor/mat_core_loss/","title":"Core loss model","text":"

The core loss combines eddy current losses and hysteresis losses for a transient solution type. It is a post-processing calculation, based on already calculated transient magnetic field quantities. It is applicable for the evaluation of core losses in steel laminations (frequently used in applications such as electric machines, transformers) or in power ferrites.

Hysteresis loss is associated with loss density fields in 2D and 3D eddy current solutions only. Hysteresis loss is short for magnetic hysteresis loss and represents power loss in some magnetic materials (electric steels or ferrites) in alternating (sinusoidal) magnetic fields. This loss is due to a phenomenon called \"magnetic viscosity\" which causes the B and H fields to have a phase shift between them. In the B-H plane, for linear materials, the relationship between these two fields describes an ellipse. The hysteresis loss is proportional to the area of the ellipse.

"},{"location":"mateditor/mat_core_loss/#core-loss-models-for-an-electromagnetic-material","title":"Core loss models for an electromagnetic material","text":"

MatEditor provides two core loss models: electrical steel and power ferrite. The coefficients are given in the table below.

Type Associated properties Electrical Steel Hystersis coefficient \\(K_h\\), Classcial eddy coefficient \\(K_c\\), Excess coefficient \\(K_e\\). Power Ferrite Steinmetz coefficients \\(C_m\\), \\(X\\), and \\(Y\\).

Note

In Transient Solver, X must be less than Y.

"},{"location":"mateditor/mat_core_loss/#calculating-properties-for-core-loss-b-p-curve","title":"Calculating properties for core loss (B-P curve)","text":"

To be able to extract parameters from the loss characteristics (B-P Curve), you first set the Core Loss Model of the material to Electrical Steel or Power Ferrite as a material property in the Property View.

Additional parameters appear in the following table Core Loss Model (\\(K_h\\), \\(K_c\\), and \\(K_e\\) for electrical steel, and \\(C_{m}\\), \\(X\\), and \\(Y\\) for power ferrite). If the P-B test data is already presented in the current material, you can add curve fitting property from the RMB context menu. This allows the electrical steel coefficients \\(K_h\\), \\(K_c\\), and \\(K_e\\), or the power ferrite coefficients \\(C_m\\), \\(X\\), and \\(Y\\) to be derived from a manufacturer-provided core loss curve.

Node

The accuracy in inputting the data for B-P Curve for the electrical steel material has a significant effect on the correctness of the analyses to the electromagnetic devices. You should input the data for B-P Curve according to accurate data provided by material manufacturers. Typically core material suppliers provide the average loss over a cycle for a peak B, of sinusoidal nature. Therefore for BP curve input in WelSim, B (Tesla) should be peak and P should be average.

As the input data (value or unit) changes, the following parameters are not automatically updated unless you resolve the curve fitting:

"},{"location":"mateditor/mat_core_loss/#calculate-core-loss-coefficients-from-loss-curves","title":"Calculate core loss coefficients from loss curves","text":"

This section introduces how to calculate core loss coefficients for electrical steel and power ferrite materials according to the given P-B test data.

  1. Add P-B Test Data material property, and edit the frequency-based data. You also can import the data from a plain text or Excel file. Check the data curves by clicking the row of frequency. Click the header of the frequency column displays all curves in the chart.

  2. Add Core Loss Model material property, and set the Core Loss Model Type of the property to Electrical Steel or Power Ferrite.

  3. Add Curve Fitting sub-property from the RMB context menu.

  4. Solve the curve fit from the RMB context menu.

  5. If the solve succeeds. The calculated parameters will be shown in the table.

  6. Copy the solved values to the properties from RMB context menu. You also can review the calculated curves in the chart.

  7. Display curves in the logarithmic axis (optional).

"},{"location":"mateditor/mat_core_loss/#computation-of-electrical-steel-core-loss-from-loss-curves","title":"Computation of electrical steel core loss from loss curves","text":"

The iron-core loss without DC flux bias is expressed as the following:

\\[ p_v=P_h+P_c+P_e=K_{f} f (B_m)^2 + K_c (fB_m)^2 + K_e(fB_m)^{1.5} = K_1B_m^2+K_2B_m^{1.5} \\]

where

Minimize the quadratic form to obtain \\(K_h\\) , \\(K_c\\), and \\(K_e\\) directly.

\\[ err(K_h,K_c,K_e)=\\sum_{i=1}^m \\sum_{j=1}^{n_i} \\left[p_{ij}-\\left(K_{h}f_{i}B_{mij}^2 +K_{c}\\left(fB_{mij}\\right)^{2}+ K_{e}\\left(f_iB_{mij}\\right)^{1.5} \\right) \\right]^2=min \\]

where \\(m\\) is the number of loss curves, \\(n_i\\) is the number of points of the \\(i\\)-th loss curve, and \\(p_{ij} = f(f_i , B_{mij})\\) is two dimensional lookup table for loss curves.

Note

Since the manufacturer-provided loss curve is obtained under sinusoidal flux conditions at a given frequency, these coefficients can be derived in the frequency domain.

"},{"location":"mateditor/mat_core_loss/#computation-of-power-ferrite-core-loss-from-loss-curves","title":"Computation of power ferrite core loss from loss curves","text":"

The principles of the computation algorithm are summarized as follows. The iron-core loss is expressed as the Steinmetz approximation

\\[ p_v=C_m f^x B_m^y \\]

where \\(p_v\\) is the average power density, \\(f\\) is the excitation frequency, and \\(B_m\\) is the peak flux density, is commonly used to characterize core loss data for sinusoidal excitation, but can also be applied to square-wave data.

To linearize the equation for curve fitting, we used base-10 logarithms. The equation above can be rewritten to

\\[ log(p_v)=c + x\\cdot log(f) + y \\cdot(B_m) \\]

where \\(c=log(C_m)\\).

Minimize the quadratic form to obtain \\(C\\), \\(x\\) and \\(y\\).

\\[ err(C_m,x,y)=\\sum_{i=1}^{m}\\sum_{j=1}^{n_i}\\left[log(p_{vij})-\\left(c+xlog(f_i)+ylog(B_{mij}) \\right) \\right]^2=min \\]

where \\(m\\) is the number of loss curves, \\(n_i\\) is the number of points of the \\(i\\)-th loss curve, and \\(P_{vij} = f(f_i , B_{mij})\\) is two dimensional lookup table for multi-frequency loss curves. Then \\(C_m\\) is calculated from the equation \\(c=log(C_m)\\).

"},{"location":"mateditor/mat_file_format/","title":"Material library file format","text":"

Material library data follows the MatML 3.1 Schema for saving material data to external libraries on disk. More information about MatML can be found at http://matml.org. For an example of the format see the Export individual data item in the Perform Basic Tasks in Material section and then open the file with a text/xml editor.

"},{"location":"mateditor/mat_gui/","title":"Graphical user interface","text":"

The MatEditor workspace is an independent interface and display relavant items as you configured.

"},{"location":"mateditor/mat_gui/#layout-reference","title":"Layout reference","text":"

Presented below are two layout configurations for the MatEditor view. The first configuration is displayed by clicking on \"Library\" tab in toolbox. The second configure is shown by clicking on \"Build\" tab in toolbox. You can switch this two layout mode by clicking the tabs.

Legend Name Description A Menu Bar Operations for MatEditor. B Toolbar Selected operations that often used for MatEditor. C Material Outline Pane Material items that are created in MatEditor. D Library Outline Pane Displays the available prebuild material sources. E Property Outline Pane Displays the available material property sources that can be included into a material. F Properties Pane Displays the properties of the current material. G Table Pane Shows the tabular data for the selected item in the Properties pane. H Chart Pane Shows the chart of the item selected in the Properties pane."},{"location":"mateditor/mat_gui/#menu-bar","title":"Menu bar","text":"

The following items in the menu bar are provided by MatEditor:

"},{"location":"mateditor/mat_gui/#file","title":"File","text":""},{"location":"mateditor/mat_gui/#edit","title":"Edit","text":""},{"location":"mateditor/mat_gui/#units","title":"Units","text":"

This menu provides all avilable unit systems and units. Once one unit (system) is chosen, the default unit is determined. The units for the newly created material data will be automatically set to the chosen unit(system).

"},{"location":"mateditor/mat_gui/#help","title":"Help","text":""},{"location":"mateditor/mat_gui/#toolbar","title":"Toolbar","text":"

The following item in the toolbar is provided by MatEditor:

Icon Name Description New Create a new material object in the tree window. Open Retrieve material data from an external XML file. This command remove all existing material data in the system. Save Save current material data into an external XML file. Help Direct the user to the online user manual. About Display the software and hardware information dialog."},{"location":"mateditor/mat_gui/#toolbox","title":"Toolbox","text":"

MatEditor Toolbox contains two tabs: Library and Build. These two tabs function as:

"},{"location":"mateditor/mat_gui/#material-outline-pane","title":"Material outline pane","text":"

The Outline pane shows an outline of the contents of the created material data source. You can perform the following actions in this pane:

"},{"location":"mateditor/mat_gui/#items-status","title":"Items status","text":"

The itmes column shows the name of the items contained in the data source. When the name of material object is in bold, the material is activated for editing.

"},{"location":"mateditor/mat_gui/#library-outline-pane","title":"Library outline pane","text":"

The Library Outline pane shows an outline of availble predefined materials. These materials are grouped into several categories.

"},{"location":"mateditor/mat_gui/#property-outline-pane","title":"Property outline pane","text":"

The Property Outline pane shows an outline of availble material properties. These material properties are grouped into several categories.

"},{"location":"mateditor/mat_gui/#properties-pane","title":"Properties pane","text":"

The Properties pane shows the properties for the item selected in the Property Outline pane. You can perform the following actions in this pane:

"},{"location":"mateditor/mat_gui/#property-column","title":"Property column","text":"

The property column lists the properties for the item selected in the Property Outline pane. Clicking a property will change the contents of the Table pane and Chart pane.

"},{"location":"mateditor/mat_gui/#material-property","title":"Material property","text":"

The status of the material property is indicated as follows:

"},{"location":"mateditor/mat_gui/#value-column","title":"Value column","text":"

The value column is used to change data for a property or indicates that the data for the property is tabular ().

"},{"location":"mateditor/mat_gui/#unit-column","title":"Unit column","text":"

The unit column displays the unit of the data shown in the value column . If the column is editable (see Units Menu), changing the unit will convert the value into the selected unit (there is no net change in the data, so the solution is still valid).

"},{"location":"mateditor/mat_gui/#suppression-column","title":"Suppression column","text":"

The suppression column shows the suppression status of the item and may also be used to switch the status (see Suppression).

"},{"location":"mateditor/mat_gui/#table-pane","title":"Table pane","text":"

The Table pane shows the tabular data for the item selected in the Properties pane. If there are independent variables (for instance, Temperature) for the selected item and the item is constant, you may change it to a table by entering a value into the independent variables data cell. If a row is shown with an index of *, you may add additional rows of data.

Note

You also can change the unit by clicking the header of table

"},{"location":"mateditor/mat_gui/#chart-pane","title":"Chart pane","text":"

The Chart pane shows the chart of the selected item in the Properties pane. The chart data is idenital to the table data.

"},{"location":"mateditor/mat_hyperelasticity_curvefit/","title":"Curve Fitting","text":""},{"location":"mateditor/mat_hyperelasticity_curvefit/#calculate-material-constants-from-test-data","title":"Calculate material constants from test data","text":"

This section introduces how to calculate material coefficients for the selected hyperelastic models according to the given uniaxial, biaxial, shear, and volumetric test data. Enginering strain and stress pair is used for input data.

  1. Add Uniaxial Test Data, Biaxial Test Data, or Shear Test Data material property, and edit the strain-stress data. You also can import the data from a plain text or Excel file. Set the temperature value if it is available. Check the data points by clicking the row of temperature.

  2. Add one of hyperelastic material properties from the toolbox, the supported hyperelastic models include Neo-Hookean, Mooney-Rivlin, Arruda-Boyce, Blatz-Ko, Gent, Ogden, Polynomial, and Yeoh. An example of Mooney-Rivlin 9 is given here.

  3. Add Curve Fitting sub-property from the RMB context menu.

  4. Solve the curve fit from the RMB context menu.

  5. If the solve succeeds. The calculated parameters will be shown in the table.

  6. Copy the solved values to the properties from RMB context menu. You also can review the calculated curves in the chart.

Note

  1. The test data should cover the entire strain range in the following simulation.
  2. It is recommended to input all uniaxial, biaxial, and shear test data if those data are available from the experiments.
"},{"location":"mateditor/mat_io/","title":"Mutually exclusive properties 1","text":"

Some properties are mutually exclusive of each other and require that only one property in the mutually exclusive set be unsuppressed. The addition or removing of the suppression for one of these properties automatically suppresses the other mutually exclusive properties.

For example, defining Isotropic Elasticity and Orthotropic Elasticity for the same material represents redundant elasticity behavior. Only one behavior can be active for the material. When such a conflict occurs, the property defined last is used and the previously defined, conflicting property is automatically suppressed.

The properties that are mutually exclusive are grouped in the following table.

Group Material Property Elastic properties Isotropic Elasticity, Orthotropic Elasticity, Anisotropic Elasticity, Mooney-Rivlin, Neo-Hookean, Polynomial, Yeoh, Ogden, Arruda-Boyce, Gent, Blatz-Ko, Ogden Foam, Extended Tube, Mullins Effect Plastic properties Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening Thermal conductivity properties Thermal Conductivity Isotropic, Thermal Conductivity Orthotropic Resistivity properties Isotropic Resistivity, Orthotropic Resistivity Electric permittivity properties Isotropic Relative Permittivity, Orthotropic Relative Permittivity Dielectric loss properties Isotropic Dielectric Loss Tangent, Orthotropic Dielectric Loss Tangent Magnetic permeability properties Isotropic Relative Permeability, Orthotropic Relative Permeability Magnetic loss properties Isotropic Relative Imaginary Permeability, Isotropic Magnetic Loss Tangent, Orthotropic Magnetic Loss Tangent"},{"location":"mateditor/mat_io_openradioss/","title":"OpenRadioss format","text":"

The format of exported material scripts is based on the OpenRadioss version 2022, more details please refer to the OpenRadioss user reference manual.

The import of OpenRadioss scripts is not supported yet in MatEditor/WELSIM.

"},{"location":"mateditor/mat_io_openradioss/#supported-openradioss-units","title":"Supported OpenRadioss units","text":"

At present, MatEditor supports eight types of unit systems commonly used in engineering simulation, which are as follows.

"},{"location":"mateditor/mat_io_openradioss/#supported-openradioss-materials","title":"Supported OpenRadioss materials","text":""},{"location":"mateditor/mat_io_openradioss/#basic","title":"Basic","text":""},{"location":"mateditor/mat_io_openradioss/#hyperelasticity-and-viscoelasticity","title":"Hyperelasticity and Viscoelasticity","text":""},{"location":"mateditor/mat_io_openradioss/#plasticity","title":"Plasticity","text":""},{"location":"mateditor/mat_io_openradioss/#failure-models","title":"Failure Models","text":""},{"location":"mateditor/mat_io_openradioss/#equation-of-state-eos","title":"Equation of State (EOS)","text":""},{"location":"mateditor/mat_io_openradioss/#fluids","title":"Fluids","text":"

More materials will be added upon user request.

"},{"location":"mateditor/mat_mutually_exclusive/","title":"Mutually exclusive properties","text":"

Some properties are mutually exclusive of each other and require that only one property in the mutually exclusive set be unsuppressed. The addition or removing of the suppression for one of these properties automatically suppresses the other mutually exclusive properties.

For example, defining Isotropic Elasticity and Orthotropic Elasticity for the same material represents redundant elasticity behavior. Only one behavior can be active for the material. When such a conflict occurs, the property defined last is used and the previously defined, conflicting property is automatically suppressed.

The properties that are mutually exclusive are grouped in the following table.

Group Material Property Elastic properties Isotropic Elasticity, Orthotropic Elasticity, Anisotropic Elasticity, Mooney-Rivlin, Neo-Hookean, Polynomial, Yeoh, Ogden, Arruda-Boyce, Gent, Blatz-Ko, Ogden Foam, Extended Tube, Mullins Effect Plastic properties Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening Thermal conductivity properties Thermal Conductivity Isotropic, Thermal Conductivity Orthotropic Resistivity properties Isotropic Resistivity, Orthotropic Resistivity Electric permittivity properties Isotropic Relative Permittivity, Orthotropic Relative Permittivity Dielectric loss properties Isotropic Dielectric Loss Tangent, Orthotropic Dielectric Loss Tangent Magnetic permeability properties Isotropic Relative Permeability, Orthotropic Relative Permeability Magnetic loss properties Isotropic Relative Imaginary Permeability, Isotropic Magnetic Loss Tangent, Orthotropic Magnetic Loss Tangent"},{"location":"mateditor/mat_overview/","title":"Overview","text":"

Material Module serves as a database for material properties used in analysis projects. The module not only provides a material library but allow you to create a material using the given properties. The properties view of a Material object is the primary user interface designed to let you create, save, and retrieve material models. The well-defined material object can be saved and used in the subsequent projects.

Note

The WELSIM Material module and MatEditor share the same features. For the completed and latest content, you can refer to the manual of MatEditor.

"},{"location":"mateditor/mat_overview/#graphical-user-interface","title":"Graphical user interface","text":"

The ease-of-use Material Module contains the following graphical user interface components:

"},{"location":"mateditor/mat_overview/#predefined-materials","title":"Predefined materials","text":"

WELSIM also provide predefined materials, which covers most of commonly used materials. Users can choose these materials and apply to the successive finite element analysis.

Category Materials General Materials Structural Steel, Stainless Steel, Aluminum Alloy, Concrete, Copper Alloy, Gray Cast Iron, Titanium Alloy Nonlinear Materials Aluminum Alloy NL, Concrete NL, Copper Alloy NL, Stainless Steel NL, Structural Steel NL, Titanium Alloy NL Hyperelastic Materials Elastomer Mooney-Rivlin, Elastomer Neo-Hookean, Elastomer Ogden, Elastomer Yeoh, Neoprene Rubber Thermal Materials Brass, Bronze, Copper, Diamond, Ferrite, Nodular Cast Iron, Solder, Teflon, Tungsten, Wood Electromagnetic Materials SS416, Supermendure Other Materials Water Liquid, Argon, Ash"},{"location":"mateditor/mat_overview/#material-properties","title":"Material properties","text":"

The supported material properties are listed in the table below.

Category Materials Basic Density, Isotropic Thermal Expansion, Isotropic Instantaneous Thermal Expansion, Orthotropic Thermal Expansion, Orthotropic Instantaneous Thermal Expansion, Constant Damping Coefficient Linear Elastic Isotropic Elasticity, Orthotropic Elasticity, Viscoelastic Hyperelastic Test Data Uniaxial Test Data, Biaxial Test Data, Shear Test Data, Volumetric Test Data, SimpleShear Test Data, Uniaxial Tension Test Data, Uniaxial Compression Test Data Hyperelastic Arruda-Boyce, Blatz-Ko, Gent, Mooney-Rivlin 2, Mooney-Rivlin 3, Mooney-Rivlin 5, Mooney-Rivlin 9, Neo-Hookean, Ogden 1st Order, Ogden 2nd Order, Ogden 3rd Order, Polynomial 1st Order, Polynomial 2nd Order, Polynomial 3rd Order, Yeoh 1st Order, Yeoh 2nd Order, Yeoh 3rd Order Plasticity Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening, Anand Viscoplasticity Creep Strain Hardening, Time Hardening, Generalized Exponential, Generalized Graham, Generalized Blackburn, Modified Time Hardening, Modified Strain Hardening, Generalized Garofalo, Exponential Form, Norton, Combined Time Hardening, Rational Polynomial, Generalized Time Hardening Visco-elastic Prony Shear Relaxation, Prony Volumetric Relaxation Other Mechanical Strain Life Parameters, Compressive Ultimate Strength, Compressive Yield Strength, LaRc0304 Constants, Orthotropic Strain Limits, Orthotropic Stress Limits, Puck Constants, Tensile Ultimate Strength, Tensile Yield Strength, Tsai-Wu Constants, Shape Memory Effect, Drucker-Prager Strength Piecewise, Drucker-Prager Strength Linear, Ideal Gas EOS, Crushable Foam, Nonlinear Elastic Model Damage, Plakin Special Hardening, Tensile Pressure Failure, Crack Softening Failure Thermal Enthalpy, Isotropic Thermal Conductivity, Orthotropic Thermal Conductivity, Specific Heat Electromagnetics B-H Curve, Isotropic Relative Permeability, Orthotropic Relative Permeability, Isotropic Resistivity, Orthotropic Resistivity"},{"location":"mateditor/mat_overview/#working-with-material-data","title":"Working with material data","text":""},{"location":"mateditor/mat_overview/#exporting","title":"Exporting","text":"

You can export the complete material data to an external XML file. The following format is supported for export:

"},{"location":"mateditor/mat_properties/","title":"Libraries and properties","text":""},{"location":"mateditor/mat_properties/#definitions","title":"Definitions","text":"

We make use of the following terminology for materials:

Term Definition Material An identifier that contains a property or multiple properties Property An identifier the singular information (for example, Density) Property data An identifier for tabular data (for example, Thermal Conductivity)"},{"location":"mateditor/mat_properties/#sample-libraries","title":"Sample libraries","text":"

MatEditor provides sample material data categorized into several libraries. However, you still need to validate that the data is consistent with the material you are using in your analysis.

The following materials are included:

"},{"location":"mateditor/mat_properties/#supported-properties","title":"Supported properties","text":"

The supported material properties are listed by category here.

"},{"location":"mateditor/mat_properties/#basics","title":"Basics","text":""},{"location":"mateditor/mat_properties/#linear-elastic","title":"Linear Elastic","text":""},{"location":"mateditor/mat_properties/#hyperelastic-test-data","title":"Hyperelastic Test Data","text":""},{"location":"mateditor/mat_properties/#hyperelastic","title":"Hyperelastic","text":""},{"location":"mateditor/mat_properties/#plasticity","title":"Plasticity","text":""},{"location":"mateditor/mat_properties/#creep","title":"Creep","text":""},{"location":"mateditor/mat_properties/#visco-elastic","title":"Visco-elastic","text":""},{"location":"mateditor/mat_properties/#thermal","title":"Thermal","text":""},{"location":"mateditor/mat_properties/#electromagnetics","title":"Electromagnetics","text":""},{"location":"mateditor/mat_table_data/","title":"Import/Export Tabular Data","text":"

Import and export tabular data is supported in MatEditor, CurveFitter and WELSIM, this feature facilitates you to input and output massive tabular data with no need to manually input and output data, specifically test data for the hyperelastic and magnetic core loss materials.

The import and export buttons are allocated on the top of the Tabular Data Window, as shown in the figure below:

"},{"location":"mateditor/mat_table_data/#default-file-format","title":"Default file format","text":"

The default file format used in MatEditor/CurveFitter/WELSIM contains a header block that gives the quantity name, unit, and dependency. This header data allows you to define the units from the external file. The latest version supports both plain text and Excel formats. Both formats share a similar schema. The details of each format are discussed below.

Note

The number of columns of import data must match the pre-defined headers.

The plain text data file looks like below:

An example of Excel file is shown below:

"},{"location":"mateditor/mat_table_data/#format-with-no-header-data","title":"Format with no header data","text":"

MatEditor/CurveFitter/WELSIM also supports the external data that contains no header information (pure value data). You need to ensure unit consistency when importing such data files. Both plain text and Excel file formats are supported.

The plain text file with no header dat looks like below:

Note

Due to the lack of the header information, the units of the imported data is determined by the current units of the Table. In addition, the pivoting column may not be set if the file does not contain such data. The number of columns must be identicial to that of the pre-defined table quantities.

"},{"location":"mateditor/mat_table_data/#examples","title":"Examples","text":"

The examples of the import/export tabular data are available at our GitHub page.

"},{"location":"mateditor/mat_theory/","title":"Material Theory","text":"

Some properties are mutually exclusive of each other and require that only one property in the mutually exclusive set be unsuppressed. The addition or removing of the suppression for one of these properties automatically suppresses the other mutually exclusive properties.

For example, defining Isotropic Elasticity and Orthotropic Elasticity for the same material represents redundant elasticity behavior. Only one behavior can be active for the material. When such a conflict occurs, the property defined last is used and the previously defined, conflicting property is automatically suppressed.

The properties that are mutually exclusive are grouped in the following table.

Group Material Property Elastic properties Isotropic Elasticity, Orthotropic Elasticity, Anisotropic Elasticity, Mooney-Rivlin, Neo-Hookean, Polynomial, Yeoh, Ogden, Arruda-Boyce, Gent, Blatz-Ko, Ogden Foam, Extended Tube, Mullins Effect Plastic properties Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening Thermal conductivity properties Thermal Conductivity Isotropic, Thermal Conductivity Orthotropic Resistivity properties Isotropic Resistivity, Orthotropic Resistivity Electric permittivity properties Isotropic Relative Permittivity, Orthotropic Relative Permittivity Dielectric loss properties Isotropic Dielectric Loss Tangent, Orthotropic Dielectric Loss Tangent Magnetic permeability properties Isotropic Relative Permeability, Orthotropic Relative Permeability Magnetic loss properties Isotropic Relative Imaginary Permeability, Isotropic Magnetic Loss Tangent, Orthotropic Magnetic Loss Tangent"},{"location":"mateditor/mat_theory_eos/","title":"Equations of State (EOS)","text":"

MatEditor allows you to define the EOS material properties. The supported properties are listed below.

"},{"location":"mateditor/mat_theory_eos/#compaction-eos","title":"Compaction EOS","text":"

Plastic compaction is along path defined by equation:

\\[ p=C_0 + C_1 \\mu +C_2 \\mu^2 + C_3 \\mu^3 \\]

where \\(P\\) is the hydrodynamic pressure in material. \\(\\mu\\) is the volumetric strain that can be obtained by \\(\\mu=\\dfrac{\\rho}{\\rho_0}-1\\).

Unloading bulk modulus \\(B\\) is the bulk modules for the unloading process.

Pressure Shift \\(P_{sh}\\) is used to model the relative pressure formulation.

"},{"location":"mateditor/mat_theory_eos/#gruneisen-eos","title":"Gruneisen EOS","text":"

In the Gruneisen EOS model, the hydrodynamic pressure is described by the following equations:

For the compressed material, \\(\\mu\\)>0

\\[ p = \\dfrac{\\rho_0C^2\\mu[1+(1-\\dfrac{\\gamma_0}{2})\\mu-\\dfrac{\\alpha}{2}\\mu^2]}{[1-(S_1-1)\\mu-S_2\\dfrac{\\mu^2}{\\mu+1}-S_3\\dfrac{\\mu^3}{(\\mu+1)^2}]^2} + (\\gamma_0+\\alpha\\mu)E \\]

For the expanding material, \\(\\mu\\)<0 $$ p = \\rho_0C^2\\mu + (\\gamma_0+\\alpha\\mu)E $$

where the \\(\\mu=\\dfrac{\\rho}{\\rho_0}-1\\).

"},{"location":"mateditor/mat_theory_eos/#ideal-gas-eos","title":"Ideal Gas EOS","text":"

The pressure in the Ideal Gas model can be represented by the function:

\\[ p = (\\gamma-1)(1+\\mu)E \\]

where unitless parameter \\(\\gamma\\) is determined by the heat capacity \\(C_v\\) and \\(C_p\\), \\(\\gamma=\\dfrac{C_p}{C_v}\\). The initial heat capacity \\(C_v\\) is calculated from the initial conditions:

\\[ C_v=\\dfrac{E_0}{\\rho_0T_0} \\]"},{"location":"mateditor/mat_theory_eos/#linear-eos","title":"Linear EOS","text":"

The pressure in linear EOS is given by

\\[ p = p_0 + B\\mu \\]

where \\(p_0\\) i initial pressure and \\(B\\) is the initial bulk modulus. Linear EOS is a simplified form of polynomial EOS:

\\[ p=C_0+C_1\\mu + C_2\\mu + C_3\\mu + (C_4+C_5)E_0 \\]

where, \\(C_0=p_0\\), \\(C_1=B\\), \\(C_2=C_3 = C_4 = C_5 = 0\\).

Bulk modulus is usually treated as \\(B=\\rho_0c_0^2\\), where \\(c_0\\) is the initial sound speed.

"},{"location":"mateditor/mat_theory_eos/#lszk-landau-stanyukovich-zeldovich-kompaneets-eos","title":"LSZK (Landau-Stanyukovich-Zeldovich-Kompaneets) EOS","text":"

This EOS model is the short for the Landau-Stanyukovich-Zeldovich-Kompaneets EOS, used for the detonation modeling. The pressure is given by

\\[ p = (\\gamma-1)\\rho e + a \\rho^b \\]

where \\(\\rho\\) is the mass density, \\(e\\) is the internal energy density by mass, \\(b\\) is the material parameter.

"},{"location":"mateditor/mat_theory_eos/#murnaghan-eos","title":"Murnaghan EOS","text":"

This EOS is also known as Tait EOS. The pressure is defined by

\\[ p = \\dfrac{K_0}{K_1}[(\\dfrac{V}{V_0})^{-K_1}-1] \\]

where \\(K_0\\), \\(K_1\\) are material parameters, \\(V\\) is the volume.

This model is also expressed in terms of the compressibility \\(\\mu\\):

\\[ p = p_0 + \\dfrac{K_0}{K_1}[(1+\\mu)^{K_1}-1] \\]

Note

Murnaghan EOS is independent to the energy.

"},{"location":"mateditor/mat_theory_eos/#nasg-noble-abel-stiffened-gas-eos","title":"NASG (Noble-Abel Stiffened Gas) EOS","text":"

The pressure can be computing by

\\[ p = \\dfrac{(\\gamma-1)(1+\\mu)(E-\\rho_0q)}{1-b\\rho_0(1+\\mu)} - \\gamma p_{\\infty} \\]

where \\(p_{\\infty}\\) is the stiffness parameter.

"},{"location":"mateditor/mat_theory_eos/#noble-abel-eos","title":"Noble-Abel EOS","text":"

This EOS can apply to dense gases at high pressure, as the volume occupied by the moledules is no longer negligible.

\\[ p = \\dfrac{(\\gamma-1)(1+\\mu)E}{1-b\\rho_0(1+\\mu)} \\]

where \\(\\gamma=\\dfrac{C_p}{C_v}\\)

Note

Covolume parameter b is usually in the range between [0.9e-3, 1.1e-3] \\(m^3/kg\\).

"},{"location":"mateditor/mat_theory_eos/#osborne-eos","title":"Osborne EOS","text":"

This EOS is also called quadratic EOS.

$$ p = \\dfrac{A_1\\mu+A_2\\mu |\\mu| + (B_0+B_1\\mu+B_2\\mu^2)E + (C_0 + C_1\\mu)E^2 }{E+D_0} $$ where \\(E\\) is the internal energy by initial volume.

"},{"location":"mateditor/mat_theory_eos/#polynomial-eos","title":"Polynomial EOS","text":"

The pressure for the linear polynomial EOS can be calculated by

\\[ p=C_0+C_1\\mu + C_2\\mu + C_3\\mu + (C_4+C_5)E \\]

where \\(E\\) is the internal energy density by volume.

Note

For the expanding status (\\(\\mu\\)<0), the term \\(C_2\\mu^2\\)=0.

"},{"location":"mateditor/mat_theory_eos/#puff-eos","title":"Puff EOS","text":"

This EOS model describes pressure accroding to the compressibility \\(\\mu\\) and sublimation energy density by volume \\(E_s\\).

When \\(\\mu\\geq\\) 0:

\\[ p = (C_1\\mu+C_2\\mu^2+C_3\\mu^3)(1-\\dfrac{\\gamma\\mu}{2})+\\gamma(1+\\mu)E \\]

when \\(\\mu\\)<0 and \\(E\\geq E_s\\):

\\[ p = (T_1\\mu+T_2\\mu^2)(1-\\dfrac{\\gamma\\mu}{2})+\\gamma(1+\\mu)E \\]

when \\(\\mu\\)<0 and \\(E<E_s\\):

\\[ p = \\eta[H+(\\gamma_0-H)\\sqrt{\\eta}][E-E_s(1-exp(\\dfrac{N(\\eta-1)}{\\eta^2}))] \\]

with \\(N=\\dfrac{C_1\\eta}{\\gamma_0E_s}\\).

"},{"location":"mateditor/mat_theory_eos/#stiffened-gas-eos","title":"Stiffened Gas EOS","text":"

This EOS was originally designed to simulate water for underwater explosions.

The pressure can be calculated by $$ p = (\\gamma-1)(1+\\mu)E - \\gamma p_{\\star} $$

where \\(E=\\dfrac{E_{int}}{V_0}\\), \\(\\mu=\\dfrac{\\rho}{\\rho_0}-1\\). The additional pressure term \\(p^{\\star}\\) is introduced here.

This EOS can be derived from the Polynomial EOS: $$ p=C_0+C_1\\mu + C_2\\mu + C_3\\mu + (C_4+C_5)E $$ when \\(C_0 = -\\gamma p^{\\star}\\), \\(C_1=C_2=C3=0\\), \\(C_4=C_5=\\gamma-1\\), \\(E_0=\\dfrac{P_0-C_0}{C_4}\\).

"},{"location":"mateditor/mat_theory_eos/#tillotson-eos","title":"Tillotson EOS","text":"

The pressure is defined by

$$ p = C_1\\mu + C_2\\mu^2 +(a+\\dfrac{b}{\\omega})\\eta E $$ with \\(\\omega=1+\\dfrac{E}{E_r}\\eta^2\\) for the region \\(\\mu \\geq\\) 0.

$$ p = C_1\\mu+(a+\\dfrac{b}{\\omega})\\eta E $$ for the region \\(\\mu<0\\), \\(\\dfrac{V}{V_0}<V_s\\), and \\(E<E_s\\).

and $$ p = C_1 e^{\\beta x} e^{-\\alpha x^2}\\mu + (a + \\dfrac{be^{-\\alpha x^2}}{\\omega}) \\eta E $$

"},{"location":"mateditor/mat_theory_failure/","title":"Failure Models","text":"

MatEditor allows you to define the failure material properties. The supported properties are listed below.

"},{"location":"mateditor/mat_theory_failure/#bi-quadratic","title":"Bi-Quadratic","text":"

The failure strain is described by two parabolic functions that user input.

"},{"location":"mateditor/mat_theory_failure/#cockcroft","title":"Cockcroft","text":"

A nonlinear stress-strain based failure criterion with linear damage accumulation.

\\[ C_0 = \\int _0 ^{\\bar{\\epsilon}_f} max(\\sigma_1, 0) \\cdot d\\bar{\\epsilon} \\]

where \\(\\epsilon_1\\) is the first principal tension stress, \\(\\bar{\\epsilon}\\) is the equivalent strain.

"},{"location":"mateditor/mat_theory_failure/#extended-mohr-coulomb","title":"Extended Mohr-Coulomb","text":"

The failure criteria is calculated as:

\\[ D = \\sum \\dfrac{\\Delta \\bar{\\epsilon}_p}{\\bar{\\epsilon}_{p,fail}} \\]

where effective failure strain is

\\[ \\bar{\\epsilon}_{p,fail} = b \\cdot (1+c)^{\\frac{1}{n}} \\cdot \\{[\\dfrac{1}{2}((f_1-f_2)^a + (f_2-f_3)^a + (f_1 - f_3)^a )]^{\\frac{1}{a}} + c(2\\eta+f_1+f_3) \\}^{-\\frac{1}{n}} \\]

the coefficient b is computed as

\\[ b = b_0[1+\\gamma ln(\\dfrac{\\dot{\\bar{\\epsilon}}_p}{\\dot{\\bar{\\epsilon}}_0})] \\quad if\\, \\dot{\\bar{\\epsilon}}_p > \\dot{\\bar{\\epsilon}}_0 \\]

or

\\[ b = b_0 \\quad if\\, \\dot{\\bar{\\epsilon}}_p \\le \\dot{\\bar{\\epsilon}}_0 \\]"},{"location":"mateditor/mat_theory_failure/#energy","title":"Energy","text":"

The damage is defined as

\\[ D = \\dfrac{E-E_1}{E_2 - E_1} \\]

where the energy density is the current internal energy of the element divided by the current element volume.

"},{"location":"mateditor/mat_theory_failure/#fabric","title":"Fabric","text":"

The failure and damage is defined independently in each direction (\\(i\\)=1,2)

\\[ D_i = \\dfrac{\\epsilon_i - \\epsilon_{fi}}{\\epsilon_{ri} - \\epsilon_{fi}} \\]

where \\(\\epsilon_i \\ge \\epsilon_{fi}\\).

"},{"location":"mateditor/mat_theory_failure/#hashin","title":"Hashin","text":"

This model can be used for the composite materials.

The damage factor is calculated as

\\[ D = Max(F_1,F_2,F_3, F_4, F_5) \\quad for\\quad uni-directional\\, lamina\\, model \\] \\[ D = Max(F_1,F_2,F_3, F_4, F_5, F_6, F_7) \\quad for\\quad fabric\\, lamina\\, model \\]"},{"location":"mateditor/mat_theory_failure/#for-the-uni-directional-lamina-model","title":"For the uni-directional lamina model:","text":"

Tensile/shear fiber mode:

\\[ F_1 = (\\dfrac{\\langle\\sigma_{11}\\rangle}{\\sigma_1^t})^2 + (\\dfrac{\\sigma_{12}^2 + \\sigma_{13}^2}{{\\sigma_{12}^f}^2}) \\]

Compression fiber mode:

\\[ F_2 = (\\dfrac{\\langle \\sigma_a \\rangle}{ \\sigma_1^c})^2 \\]

with \\(\\sigma_{\\alpha} = -\\sigma_{11}+\\langle -\\dfrac{\\sigma_{22}+\\sigma_{33}}{2} \\rangle\\).

Crush mode:

\\[ F_3 = (\\dfrac{\\langle p \\rangle}{\\sigma_c})^2 \\]

with \\(p=-\\dfrac{\\sigma_{11}+\\sigma_{22}+\\sigma_{33}}{3}\\).

Failure matrix mode:

\\[ F_4 = (\\dfrac{\\langle \\sigma_{22} \\rangle}{\\sigma_2^t})^2 + (\\dfrac{\\sigma_{23}}{S_{23}})^2 + (\\dfrac{\\sigma_{12}}{S_{12}})^2 \\]

Delamination mode:

\\[ F_5 = S^2_{del}[(\\dfrac{\\langle \\sigma_{33} \\rangle}{\\sigma^t_2})^2 + (\\dfrac{\\sigma_{23}}{\\tilde{S}_{23}})^2 + (\\dfrac{\\sigma_{12}}{S_{12}})^2 ] \\]"},{"location":"mateditor/mat_theory_failure/#for-the-fabirc-lamina-model","title":"For the fabirc lamina model:","text":"

Tensile/shear fiber mode

\\[ F_1 = (\\dfrac{\\langle\\sigma_{11}\\rangle}{\\sigma_1^t})^2 + (\\dfrac{\\sigma_{12}^2 + \\sigma_{13}^2}{{\\sigma_{a}^f}^2}) \\] \\[ F_2 = (\\dfrac{\\langle\\sigma_{22}\\rangle}{\\sigma_2^t})^2 + (\\dfrac{\\sigma_{12}^2 + \\sigma_{23}^2}{{\\sigma_{b}^f}^2}) \\]

Compression fiber mode:

\\[ F_3 = (\\dfrac{\\langle \\sigma_a \\rangle}{ \\sigma_1^c})^2 \\] \\[ F_4 = (\\dfrac{\\langle \\sigma_b \\rangle}{ \\sigma_2^c})^2 \\]

Crush mode:

\\[ F_5 = (\\dfrac{\\langle p \\rangle}{\\sigma_c})^2 \\]

Shear failure matrix mode:

\\[ F_6 = (\\dfrac{\\sigma_12}{\\sigma_12^m})^2 \\]

Matrix failure mode:

\\[ F_7 = S^2_{del}[(\\dfrac{\\langle \\sigma_{33} \\rangle}{\\sigma^t_3})^2 + (\\dfrac{\\sigma_{23}}{\\tilde{S}_{23}})^2 + (\\dfrac{\\sigma_{12}}{S_{12}})^2 ] \\]"},{"location":"mateditor/mat_theory_failure/#hosford-coulomb","title":"Hosford-Coulomb","text":"

The failure strain is described y the Hosford-Coulomb function.

The damage is defined as

\\[ D = \\sum \\dfrac{\\Delta \\bar{\\epsilon}_p} {\\bar{\\epsilon}^{pr}_{HC}(\\eta) } \\]

where the strain is calcualted as

\\[ \\bar{\\epsilon}^{pr}_{HC}(\\eta, \\theta) = b(1+c)^{\\frac{1}{n_f}} \\{[\\dfrac{1}{2}((f_1-f_2)^a + (f_2-f_3)^a + (f_1-f_3)^a)]^{\\frac{1}{a}} + c(a\\eta + f_1 +f_2) \\}^{\\frac{1}{n_f}} \\]"},{"location":"mateditor/mat_theory_failure/#johnson-cook","title":"Johnson-Cook","text":"

The failure strain is calculated by the constutitive relation:

\\[ \\epsilon_f = [D_1+D_2exp(D_3\\sigma^*)] [1+D_4 ln(\\dot{\\epsilon}^*)] (1 + D_5 T^*) \\]

The damage factor is defined as

\\[ D = \\sum \\dfrac{\\Delta \\epsilon_p}{\\epsilon_f} \\]"},{"location":"mateditor/mat_theory_failure/#ladeveze-delamination","title":"Ladeveze Delamination","text":"

This is the Ladeveze failure model for delamination (interlaminar fracture). The damage parameters are defined as

\\[ Y_{d_3} = \\dfrac{\\partial E_D}{\\partial d_3} \\vert _{\\sigma=cst}=\\dfrac{1}{2} \\dfrac{\\langle\\sigma_{33}\\rangle^2}{K_3(1-d_3)^2} \\quad Mode\\,I \\] \\[ Y_{d_2} = \\dfrac{\\partial E_D}{\\partial d_2} \\vert _{\\sigma=cst}=\\dfrac{1}{2} \\dfrac{\\langle\\sigma_{32}\\rangle^2}{K_2(1-d_2)^2} \\quad Mode\\,II \\] \\[ Y_{d_1} = \\dfrac{\\partial E_D}{\\partial d_1} \\vert _{\\sigma=cst}=\\dfrac{1}{2} \\dfrac{\\langle\\sigma_{31}\\rangle^2}{K_1(1-d_1)^2} \\quad Mode\\,III \\]

The damage value can be

\\[ D = \\dfrac{k}{a}[1- exp(-a\\langle w(Y)-d\\rangle)] \\]"},{"location":"mateditor/mat_theory_failure/#mullins-effect","title":"Mullins Effect","text":"

This failure model is used with the hyperelastic materials. The stress during the first loading process is equal to the undamaged stress. Upon unloading and reloading the strss is multiplied by a positive softening factor as

\\[ \\sigma = \\eta dev(\\sigma) - pI \\]

where dev(\\(\\sigma\\)) is the deviatoric part of the stress, \\(p\\) is the hydrostatic pressure. The damage factor \\(\\eta\\) is given as

\\[ \\eta = 1 - \\dfrac{1}{R} erf(\\dfrac{W_{max}-W}{m+\\beta W_{max}}) \\]

where \\(erf\\) is the Gauss error function.

"},{"location":"mateditor/mat_theory_failure/#nxt","title":"NXT","text":"

This model describes the forming limit baed on stresses. This failure is used for shell elements only.

An instability factor is defined as:

\\[ \\lambda_f=\\dfrac{\\sigma/h - (\\sigma/h)_{SR}}{(\\sigma/h)_{3D}-(\\sigma/h)_{SR}} + 1 \\]

The material is defined as free if \\(0<\\lambda_f<1\\), warning if \\(1<\\lambda_f<2\\), failure if \\(\\lambda_f \\ge 2\\).

"},{"location":"mateditor/mat_theory_failure/#orthotropic-bi-quadratic","title":"Orthotropic Bi-Quadratic","text":"

The failure strain is described by two parabolicfunctions calculated using curve fitting from user input failure strains.

"},{"location":"mateditor/mat_theory_failure/#orthotropic-strain","title":"Orthotropic Strain","text":"

A damage factor is the maximum over time and is calculated for each direction and stress state via:

\\[ d_ijl = \\dfrac{\\epsilon_{ijf\\_l}}{\\epsilon_{ijl}} \\cdot \\dfrac{\\epsilon_{ijl}-\\alpha\\cdot\\epsilon_{ijd\\_l}}{\\epsilon_{ijf\\_l}-\\epsilon_{ijd\\_l}} \\]

where the direction is indicated by using the common \\(ij\\) notation and loading state is either compression (\\(l=c\\)) or tension (\\(l=t\\)). The parameter \\(\\alpha=factor_{el}\\cdot factor_{rate}\\).

The element size correction factor is :

\\[ factor_{el} = Fscale_{el} \\cdot f_{el} \\dfrac{Size_{el}}{El_ref} \\]

where \\(f_{el}\\) is the element size correction factor function, \\(Size_{el}\\) is the characteristic element size.

The strain rate factor is

\\[ factor_{rate} = f_{ijl}(\\dfrac{\\dot{\\epsilon}_{ijl}}{\\dot{\\epsilon}_0}) \\]

where \\(f_ijl\\) is strain rate factor function, \\(\\dot{\\epsilon}_{ijl}\\) is the current strain rate in direction ij and load case l, and \\(\\dot\\epsilon_0\\) is the reference strate rate.

Generally, the damange for this model is

\\[ D = Max(d_{ijl}) = Max(\\dfrac{\\epsilon_{ijf\\_l}}{\\epsilon_{ijl}} \\cdot \\dfrac{\\epsilon_{ijl}-\\alpha\\cdot\\epsilon_{ijd\\_l}}{\\epsilon_{ijf\\_l}-\\epsilon_{ijd\\_l}}) \\]"},{"location":"mateditor/mat_theory_failure/#puck","title":"Puck","text":"

This failure model can be applied for both solid and shell elements.

For the fiber fraction failure, the damage parameter \\(e_f\\) is defined by

\\[ e_f=\\dfrac{\\sigma_{11}}{\\sigma_{1}^t} \\quad for\\, tensile \\]

or

\\[ e_f=\\dfrac{|\\sigma_{11}|}{\\sigma_{1}^c} \\quad for\\, compression \\]

For the inter fiber failure: the damage parameter \\(e_f\\) is

\\[ e_f=\\dfrac{1}{\\bar{\\sigma}_{12}} [ \\sqrt{(\\dfrac{\\bar{\\sigma}_{12}}{\\sigma_2^t} -p^+_{12})^2\\sigma_{22}^2 + \\sigma_{12}^2}+p^+_{12}\\sigma_{22}] \\quad for\\, Mode\\, A \\]

or

\\[ e_f=[(\\dfrac{\\sigma_{12}}{2(1+p^-_{22})\\bar{\\sigma}_{12}})^2 + (\\dfrac{\\sigma_{22}}{\\sigma_2^c})^2](\\dfrac{\\sigma^c_2}{-\\sigma_{22}}) \\quad for\\, Mode\\, C \\]

or

\\[ e_f=\\dfrac{1}{\\bar{\\sigma}_{12}} ( \\sqrt{\\sigma_{12}^2+(p^-_{12}\\sigma_{22})^2}+p^-_{12}\\sigma_{22}) \\quad for\\, Mode\\, B \\]

when the damage parameter \\(e_f \\ge 1.0\\), the stresses are decreased by using an exponential function to avoid numerical instabilities.

The damage is defined by

\\[ D = Max(e_f(tensile),e_f(compression), e_f(ModaA), e_f(ModeB), e_f(ModeC) ) \\]"},{"location":"mateditor/mat_theory_failure/#tuler-butcher","title":"Tuler-Butcher","text":"

An element fails once the damage is greater than specified critical damage value K. For ductile materials, the cumulative damage parameter is:

\\[ D=\\int_0^t{max(0, \\sigma-\\sigma_r)^{\\lambda})dt}>K \\]

where \\(\\sigma_r\\) is initial fracture stress, \\(\\sigma\\) maximum principal stress, \\(\\lambda\\) is material constant, \\(t\\) is the time when the element cracks, \\(D\\) is the damage integral, \\(K\\) is the critical value of the damage integral.

For brittle materials (shells only), the damage parameter is: $$ \\dot{D} = \\dfrac{1}{K}(\\sigma - \\sigma_r)^a $$ $$ \\sigma_r=\\sigma_0(1-D)^b $$ $$ D=D+\\dot{D}\\Delta t $$

"},{"location":"mateditor/mat_theory_failure/#tensile-strain","title":"Tensile Strain","text":"

This is a strain-based failure model that is compatible with both solid and shell elements. The damage is calculated by:

\\[ D = \\dfrac{\\epsilon - \\epsilon_{t1}}{\\epsilon_{t2} - \\epsilon_{t1}} \\]

where \\(\\epsilon\\) is either the quivlent strain or maximum principal tensile strain.

"},{"location":"mateditor/mat_theory_failure/#wierzbicki-model","title":"Wierzbicki model","text":"

This model describes the Bao-Xue-Wierzbicki failure model. The damage is defined by

\\[ D=\\sum{\\dfrac{\\Delta\\epsilon_{p}}{\\bar{\\epsilon}_f}} \\]

where the effective failure strain is

\\[ \\bar{\\epsilon}_f =\\{ \\bar{\\epsilon}_{max}n-[\\bar{\\epsilon}_{max}n - \\bar{\\epsilon}_{min}n](1-\\bar{\\xi}^m)^{\\dfrac{1}{m}} \\}^{\\dfrac{1}{n}} \\]

where \\(\\bar{\\epsilon}_{max} = C_1 e^{-1C_{2}\\eta}\\), and \\(\\bar{\\epsilon}_{min} = C_{3} e^{-1C_{4}\\eta}\\).

For solid element, the parameters \\(\\bar{\\xi}\\) and \\(\\bar{\\eta}\\) are defined by the two options.

The option 1 (default) is : $$ \\bar{\\xi}=\\dfrac{\\sigma_m}{\\sigma_{VM}} \\quad \\bar{\\eta}=\\dfrac{27J_3}{2\\sigma^3_{VM}} $$

The option 2 is: $$ \\bar{\\xi}=\\dfrac{\\int_0^{\\epsilon_p}\\dfrac{\\sigma_m}{\\sigma_{VM}}d\\epsilon_p}{\\epsilon_p} \\quad \\bar{\\eta}=\\dfrac{\\int_0^{\\epsilon_p} \\dfrac{27J_3}{2\\sigma^3_{VM}} d\\epsilon_p}{\\epsilon_p} $$

For shell element, the parameters \\(\\bar{\\xi}\\) and \\(\\bar{\\eta}\\) are $$ \\bar{\\xi}=\\dfrac{\\sigma_m}{\\sigma_{VM}} \\quad \\bar{\\eta}=-\\dfrac{27}{2}\\bar{\\eta}(\\bar{\\eta}^2-\\dfrac{1}{3}) $$

where \\(\\sigma_m\\) is Hydrostatic stress, \\(\\sigma_{VM}\\) is von Mises stress, and \\(J_3\\) is the third invariant deviatoric stress.

"},{"location":"mateditor/mat_theory_failure/#wilkins-model","title":"Wilkins model","text":"

The cumulative damage is given by:

\\[ D_c = \\int W_1 W_2 d \\bar{\\epsilon_p} \\]

where \\(W_1=(\\dfrac{1}{1-\\dfrac{P}{P_{lim}}})^{\\alpha}\\), \\(W_2=(2-A)^{\\beta}\\), and hydro-pressure \\(P=-\\dfrac{1}{3}\\sum_{j=1}^{3}\\sigma_{jj}\\), \\(A=max(\\dfrac{s_2}{s_1}, \\dfrac{s_2}{s_3})\\). \\(s_1\\), \\(s_2\\), \\(s_3\\) are the deviatoric stresses, and \\(s_1 \\ge s_2 \\ge s_3\\).

"},{"location":"mateditor/mat_theory_hyper-elasticity/","title":"Hyperelasticity and Curve Fitting","text":""},{"location":"mateditor/mat_theory_hyper-elasticity/#isotropic-hyperelasticity","title":"Isotropic hyperelasticity","text":"

The elastic potential energy in hyperelastic material can be obtained from the initial state with no stress activation. Therefore, we have the main invariable terms of the right Cauchy-Green deformation tensor C(\\(I_{1}\\), \\(I_{2}\\), \\(I_{3}\\)), or the main invariable of the deformation tensor excluding the volume changes (\\(\\bar{I}_{1}\\), \\(\\bar{I}_{2}\\), \\(\\bar{I}_{3}\\)). The potential can be expressed as \\(\\mathbf{W}=\\mathbf{W}(I_{1},I_{2},I_{3})\\), or \\(\\mathbf{W}=\\mathbf{W}(\\bar{I}_{1},\\bar{I}_{2},\\bar{I}_{3})\\).

The nonlinear constitutive relation of a hyperelastic material is defined by the relation between the second-order Piola-Kirchhoff stress and the Green-Lagrange strain, the total Lagrange method is more efficient in solving such models.

When the elastic potential energy \\(W\\) of the hyperelasticity is known, the second Piola-Kirchhoff stress and strain-stress relationship can be calculated as follows

\\[ S=2\\dfrac{\\partial W}{\\partial C} \\] \\[ C=4\\dfrac{\\partial^{2}W}{\\partial C\\partial C} \\]

The following are several forms of strain-energy potential (W) provided for the modeling of incompressible or nearly incompressible hyperelastic materials.

"},{"location":"mateditor/mat_theory_hyper-elasticity/#arruda-boyce-model","title":"Arruda-Boyce model","text":"

The form of the strain-energy potential for Arruda-Boyce model is

\\[ \\begin{array}{ccl} W & = & \\mu[\\dfrac{1}{2}(\\bar{I}_{1}-3)+\\dfrac{1}{20\\lambda_{m}^{2}}(\\bar{I_{1}^{2}}-9)+\\dfrac{11}{1050\\lambda_{m}^{4}}(\\bar{I_{1}^{3}}-27)\\\\ & + & \\dfrac{19}{7000\\lambda_{m}^{6}}(\\bar{I_{1}^{4}}-81) + \\dfrac{519}{673750\\lambda_{m}^{8}}(\\bar{I_{1}^{5}}-243)]\\\\ & + & \\dfrac{1}{D_1}(\\dfrac{J^{2}-1}{2}-\\mathrm{ln}J) \\end{array} \\]

where \\(\\mu\\) is the initial shear modulus of the material, \\(\\lambda_{m}\\) is limiting network stretch, and \\(D_1\\) is the material incompressibility parameter.

The initial shear modulus is

\\[ \\mu=\\dfrac{\\mu_{0}}{1+\\dfrac{3}{5\\lambda_{m}^{2}}+\\dfrac{99}{175\\lambda_{m}^{4}}+\\dfrac{513}{875\\lambda_{m}^{6}}+\\dfrac{42039}{67375\\lambda_{m}^{8}}} \\]

The initial bulk modulus is

\\[ K=\\dfrac{2}{D_1} \\]

As the parameter \\(\\lambda_L\\) goes to infinity, the model is equivalent to neo-Hookean form.

"},{"location":"mateditor/mat_theory_hyper-elasticity/#blatz-ko-foam-model","title":"Blatz-Ko foam model","text":"

The form of strain-energy potential for the Blatz-Ko model is:

\\[ W=\\frac{\\mu}{2}\\left(\\frac{I_{2}}{I_{3}}+2\\sqrt{I_{3}}-5\\right) \\]

where \\(\\mu\\) is the initial shear modulus of material. The initial bulk modulus is defined as :

\\[ K = \\frac{5}{3}\\mu \\]"},{"location":"mateditor/mat_theory_hyper-elasticity/#gent-model","title":"Gent model","text":"

The form of the strain-energy potential for the Gent model is:

\\[ W=-\\frac{\\mu J_{m}}{2}\\mathrm{ln}\\left(1-\\frac{\\bar{I}_{1}-3}{J_{m}}\\right)+\\frac{1}{D_1}\\left(\\frac{J^{2}-1}{2}-\\mathrm{ln}J\\right) \\]

where \\(\\mu\\) is the initial shear modulus of material, \\(J_m\\) is limiting value of \\(\\bar{I}_1-3\\), \\(D_1\\) is material incompressibility parameter.

The initial bulk modulus is

\\[ K=\\dfrac{2}{D_1} \\]

When the parameter \\(J_m\\) goes to infinity, the Gent model is equivalent to neo-Hookean form.

"},{"location":"mateditor/mat_theory_hyper-elasticity/#mooney-rivlin-model","title":"Mooney-Rivlin model","text":"

This model includes two-, three-, five-, and nine-terma Mooney-Rivlin models. The form of the strain-energy potential for a two-parameter Mooney-Rivlin model is

\\[ W=C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right)+\\frac{1}{D_1}\\left(J-1\\right)^{2} \\]

where \\(C_{10}\\), \\(C_{01}\\), and \\(D_{1}\\) are the material constants.

The form of strain-energy potential for a three-parameter Mooney-Rivlin model is

\\[ W=C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right)+C_{11}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right)+\\frac{1}{D_1}\\left(J-1\\right)^{2} \\]

where \\(C_{10}\\), \\(C_{01}\\), \\(C_{11}\\), and \\(D_1\\) are material constants.

The form of strain-energy potential for a five-parameter Mooney-Rivlin model is

\\[ \\begin{array}{ccl} W & = & C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right)+C_{20}\\left(\\bar{I}_{1}-3\\right)^{2}\\\\ & + & C_{11}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right)+C_{02}\\left(\\bar{I}_{2}-3\\right)^{2}+\\frac{1}{D_1}\\left(J-1\\right)^{2} \\end{array} \\]

where \\(C_{10}\\), \\(C_{01}\\), \\(C_{20}\\), \\(C_{11}\\), \\(C_{02}\\), and \\(D_1\\) are material constants.

The form of strain-energy potential for a nine-parameter Mooney-Rivlin model is

\\[ \\begin{array}{ccl} W & = & C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right)+C_{20}\\left(\\bar{I}_{1}-3\\right)^{2}\\\\ & + & C_{11}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right)+C_{02}\\left(\\bar{I}_{2}-3\\right)^{2}+C_{30}\\left(\\bar{I}_{1}-3\\right)^{3}\\\\ & + & C_{21}\\left(\\bar{I}_{1}-3\\right)^{2}\\left(\\bar{I}_{2}-3\\right)+C_{12}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right)^{2}+C_{03}\\left(\\bar{I}_{2}-3\\right)^{3}\\\\ & + & \\frac{1}{D_1}\\left(J-1\\right)^{2} \\end{array} \\]

where \\(C_{10}\\), \\(C_{01}\\), \\(C_{20}\\), \\(C_{11}\\), \\(C_{02}\\), \\(C_{30}\\), \\(C_{21}\\), \\(C_{12}\\), \\(C_{03}\\), and \\(D_1\\) are material constants.

The initial shear modulus is given by:

\\[ \\mu=2(C_{10}+C_{01}) \\]

The initial bulk modulus is

\\[ K=\\dfrac{2}{D_1} \\]"},{"location":"mateditor/mat_theory_hyper-elasticity/#neo-hookean-model","title":"Neo-Hookean model","text":"

The Neo-Hookean model is a well-known hyperelastic model with an expanded linear rule (Hooke rule) having isotropy so that it can respond to finite deformation problems. The elastic potential is as follows.

\\[ W=\\frac{\\mu}{2}(\\bar{I}_{1}-3)+\\dfrac{1}{D_{1}}(J-1)^{2} \\]

where \\(\\mu\\) is initial shear modulus of materials, \\(D_{1}\\) is the material constant.

The initial bulk modulus is given by:

\\[ K=\\dfrac{2}{D_1} \\]"},{"location":"mateditor/mat_theory_hyper-elasticity/#ogden-compressible-foam-model","title":"Ogden compressible foam model","text":"

The strain-energy potential of the Ogden compressible foam model is based on the principal stretches of left Cauchy strain tensor, which has the form:

\\[ W=\\sum_{i=1}^{N}\\frac{\\mu_{i}}{\\alpha_{i}}\\left(J^{\\alpha_{i}/3}\\left(\\bar{\\lambda}_{1}^{\\alpha_{i}}+\\bar{\\lambda}_{2}^{\\alpha_{i}}+\\bar{\\lambda}_{3}^{\\alpha_{i}}\\right)-3\\right)+\\sum_{i=1}^{N}\\frac{\\mu_{i}}{\\alpha_{i}\\beta_{i}}\\left(J^{-\\alpha_{i}\\beta_{i}}-1\\right) \\]

where N determines the order of the polynomial, \\(\\mu_i\\), \\(\\alpha_i\\) are material constants, \\(D_k\\) is incompressiblity parameter. The reduced principal strench is defined by:

\\[ \\bar{\\lambda}_{p}=J^{-\\frac{1}{3}}\\lambda_p,\\; J=(\\lambda_{1}\\lambda_{2}\\lambda_{3})^{\\frac{1}{2}} \\]

The initial shear modulus is given by:

\\[ \\mu=\\dfrac{\\sum_{i=1}^{N}\\mu_{i}\\alpha_{i}}{2} \\]

The initial bulk modulus K is defined by

\\[ K = \\sum_{i=1}^{N}\\mu_{i}\\alpha_{i}\\left(\\dfrac{1}{3}+\\beta_{i}\\right) \\]

When parameters N=1, \\(\\alpha_1\\)=-2, \\(\\mu_1\\)=-\\(\\mu\\), and \\(\\beta\\)=0.5, the Ogden compressible model is converted to the Blatz-Ko model.

"},{"location":"mateditor/mat_theory_hyper-elasticity/#ogden-model","title":"Ogden model","text":"

The strain-energy potential of the Ogden compressible foam model is based on the principal stretches of left Cauchy strain tensor, which has the form:

\\[ W=\\sum_{i=1}^{N}\\frac{\\mu_{i}}{\\alpha_{i}}\\left(\\bar{\\lambda}_{1}^{\\alpha_{i}}+\\bar{\\lambda}_{2}^{\\alpha_{i}}+\\bar{\\lambda}_{3}^{\\alpha_{i}}-3\\right)+\\sum_{k=1}^{N}\\frac{1}{D_{k}}\\left(J-1\\right)^{2k} \\]

where N determines the order of the polynomial, \\(\\mu_i\\), \\(\\alpha_i\\) are material constants, \\(D_k\\) is incompressiblity parameter. The reduced principal strench is defined by:

\\[ \\bar{\\lambda}_{p}=J^{-\\frac{1}{3}}\\lambda_p,\\; J=(\\lambda_{1}\\lambda_{2}\\lambda_{3})^{\\frac{1}{2}} \\]

The initial shear modulus is given by:

\\[ \\mu=\\dfrac{\\sum_{i=1}^{N}\\mu_{i}\\alpha_{i}}{2} \\]

The initial bulk modulus K is defined by

\\[ K = \\dfrac{2}{D_1} \\]

When parameters N=1, \\(\\alpha_1\\)=2, the Ogden model is converted to the neo-Hookean model. When parameters N=2, \\(\\alpha_1\\)=2 and \\(\\alpha_2\\)=-2, the Ogden model is converted to the 2-parameter Mooney-Rivlin model.

"},{"location":"mateditor/mat_theory_hyper-elasticity/#polynomial-form","title":"Polynomial form","text":"

The polynomial form of strain-energy potential is:

\\[ W=\\sum_{i+j=1}^{N}c_{ij}\\left(\\bar{I}_{1}-3\\right)^{i}\\left(\\bar{I_{2}}-3\\right)^{j}+\\sum_{k=1}^{N}\\frac{1}{D_{k}}\\left(J-1\\right)^{2k} \\]

where \\(N\\) determines the order of polynomial, \\(c_{ij}\\), \\(D_k\\) are material constants.

The initial shear modulus is given by:

\\[ \\mu=2\\left(C_{10}+C_{01}\\right) \\]

The initial bulk modulus K is defined by

\\[ K = \\dfrac{2}{D_1} \\]

The Polynomial model is converted to following models with specific parameters:

Parameters of Polynomial model Equivalent model N=1, \\(C_{01}\\)=0 neo-Hookean N=1 2-parameter Mooney-Rivlin N=2 5-parameter Mooney-Rivlin N=3 9-parameter Mooney-Rivlin"},{"location":"mateditor/mat_theory_hyper-elasticity/#yeoh-model","title":"Yeoh model","text":"

The Yeoh model is also called the reduced polynomial form. The strain-energy potential is

\\[ W=\\sum_{i=1}^{N}c_{i0}\\left(\\bar{I}_{1}-3\\right)^{i}+\\sum_{k=1}^{N}\\frac{1}{D_{k}}\\left(J-1\\right)^{2k} \\]

where N denotes the order of the polynomial, \\(C_{i0}\\) and \\(D_k\\) are material constants. When N=1, Yeoh becomes neo-Hookean model.

The initial shear modulus is defined:

\\[ \\mu=2c_{10} \\]

The initial bulk modulus is:

\\[ K=\\frac{2}{D_1} \\]"},{"location":"mateditor/mat_theory_hyper-elasticity/#hyperelasticity-material-curve-fitting","title":"Hyperelasticity Material Curve Fitting","text":"

The mechanical response of hyperelastic materials is determined by the hyperelastic constants in the strain energy density function of a model. To get correct results during a hyperelastic analysis, it is required to precisely assess the material constants of the materials being tested. These constants are usually derived for a material based on the experimental strain-stress data. The test data are generally taken from several modes of deformation over a wide range of strain values. The material constants could be fit using test data in at least as many deformation states as will be experienced in the finite element analysis.

For hyperelastic materials, simple deformation tests can be used to characterize the material constants. The six different deformation modes are graphically illustrated in the figure below. Combinations of data from multiple tests will enhance the characterization of the hyperelastic behavior of a material.

Although these six different deformation states are accepted, we find that upon the addition of hydrostatic stresses, the following modes of deformation are the same:

  1. Uniaxial Tension and Equibiaxial Compression.
  2. Uniaxial Compression and Equibiaxial Tension.
  3. Planar Tension and Planar Compression.

With these equivalent modes of testing, we now have only three independent deformation modes for which one can get experimental data.

In the analysis, when the coordinate system is chosen to consistent with the principal directions of deformation, the right Cauchy-Green strain tensor can be written in matrix form by:

\\[ [C] = \\begin{bmatrix} \\lambda_1^2 & 0 & 0\\\\ 0 & \\lambda_2^2 & 0\\\\ 0 & 0 & \\lambda_3^2 \\end{bmatrix} \\]

where \\(\\lambda_i\\)=1+\\(\\epsilon_i\\) is principal stretch ratio in the i-th direction, \\(epsilon_i\\) is principal value of the engineering strain tensor in the i-th direction. The principal invariants of right Cauchy-Green strain tensor \\(C_{ij}\\) are:

\\[ I_1 = \\lambda_1^2+\\lambda_2^2+\\lambda_3^2 \\] \\[ I_2 = \\lambda_1^2\\lambda_2^2 + \\lambda_1^2\\lambda_3^2 + \\lambda_2^2\\lambda_3^2 \\] \\[ I_3 = \\lambda_1^2\\lambda_2^2\\lambda_3^2 \\]

For the fully incompressible material, the principal invariant \\(I_3\\) is one:

\\[ \\lambda_1^2\\lambda_2^2\\lambda_3^2=1 \\]"},{"location":"mateditor/mat_theory_hyper-elasticity/#uniaxial-tension-equibiaxial-compression","title":"Uniaxial tension (Equibiaxial compression)","text":"

For the uniaxial tension deformation, the principal stretch ratios in the directions orthogonal to the 'pulling' axis is identical. Thus, the principal stretches during uniaxial tension \\(\\lambda_i\\) are given by:

Due to incompressibility:

\\[ \\lambda_2\\lambda_3=\\lambda^{-1} \\]

and with

\\[ \\lambda_2=\\lambda_3=\\lambda_1^{-1/2} \\]

For uniaxial tension, the first and second strain invariants then become:

\\[ I_1= \\lambda_1^2+2\\lambda_1^{-1}\\\\ I_2=2\\lambda_1+\\lambda_1^{-2} \\]

The corresponding engineering stress can be expressed using principal stretch ratio:

\\[ T_1=2(\\lambda_1-\\lambda_1^{-2})[\\dfrac{\\partial W}{\\partial I_1}+\\lambda_1^{-1}\\dfrac{\\partial W}{\\partial I_2}] \\]"},{"location":"mateditor/mat_theory_hyper-elasticity/#equibiaxial-tension-uniaxial-compression","title":"Equibiaxial tension (Uniaxial compression)","text":"

During an equibiaxial tension test, the principal stretch ratios in the directions being loaded are identical. Therefore, for quibiaxial tension, the principal stretches, \\(\\lambda_i\\) are given by:

According to incompressibility, we have

\\[ \\lambda_3=\\lambda_1^{-2} \\]

For equibiaxial tension, the first and second strain invariants then become:

\\[ I_1=2\\lambda_1^2+\\lambda_1^{-4} \\\\ I_2=\\lambda_1^4+2\\lambda_1^{-2} \\]

The corresponding engineering stress can be expressed using principal stretch ratio:

\\[ T_1=2(\\lambda_1-\\lambda_1^{-5})[\\dfrac{\\partial W}{\\partial I_1} + \\lambda_1^2\\dfrac{\\partial W}{\\partial I_2}] \\]"},{"location":"mateditor/mat_theory_hyper-elasticity/#pure-shear-uniaxial-tension-and-uniaxial-compression-in-orthogonal-directions","title":"Pure Shear (Uniaxial tension and uniaxial compression in orthogonal directions)","text":"

For pure shear deformation mode, plane strain is generally assumed so that there is no deformation in the 'wide' direction of the specimen. Including the incompressibility, we have

\\[ \\lambda_2=1 \\\\ \\lambda_3 = \\lambda_1^{-1} \\]

For pure shear, the first and second strain invariants are:

\\[ I_1=I_2=\\lambda_1^2+\\lambda_1^{-2}+1 \\]

The corresponding engineering stress can be expressed using principal stretch ratio:

\\[ T_1=2(\\lambda_1 - \\lambda_1^{-3})[\\dfrac{\\partial W}{\\partial I_1} + \\dfrac{\\partial W}{\\partial I_2}] \\]"},{"location":"mateditor/mat_theory_hyper-elasticity/#volumetric-deformation","title":"Volumetric Deformation","text":"

The volumetric deformation is given as:

\\[ \\lambda_1=\\lambda_2=\\lambda_3=\\lambda\\\\ J=\\lambda^3 \\]

As nearly incompressible is assumed, we have:

\\[ \\lambda \\approx 1 \\]

The pressure P is directly related to the volume ratio J:

\\[ P=\\dfrac{\\partial W}{\\partial J} \\]"},{"location":"mateditor/mat_theory_hyper-elasticity/#deformations-for-principal-stretches-based-models","title":"Deformations for principal stretches based models","text":"

For the models based on the principal stretches, such Ogden model, the strain-stress relation can be obtained by deriving the strain energy with respect to the stretch.

\\[ \\sigma(\\lambda)=\\dfrac{\\partial W(\\lambda)}{\\partial \\lambda} \\]

The corresponding engineering stress is:

\\[ T_1 = \\dfrac{\\partial W(\\lambda_1)}{\\partial \\lambda_1} \\lambda_1^{-1} \\]"},{"location":"mateditor/mat_theory_hyper-elasticity/#material-stability-check","title":"Material stability check","text":"

Stability checks are critical for the following analysis. A nonlinear material is stable if the secondary work required for an arbitrary change in the deformation is always positive. We usually use the Drucker stability criterion to determine the stability of the hyperelastic materials. Mathematically, this is:

\\[ d\\sigma_{ij}d\\epsilon_{ij}>0 \\]

where \\(d\\sigma\\) is the change in the Cauchy stress tensor corresponding to a change in the logarithmic strain.

The material stability checks can be done at the end of preprocessing but before an analysis actually begins. Checking for the stability of a material can be more conveniently accomplished by checking for the positive definiteness of the material stiffness. The program checks for the loss of stability of six typical stress paths including uniaxial tension and compression, equibiaxial tension and compression, and planar tension and compression. the range of the stretch ratio over which the stability is checked is chosen from 0.1 to 10.

"},{"location":"mateditor/mat_theory_io/","title":"Theory IO","text":"

Some properties are mutually exclusive of each other and require that only one property in the mutually exclusive set be unsuppressed. The addition or removing of the suppression for one of these properties automatically suppresses the other mutually exclusive properties.

For example, defining Isotropic Elasticity and Orthotropic Elasticity for the same material represents redundant elasticity behavior. Only one behavior can be active for the material. When such a conflict occurs, the property defined last is used and the previously defined, conflicting property is automatically suppressed.

The properties that are mutually exclusive are grouped in the following table.

Group Material Property Elastic properties Isotropic Elasticity, Orthotropic Elasticity, Anisotropic Elasticity, Mooney-Rivlin, Neo-Hookean, Polynomial, Yeoh, Ogden, Arruda-Boyce, Gent, Blatz-Ko, Ogden Foam, Extended Tube, Mullins Effect Plastic properties Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening Thermal conductivity properties Thermal Conductivity Isotropic, Thermal Conductivity Orthotropic Resistivity properties Isotropic Resistivity, Orthotropic Resistivity Electric permittivity properties Isotropic Relative Permittivity, Orthotropic Relative Permittivity Dielectric loss properties Isotropic Dielectric Loss Tangent, Orthotropic Dielectric Loss Tangent Magnetic permeability properties Isotropic Relative Permeability, Orthotropic Relative Permeability Magnetic loss properties Isotropic Relative Imaginary Permeability, Isotropic Magnetic Loss Tangent, Orthotropic Magnetic Loss Tangent"},{"location":"mateditor/mat_theory_plasticity/","title":"Plasticity","text":"

This section describes the plastic laws in details.

"},{"location":"mateditor/mat_theory_plasticity/#johnson-cook-model","title":"Johnson-Cook Model","text":"

In this model the material behaves as a linear-elastic material when the quivalent stress is lower than the plastic yield stress. For higher stress values, the material behavior is plastic, and the true stress is calculated as:

\\[ \\sigma = (a+b\\epsilon_p^n)(1+c\\cdot ln\\dfrac{\\dot{\\epsilon}}{\\dot{\\epsilon}_0})(1-(\\dfrac{T-T_r}{T_{melt}-T_r})^m) \\]

where \\(\\epsilon_p\\) is the plastic strain, \\(\\dot{\\epsilon}\\) is strain rate, \\(T\\) is the temperature, \\(T_r\\) is the ambient temperature, \\(T_{melt}\\) is the melting temperature. The plastic yield stress \\(a\\) should always be greater than zero. The plastic hardening exponent \\(n\\) must be less than or equal to 1.

"},{"location":"mateditor/mat_theory_plasticity/#zerilli-armstrong-model","title":"Zerilli-Armstrong Model","text":"

The stress during plastic deformation is defined by

\\[ \\sigma = C_0 + C_1 exp(-C_3 T + C_4 T ln \\dfrac{\\dot{\\epsilon}}{\\dot{\\epsilon}_0} ) + C_5 \\epsilon_p ^n \\]

where the yield stress \\(C_0\\) should be positive, plastic hardening exponent \\(n\\) must be less than 1.

"},{"location":"mateditor/mat_theory_plasticity/#hill-model","title":"Hill Model","text":"

The Hill model describes the orthotropic plastic material. The yield stress can be input by parameters or tabular data. The yield stress is defined as:

\\[ \\sigma_y = a(\\epsilon_0+\\epsilon_p)^n \\mathrm{max}(\\dot{\\epsilon}, \\dot{\\epsilon}_0)^m \\]

The maximum elastic stress is given by

\\[ \\sigma_0 = a(\\epsilon_0)^n (\\dot{\\epsilon}_0)^m \\]

The yield stress is compresed to the equivalent stress: $$ \\sigma_{eq} = \\sqrt{A_1 \\sigma_1^2 + A_2 \\sigma_2^2 -A_3 \\sigma_1 \\sigma_2 +A_{12} \\sigma_{12}^2} $$

where parameters \\(A_1\\), \\(A_2\\), \\(A_3\\), and \\(A_{12}\\) are defined by the Lankford constants.

"},{"location":"mateditor/mat_theory_plasticity/#orthotropic-hill-model","title":"Orthotropic Hill Model","text":"

This model describes the orthotropic elastic behavior material with Hill plasticity. The yield stress is compared to an equivalent stress for the orthotropic materials. The equivalent stress for solid elements is defined as:

\\[ \\sigma_{eq} = \\sqrt{F(\\sigma_{22}^2 - \\sigma_{33}^2) + G(\\sigma_{33}^2 - \\sigma_{11}^2) + H(\\sigma_{11} - \\sigma_{22}^2) + 2L\\sigma_{23}^2 + 2M\\sigma_{31}^2 + 2N\\sigma_{12}^2} \\]

For the shell element, the equivalent yield stress is :

\\[ \\sigma_{eq} = \\sqrt{(G+H)\\sigma_{11}^2 +(F+H) \\sigma_{22}^2 - 2H \\sigma_{11} \\sigma_{22} + 2N\\sigma_{12}^2} \\]"},{"location":"mateditor/mat_theory_plasticity/#rate-dependent-multilinear-hardening","title":"Rate-Dependent MultiLinear Hardening","text":"

This model describes an isotropic elasto-plastic material using user-input funcitons for the strain-stress curves at the different strain rates. No yield stress equations are needed because constitutive relations are given by the tabular data.

"},{"location":"mateditor/mat_theory_plasticity/#cowper-symonds-model","title":"Cowper-Symonds Model","text":"

Similar to the Johnson-Cook model, Cowper-Symonds law models isotropic elasto-plastic materials. The yield stress is defined by the stress constants, tabular data, or a combination of both. The pure constant formulation is given here:

\\[ \\sigma = (a+b\\epsilon_p^n)(1+(\\dfrac{\\dot{\\epsilon}}{c})^{\\frac{1}{p}}) \\]

where the yield stress \\(a\\) should be positive, plastic hardening exponent \\(n\\) must be less than 1.

"},{"location":"mateditor/mat_theory_plasticity/#zhao-model","title":"Zhao Model","text":"

Zhao model describes the isotropic plastic strain rate-dependent materials. The strain-stress relation is based on the formula below:

\\[ \\sigma = (A + B \\epsilon_p^n) + (C-D\\epsilon_p^m)\\cdot \\mathrm{ln}\\dfrac{\\dot{\\epsilon}}{\\dot{\\epsilon}_0}+E_1 \\dot{\\epsilon}^k \\]

where the yield stress \\(A\\) should be positive, plastic hardening exponent \\(n\\) must be less than 1. If \\(\\dot{\\epsilon} \\le \\dot{\\epsilon}_0\\), the term \\((C-D\\epsilon_p^m)\\cdot \\mathrm{ln}\\dfrac{\\dot{\\epsilon}}{\\dot{\\epsilon}_0}=0\\), the stress becomes:

\\[ \\sigma = (A + B \\epsilon_p^n) + E_1 \\dot{\\epsilon}^k \\]"},{"location":"mateditor/mat_theory_plasticity/#steinberg-guinan-model","title":"Steinberg-Guinan Model","text":"

This model defines an isotropic elasto-plastic mateial with thermal softening. When the material approaches melting temperature, the yield strength and shear modulus decrease to zeero. The melting energy is given as

\\[ E_m = E_c + \\rho_0 C_p T_m \\]

where \\(E_c\\) is the cold compression energy.

When the internal energy \\(E\\) is less than \\(Em\\), the shear modulus and the yield stress are :

\\[ G = G_0 [1 + b_1 p V^{\\frac{1}{3}} - h(T-T_0)] e^{-\\frac{fE}{E-E_m}} \\] \\[ \\sigma_y = \\sigma_0(1+\\beta \\epsilon_p^{\\mathrm{(max)}})^n [1 + b_2 p V^{\\frac{1}{3}} -h(T-T_0)]e^{-\\frac{fE}{E-E_m}} \\]

where initial shear modulus \\(G_0 = \\dfrac{E_0}{2(1+\\nu)}\\).

"},{"location":"mateditor/mat_theory_plasticity/#gurson-model","title":"Gurson Model","text":"

The Gurson law can be used to model visco-elasto-plastic strain rate-depdent porous materials. The yield stress can be obtained from the tabular data or the Cowper-Symond's law, the latter formulation is defined as:

\\[ \\sigma_M = (A + B \\epsilon_M^n) (1 + (\\dfrac{\\dot{\\epsilon}}{c})^{\\frac{1}{p}}) \\]

The von Mises critera for the viscoplastic flow are given as

\\[ \\Omega_{vm} = \\sigma_{qt} - \\sigma_{M}\\sqrt{1 + q_3 f^{*2} - 2q_1 f^{*2} \\mathrm{cosh}(\\dfrac{3q_2\\sigma_m}{2\\sigma_M})} \\]

or

\\[ \\Omega_{vm} =\\dfrac{\\sigma^2_{qe}}{\\sigma^2_M} + 2q_1 f^* \\mathrm{cosh}(\\dfrac{3}{2}q_2 \\dfrac{\\sigma_m}{\\sigma_M}) - (1 + q_3 f^{*2}) \\]

where \\(\\sigma_M\\) is the admissible stress, \\(\\sigma_m\\) is the trace, \\(\\sigma_eq\\) is the von Mises stress, \\(q_1\\), \\(q_2\\), and \\(q_3\\) are the Gurson material constants. The specific coalescence function \\(f*\\) is defined as

\\[ f^* = f_c + \\dfrac{f_u - f_c}{f_F - f_c}(f - f_c) \\quad \\mathrm{if}\\, f \\gt f_c \\]"},{"location":"mateditor/mat_theory_plasticity/#barlat3-model","title":"Barlat3 Model","text":"

This is an orthotropic elastoplastic law for modeling anisotropic materials in metal forming process. Thus it is widely applied in the shell elements. The plastic hardening is described by the input parameters or user-defined tabular data. The anisotropic yield criteria F for plane stress is given by:

\\[ F = a |K_1 + K_2|^m + a |K_1 - K_2|^m + c |2K_2|^m - 2\\sigma_y^m = 0 \\]

where coefficient \\(K_1 = \\frac{\\sigma_{xx} + h \\sigma_{yy}}{2}\\) and \\(K_2 = \\sqrt{(\\frac{\\sigma_{xx} - h \\sigma_{yy}}{2})^2 + p^2 \\sigma_{xy}^2}\\). The constants \\(a\\), \\(c\\), and \\(h\\) can be obtained from the Lankford constants.

When the Young's modulus is based on the input parameters. The expression is

\\[ E(t) = E - (E_0-E_{inf})[1-\\mathrm{exp}(-C_E \\bar{\\epsilon}_p)] \\]

where \\(E_0\\) is the initial Youngs' modulus, \\(E_{inf}\\) is the asymptotic Young's modulus, and \\(\\bar{\\epsilon}_p\\) is the accumulated equivalent plastic strain.

"},{"location":"mateditor/mat_theory_plasticity/#yoshida-uemori-model","title":"Yoshida-Uemori Model","text":"

This model can describe the large strain cyclic plasticity of metals. The law is based on the yielding and bounding surfaces.

For solid elements, von Mises yield criterion is used as:

\\[ f = \\dfrac{3}{2} (\\mathbf{s} - \\mathbf{\\alpha}) \\colon (\\mathbf{s} - \\mathbf{\\alpha}) - Y^2 \\]

For shell elements, Hill or Barlat3 yield criterion is used. The Hill law is expressed as:

\\[ f_{Hill} = \\varphi(\\mathbf{\\sigma} - \\mathbf{\\alpha})- Y^2 \\]

where \\(Y\\) is yield stress, and \\(\\mathbf{\\alpha}\\) is total back stress. Let \\(\\mathbf{A}=\\mathbf{\\sigma}-\\mathbf{\\alpha}\\), the function \\(\\varphi\\) becomes

\\[ \\varphi(A) = A_{xx}^2 - \\dfrac{2r_0}{1+r_0}A_{xx}A_{yy} + \\dfrac{r_0(1+r_{90})}{r_{90}(1+r_0)}A_{yy}^2 + \\frac{r_0 + r_{90}}{r_{90}(1+r_0)}(2r_{45}+1)A_{xy}^2 \\]

The Barlat law is defined as:

\\[ f_{Barlat} = \\phi(\\sigma - \\alpha) - 2Y^M \\]

where \\(M\\) is the exponent in Barlat's yield criterion.

"},{"location":"mateditor/mat_theory_plasticity/#hohnson-holmquist-model","title":"Hohnson-Holmquist Model","text":"

This law describes the behaivor of brittle materials, such as glass and ceramics.

\\[ \\sigma^* = (1-D)\\sigma^*_i + D \\sigma_f^* \\]

where the equivalent stress of the intact materials \\(\\sigma_i^*\\) can be expressed as

\\[ \\sigma_i^* = a (P^* + T^*)^n (1 + c\\mathrm{ln}\\dfrac{\\dot{\\epsilon}}{\\dot{\\epsilon}_0}) \\]

and the equivalent stress of the failed materials \\(\\sigma_f^*\\) is

\\[ \\sigma_f^* = b(P^*)^m (1+c\\mathrm{ln}\\dfrac{\\dot{\\epsilon}}{\\dot{\\epsilon}_0}) \\]"},{"location":"mateditor/mat_theory_plasticity/#swift-voce-model","title":"Swift-Voce Model","text":"

Swift-Voce elastoplastic model can combine the Johnson-Cook strain rate hardening and temperature softening. This model can be applied for the orthotropic materials and allows a quadratic non-assoicated flow rule. The yield stress can be calculated using a combination of Swift and Voce models as shown below.

\\(\\sigma_y = \\{ \\alpha [A(\\bar{\\epsilon}_p + \\epsilon_0)^n] + (1+\\alpha)[K_0 + Q(1-\\mathrm{exp}(-B\\bar{\\epsilon }_p))]\\} (1+C \\mathrm{ln}\\dfrac{\\dot{\\bar{\\epsilon}}_p}{\\dot{\\epsilon}_0}) [1 - (\\dfrac{T-T_{ref}}{T_{melt} - T_{ref}})^m]\\)

The plastic non-associated flow rule is computed as:

\\[ \\Delta \\epsilon_p = \\Delta \\bar{\\epsilon}_p \\dfrac{\\partial g(\\sigma)}{\\partial \\sigma} \\]

where \\(g(\\sigma) = \\sqrt{\\sigma^TG\\sigma}\\).

"},{"location":"mateditor/mat_theory_plasticity/#hensel-spittel-model","title":"Hensel-Spittel Model","text":"

The hensel-Spittel yield stress is a function of strain, strain rate, and temperature. This model is often used in hot forging simulations. The yield stress is defined as :

\\[ \\sigma_y = A_0 e^{m_1 T} \\epsilon^{m_2} \\dot{\\epsilon}^{m_3} e^{\\frac{m_4}{\\epsilon}} (1+\\epsilon)^{m_5T} e^{m_7\\epsilon} \\]

where true strain \\(\\epsilon = \\epsilon_0 + \\bar{\\epsilon}_p\\), \\(\\dot{\\epsilon}\\) is the true strain rate.

"},{"location":"mateditor/mat_theory_plasticity/#vegter-model","title":"Vegter Model","text":"

The yield function is defined as

\\[ \\phi = \\bar{\\sigma} - \\sigma_Y \\]

where \\(\\bar{\\sigma}\\) is the interpolated Vegter equivalent stress.

"},{"location":"mateditor/mat_workflow/","title":"Material workflow","text":"

This section discusses about the material data, and precedures for working with MatEditor.

"},{"location":"mateditor/mat_workflow/#material-data","title":"Material data","text":"

Material data is the source of the material information that is used for the analysis of the system it is contained in. The information in a material data component system is used if shared to an analysis system. MatEditor allows you to view, edit, and add data for use in your analysis system.

"},{"location":"mateditor/mat_workflow/#importing","title":"Importing","text":"

You can import data into an system as a new material. The following types of files are supported for import:

Note

When you import material data, the materials contained in that source will be added to the material outline.

"},{"location":"mateditor/mat_workflow/#editing","title":"Editing","text":"

Property and Table panes provide constant and tabular data input. You can edit both constant and tabular data.

"},{"location":"mateditor/mat_workflow/#constant-data","title":"Constant data","text":"

You edit constant data by changing the value and/or unit of that data in the Properties pane. The value is modified by clicking the cell in the Value column and typing in the new value. If available, changing the unit will convert the value to correspond to the new unit. If the value entered is invalid or not acceptable it will be indicated in yellow or red to gain users' attention.

"},{"location":"mateditor/mat_workflow/#tabular-data","title":"Tabular data","text":"

If Value cell shows a tabular format indication. This data is edited in the Table pane and each datum is a value and unit as one integral piece. If the value entered is invalid or not acceptable it will be indicated in yellow or red to gain users' attention. The unit is shown in the header, and you can change unit if necessary. The units between table header and Property pane column are connnected. Modifying either one of them changes units on both areas.

"},{"location":"mateditor/mat_workflow/#suppression","title":"Suppression","text":"

A material property may be defined but suppressed to prevent it from being sent to analysis process in the system. A data item may be suppressed by selecting the dropdown in the suppression column. Suppressed items and its children are shown by a strike through the name (for example, ) and the dropdown being set to True in the suppression column.

"},{"location":"mateditor/mat_workflow/#perform-material-tasks-in-mateditor","title":"Perform material tasks in MatEditor","text":"

All material related tasks require that you perform the following basic tasks:

Task Procedure Create new material. In the Menu or Toolbar, click New Material to add a new material. Add material properties.
  1. Activate the material in the Material Outline pane that is to receive the additional property.
  2. Toggle the property in the Property Outline pane that you want to add.
Delete material properties.
  1. Activate the material in the Material Outline pane whose property is to be deleted.
  2. Select the material property in the Properties pane.
  3. Right-click and choose Delete or on the menu bar, choose Delete.
Modify material properties.
  1. Activate the material in the Material Outline pane that contains the property you want to modify.
  2. In the Properties pane change the value or unit for constant data.
  3. Perform one of the following:
Suppress material properties.
  1. Activate the material in the Material Outline pane that contains the property you want to suppress.
  2. Select the dropdown in the suppression column for the property you want to suppress.
"},{"location":"mateditor/mateditor_overview/","title":"Overview","text":"

MatEditor is a free material editor software program for engineers. This tool provides you comprehensive material properties those are often used in engineering simulation and finite element analysis.

"},{"location":"mateditor/mateditor_overview/#specification","title":"Specification","text":"Specification Description Operation system Microsoft Windows 7 to 10; 64-bit Physical memory At least 4 GB

Supported unit systems :

"},{"location":"mateditor/mateditor_overview/#material-properties","title":"Material properties","text":"

The supported material properties are listed in the table below.

Category Materials Basic Density, Isotropic Thermal Expansion, Isotropic Instantaneous Thermal Expansion, Orthotropic Thermal Expansion, Orthotropic Instantaneous Thermal Expansion, Constant Damping Coefficient Linear Elastic Isotropic Elasticity, Orthotropic Elasticity, Viscoelastic Hyperelastic Test Data Uniaxial Test Data, Biaxial Test Data, Shear Test Data, Volumetric Test Data, SimpleShear Test Data, Uniaxial Tension Test Data, Uniaxial Compression Test Data Hyperelastic Arruda-Boyce, Blatz-Ko, Gent, Mooney-Rivlin 2, Mooney-Rivlin 3, Mooney-Rivlin 5, Mooney-Rivlin 9, Neo-Hookean, Ogden 1st Order, Ogden 2nd Order, Ogden 3rd Order, Polynomial 1st Order, Polynomial 2nd Order, Polynomial 3rd Order, Yeoh 1st Order, Yeoh 2nd Order, Yeoh 3rd Order Plasticity Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening, Anand Viscoplasticity, Johnson-Cook, Zerilli-Armstrong Creep Strain Hardening, Time Hardening, Generalized Exponential, Generalized Graham, Generalized Blackburn, Modified Time Hardening, Modified Strain Hardening, Generalized Garofalo, Exponential Form, Norton, Combined Time Hardening, Rational Polynomial, Generalized Time Hardening Visco-elastic Prony Shear Relaxation, Prony Volumetric Relaxation Equations of State (EOS) Compaction, Gruneisen, Ideal Gas, Linear, LSZK, Murnaghan, NASG, Noble-Abel, Osborne, Polynomial, Puff, Stiff Gas, Tillotson Failure Johnson Other Mechanical Strain Life Parameters, Compressive Ultimate Strength, Compressive Yield Strength, LaRc0304 Constants, Orthotropic Strain Limits, Orthotropic Stress Limits, Puck Constants, Tensile Ultimate Strength, Tensile Yield Strength, Tsai-Wu Constants, Shape Memory Effect, Drucker-Prager Strength Piecewise, Drucker-Prager Strength Linear, Ideal Gas EOS, Crushable Foam, Nonlinear Elastic Model Damage, Plakin Special Hardening, Tensile Pressure Failure, Crack Softening Failure Thermal Enthalpy, Isotropic Thermal Conductivity, Orthotropic Thermal Conductivity, Specific Heat Electromagnetics B-H Curve, Isotropic Relative Permeability, Orthotropic Relative Permeability, Isotropic Resistivity, Orthotropic Resistivity, Isotropic Relative Permittivity, Orthotropic Relative Permittivity, Isotropic Dielectric Loss Tangent, Isotropic Magnetic Loss Tangent, Isotropic Relative Imaginary Permeability, Orthotropic Dielectric Loss Tangent, Orthotropic Magnetic Loss Tangent Fluid Dynamic Viscosity, Kinematic Viscosity, Lemalar Prandtl Number, Turbulent Prandtl Number, ALE"},{"location":"mateditor/mateditor_overview/#predefined-materials","title":"Predefined materials","text":"

WELSIM also provide predefined materials, which covers most of commonly used materials. Users can choose these materials and apply to the successive finite element analysis.

Category Materials General Materials Structural Steel, Stainless Steel, Aluminum Alloy, Concrete, Copper Alloy, Gray Cast Iron, Titanium Alloy Nonlinear Materials Aluminum Alloy NL, Concrete NL, Copper Alloy NL, Stainless Steel NL, Structural Steel NL, Titanium Alloy NL Hyperelastic Materials Elastomer Mooney-Rivlin, Elastomer Neo-Hookean, Elastomer Ogden, Elastomer Yeoh, Neoprene Rubber Thermal Materials Brass, Bronze, Copper, Diamond, Ferrite, Nodular Cast Iron, Solder, Teflon, Tungsten, Wood Electromagnetic Materials SS416, Supermendure, TDK-K1, TDK-M33, TDK-N30, TDK-N41, TDK-N45, TDK-N48, TDK-N49, TDK-N87, TDK-N97, TDK-T38, TDK-T66 Other Materials Water Liquid, Argon, Ash"},{"location":"mateditor/mateditor_overview/#download","title":"Download","text":"

MatEditor software is available at our official website.

"},{"location":"mateditor/material_data/","title":"Defining materials","text":"

This section describes how to create material objects and define material properties in the WELSIM application.

"},{"location":"mateditor/material_data/#overview","title":"Overview","text":"

Material Module serves as a database for material properties used in a modeling project. The module not only provides a material library but also allow you to create a material using the given properties. The spreadsheet of a Material object is the primary user interface designed to let you create, save, and retrieve material models. The well-defined material object can be saved and used in the subsequent projects.

Material Module is shown as a Material Project and Material Objects in the Project Explorer (tree) window. The solution system contains only one Material Project, which acts as a material repository in the modeling system. The Material Project may include multiple Material Objects, where the properties can be added or edited by users.

To access Material Object properties, you can choose one of the following methods: * Double click on the Material Object. * Right click on a Material Object, and select Edit item from the context menu.

"},{"location":"mateditor/material_data/#modes-of-operation","title":"Modes of operation","text":"

The data included in the Material Module is automatically saved as you save the project.

"},{"location":"mateditor/material_data/#user-interface","title":"User interface","text":"

The Material Editor spreadsheet is an essential portion of the WELSIM user interface, and it displays material-related components that allow users to edit material data easily.

"},{"location":"mateditor/material_data/#editing-mode","title":"Editing mode","text":"

Presented in this section are two configurations for the material property editing. The first configuration method is based on the library as shown in Figure\u00a0[fig:ch3_guide_mat_ui_lib], and the second configuration is designed to manually combine the properties for the material object as shown in Figure\u00a0[fig:ch3_guide_mat_ui_build]. You can click on the Library or Build tab to switch these two editing modes.

Note

  1. You can click on category tabs to browse different materials.
  2. Loading a material dataset from the library removes all pre-existing properties.
"},{"location":"mateditor/material_data/#build-outline-tab","title":"Build outline tab","text":"

The Build Outline Tab shows an outline of the contents of the togglable material properties. You can add a property data entry to the material by toggling on the property entry or remove property by toggling off the property entry.

"},{"location":"mateditor/material_data/#properties-pane","title":"Properties pane","text":"

The Properties pane displays all properties that are going to be added to the Material Object. You can tune the property values at this pane. The columns in this spreadsheet pane are:

You can delete a property by right-clicking on a row and select Remove Rows from the pop-up context menu.

The Material Properties pane provides the following command buttons to the bottom of the window:

"},{"location":"mateditor/material_data/#working-with-material-data","title":"Working with material data","text":""},{"location":"mateditor/material_data/#exporting","title":"Exporting","text":"

You can export the complete material data to an external file. The following format is supported for export:

To implement the exporting, you can use one of the following methods:

"},{"location":"mateditor/material_data/#mateditor-applicaiton","title":"MatEditor applicaiton","text":"

MatEditor is a free application allow you to create and edit material data for the computer aided engineering. It is a smaller and concise application but has most of features that material module of WELSIM has. More details about MatEditor, please visit MatEditor page.

"},{"location":"unitconverter/unitconverter/","title":"UnitConverter","text":"

UnitConverter is a free unit conversion software program for engineers. This tool allows you to convert a large number of engineering units quickly and accurately.

"},{"location":"unitconverter/unitconverter/#specification","title":"Specification","text":"Specification Description Operation system Microsoft Windows 7 to 10; 64-bit Physical memory At least 4 GB

Supported unit systems :

"},{"location":"unitconverter/unitconverter/#supported-units","title":"Supported units","text":"

The supported units are listed in the table below.

Category Materials Base Angle, Current, Length, Mass, Temperature, Time Common Area, Density, Energy, Frequency, Volume Mechanical Acceleration, Angular Acceleration, Angular Velocity, Force, Moment of Inertia, Power, Pressure, Torque, Velocity Thermal Heat Flux Density, Heat Transfer Coefficient, Specific Heat Capacity, Thermal Conductivity, Thermal Expansivity Electrical Capacitance, Electric Charge, Electrical Conductance, Electrical Conductivity, Inductance, Surface Charge Density, Surface Current Density, Voltage, Volume Charge Density Magnetic Magnetic field strength, Magnetic flux density"},{"location":"unitconverter/unitconverter/#download","title":"Download","text":"

UnitConverter software is available at our official website.

"},{"location":"welsim/release_notes/","title":"WELSIM release notes","text":"

This release notes are specific to WELSIM 2024R1 and arranged by the version and features.

"},{"location":"welsim/release_notes/#upgrading","title":"Upgrading","text":"

To upgrade WELSIM to the latest version, download the installer from our official website . \u200b

Since version 2.1, WelSim provides a version checker in the application, users can click Help -> Check for Updates on the menu and know if a new version is available.

To inspect the currently installed version, open the About dialog in WELSIM application.

"},{"location":"welsim/release_notes/#changelog","title":"Changelog","text":""},{"location":"welsim/release_notes/#2024r1-28-jan-at-2024","title":"2024R1 (2.8) Jan. at 2024","text":""},{"location":"welsim/release_notes/#2023r3-27-sept-at-2023","title":"2023R3 (2.7) Sept. at 2023","text":""},{"location":"welsim/release_notes/#2023r2-26-april-at-2023","title":"2023R2 (2.6) April at 2023","text":""},{"location":"welsim/release_notes/#2023r1-25-jan-at-2023","title":"2023R1 (2.5) Jan. at 2023","text":""},{"location":"welsim/release_notes/#24-dec-at-2022","title":"2.4 Dec. at 2022","text":""},{"location":"welsim/release_notes/#23-july-at-2022","title":"2.3 July at 2022","text":""},{"location":"welsim/release_notes/#22-may-at-2022","title":"2.2 May at 2022","text":""},{"location":"welsim/release_notes/#21-dec-at-2021","title":"2.1 Dec. at 2021","text":""},{"location":"welsim/release_notes/#20-january-at-2021","title":"2.0 January at 2021","text":""},{"location":"welsim/release_notes/#191-july-at-2020","title":"1.9.1 July at 2020","text":""},{"location":"welsim/release_notes/#19-november-2019","title":"1.9 November, 2019","text":""},{"location":"welsim/release_notes/#18-december-2018","title":"1.8 December, 2018","text":""},{"location":"welsim/release_notes/#17-july-2018","title":"1.7 July, 2018","text":""},{"location":"welsim/release_notes/#16-april-2018","title":"1.6 April, 2018","text":""},{"location":"welsim/release_notes/#15-february-2018","title":"1.5 February, 2018","text":""},{"location":"welsim/release_notes/#14-november-2017","title":"1.4 November, 2017","text":""},{"location":"welsim/release_notes/#13-september-2017","title":"1.3 September, 2017","text":""},{"location":"welsim/release_notes/#12-august-2017","title":"1.2 August, 2017","text":""},{"location":"welsim/release_notes/#11-july-2017","title":"1.1 July, 2017","text":""},{"location":"welsim/release_notes/#10-march-2017","title":"1.0 March 2017","text":""},{"location":"welsim/troubleshooting/","title":"Troubleshooting","text":"

If you encounter an issue that cannot be resolved here, please send the project file (*.wsdb and the associated folder), and the system information to info@welsim.com. Your computer information can be acquired by clicking About button on the toolbar.

"},{"location":"welsim/troubleshooting/#graphical-window-issue","title":"Graphical window issue","text":"

The graphics window fails to display items, and the context is all black. The screen capture of this issue is shown in Figure\u00a0[fig:ch6_issue_opengl].

"},{"location":"welsim/get_started/quick_start/","title":"Quick start","text":"

This section demonstrates you the primary GUI features and workflow of WELSIM application.

"},{"location":"welsim/get_started/quick_start/#graphical-user-interface","title":"Graphical user interface","text":""},{"location":"welsim/get_started/quick_start/#overview","title":"Overview","text":"

The WELSIM application provides you an ease-of-use graphical interface to customize the finite element analysis settings. The primary components of graphical user interface include:

An overview of graphical user interface is shown in Figure below.

.

"},{"location":"welsim/get_started/quick_start/#menu-and-toolbar","title":"Menu and toolbar","text":"

Menus and toolbar contain primary commands of the application as shown in Figure below. Sections Main Menus and Toolbars of have more details.

.

"},{"location":"welsim/get_started/quick_start/#graphics-window","title":"Graphics window","text":"

The Graphics window displays the geometries and associated symbols, text, and annotations. In this window, you can pan, rotate, and zoom the 3D geometries using mouse and key. In addition to the geometries, this window may contain annotation, Graphics Toolbar, coordinate system symbol, ruler, logo, etc. A schematic view of the Graphics window is shown in Figure below.

.

"},{"location":"welsim/get_started/quick_start/#material-definition-spreadsheet","title":"Material definition spreadsheet","text":"

The material module provides a spreadsheet panel for you to define and review material properties. An overview of the material property spreadsheet is shown in Figure\u00a0below.

.

"},{"location":"welsim/get_started/quick_start/#geometry-display","title":"Geometry display","text":"

The Graphics window displays the 3D geometries, meshed elements, result contours, etc. A 3D geometry and object properties are shown in Figure below.

.

"},{"location":"welsim/get_started/quick_start/#mesh-display","title":"Mesh display","text":"

Graphics window displays the mesh as you select the mesh related objects in the tree. The Properties View shows the statistical data of the mesh as shown in Figure\u00a0below.

.

"},{"location":"welsim/get_started/quick_start/#boundary-condition-display","title":"Boundary condition display","text":"

For the boundary conditions, the Graphics window displays the highlighted entities (faces, edges, vertices), the Property View, Tabular Data, and Chart windows show the boundary values over time. The Properties View window also allows you to scope the geometry entities and set values, as shown in Figure\u00a0below.

.

"},{"location":"welsim/get_started/quick_start/#solution-display","title":"Solution display","text":"

After solving, the user interface displays the solution and results. The Graphics window displays the result contour and legend. The Properties View shows the Maximum and Minimum values of the result at the given Set Number. The Tabular Data and Chart Windows illustrate the maximum and minimum values over the time as shown in Figure \u00a0below.

.

"},{"location":"welsim/get_started/quick_start/#result-legend","title":"Result legend","text":"

You can adjust the result contour and legend by right clicking on the legend field and set the parameters in the context menu, as shown in Figure\u00a0below.

.

"},{"location":"welsim/get_started/quick_start/#workflow","title":"Workflow","text":"

Using WELSIM is straightforward. The following gives you the primary workflow steps in starting a finite element analysis project from scratch:

"},{"location":"welsim/get_started/quick_start/#create-a-new-project","title":"Create a new project","text":"

Clicking New command from Toolbar or File Menu creates a new simulation project. Several default objects are automatically generated in the tree, and the Graphics window is filled with the 3D modeling interface. The following shows the behaviors of creating a new project:

"},{"location":"welsim/get_started/quick_start/#defining-materials","title":"Defining materials","text":"

In addition to the default Structural Steel material, you can add new materials and define the properties. A Material object represents a material database. The following gives the behaviors of material definition.

"},{"location":"welsim/get_started/quick_start/#importing-or-creating-geometries","title":"Importing or creating geometries","text":"

You can add geometry data by importing a CAD file or creating primitive shapes using the commands from Toolbar or Geometry Menu.

"},{"location":"welsim/get_started/quick_start/#meshing","title":"Meshing","text":"

You can skip meshing at this moment because the system automatically meshes the domain at solving step if no mesh is generated. However, meshing at this step provides you an insight of the mesh quality and a chance to optimize the mesh. You can click the Mesh commands from the Toolbar or FEM Menu to perform the meshing operations.

"},{"location":"welsim/get_started/quick_start/#analysis-settings","title":"Analysis settings","text":"

You can define the analysis settings in the following order:

"},{"location":"welsim/get_started/quick_start/#imposing-initial-conditions","title":"Imposing initial conditions","text":"

For the transient analysis, you can define initial conditions. The available initial conditions are

"},{"location":"welsim/get_started/quick_start/#imposing-boundary-conditions","title":"Imposing boundary conditions","text":"

The boundary and body conditions are essential for the conducted analysis. Depending on the Physics Type and Analysis Type, you can insert various condition objects into the tree via the Toolbar or Menu. The following gives the behaviors of the body and boundary conditions.

"},{"location":"welsim/get_started/quick_start/#solve","title":"Solve","text":"

To solve the customized model, you can click the Compute command from the Toolbar or FEM Menu. The behaviors of solving are

"},{"location":"welsim/get_started/quick_start/#displaying-results","title":"Displaying results","text":"

Depending on the Physics Type and Analysis Type, you can insert various result objects into the tree via the Toolbar or Menu. The following gives the behaviors of the solution and results.

"},{"location":"welsim/get_started/quick_start/#completed","title":"Completed","text":"

The analysis is completed. You can Save the projects to an external \u201cwsdb\u201d file and close the application.

Note

The *.wsdb file and associated folder are the WELSIM database for project data persistence, you can open this project file later, on another computer, and on different operation systems.

"},{"location":"welsim/get_started/electromagnetics/electrostatic/","title":"Electrostatic analysis","text":"

This example shows you how to conduct a 3D electrostatic analysis for a unibody part.

"},{"location":"welsim/get_started/electromagnetics/electrostatic/#specifying-analysis","title":"Specifying analysis","text":"

In the Properties View of the FEM Project object, you set the Physics Type property to Electromagnetic and Analysis Type to Electrostatic. An Electro-Static analysis is defined as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/electromagnetics/electrostatic/#preparing-geometry","title":"Preparing geometry","text":"

Next, you can import the geometry file \u201ch_section_unibody.step\u201d by clicking the Import... command from the Toolbar or Geometry Menu. The imported geometry and material property are shown in Figure\u00a0below.

"},{"location":"welsim/get_started/electromagnetics/electrostatic/#setting-mesh","title":"Setting mesh","text":"

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 3e-3.

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 34,764 nodes, and 20,657 Tet10 elements generated as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/electromagnetics/electrostatic/#imposing-conditions","title":"Imposing conditions","text":"

Next, you impose two boundary conditions, a Ground, and Voltage by clicking the corresponding commands from the Toolbar and Electromagnetic Menu. In the Properties View of the Ground object, holding the Ctrl or Shift key and select left bottom and right top surfaces for the Geometry property, as shown in Figure\u00a0below.

In the Properties View of Voltage object, set the Voltage value to 5, and scope surfaces for the Geometry property, as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/electromagnetics/electrostatic/#solving-the-model","title":"Solving the model","text":"

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process. As shown in Figure\u00a0[fig:ch2_start_ex1_output_solver], this model is solved successfully.

"},{"location":"welsim/get_started/electromagnetics/electrostatic/#evaluating-results","title":"Evaluating results","text":"

To evaluate the deformation of the structure, you can add a Voltage object to the tree by clicking the Voltage item from the Toolbar, Electromagnetic Menu. Next, double-clicking the result object or clicking the Evaluate item from the Toolbar or FEM Menu, you display the contour in the Graphics window as shown in Figure\u00a0below.

Adding an electric field result object is similar. Clicking the Electric Field result from Toolbar or Electromagnetic Menu, you insert a Electric Field result object to the tree. Evaluating the default Total Electric Field Type, you obtain the magnitude of the electric field vector contour on the body in the Graphics window. The Maximum and Minimum values of field data are displayed in the Properties View window as shown in Figure\u00a0below.

Info

This project file is located at examples/quick_electrostatic_01.wsdb.

"},{"location":"welsim/get_started/structural/structural_modal/","title":"Structural modal analysis","text":"

This example shows you how to conduct a 3D transient structural analysis for an assembly.

"},{"location":"welsim/get_started/structural/structural_modal/#defining-materials","title":"Defining materials","text":"

In this multi-body analysis, we assign Structural Steel and Aluminum materials to different parts. Since a Structural Steel object is already added as you initialize a FEM Project, you only need to insert an aluminum material object by clicking Add Material from Toolbar or FEM Menu.

To edit the material properties, you can double-click the Material object, or right-click on the Material object and select the Edit command from the context menu. In the material editor, you select the Library tab > General Materials > Aluminum Alloy, then click Import button or double-click the Aluminum Alloy entry. Click the OK to save and exit the material editing.

You can rename this new material object to Aluminum by press F2 key or right-clicking.

"},{"location":"welsim/get_started/structural/structural_modal/#specifying-analysis","title":"Specifying analysis","text":"

In the Properties View of the FEM Project object, you set the Analysis Type property to Modal. A Modal Structural analysis is defined as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/structural/structural_modal/#preparing-geometry","title":"Preparing geometry","text":"

Next, you can import the geometry file \u201ch_section_multibody.step\u201d and assign the materials to the corresponding parts. Three Part objects in the Geometry group represent three bodies in the Graphics window, respectively. You assign the Aluminum material to the Part2, which is the connection body in the middle, the rest bodies are assigned with Structural Steel material.

"},{"location":"welsim/get_started/structural/structural_modal/#setting-mesh","title":"Setting mesh","text":"

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 3e-3, as shown in Figure\u00a0below.

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 42,329 nodes, and 25,920 Tet10 elements generated as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/structural/structural_modal/#specifying-contacts","title":"Specifying contacts","text":"

Next, you need to define two Contact Pairs to bond the three parts into one uni-body for the analysis. Clicking the Add Contact command from the Toolbar or FEM Menu, you add two Contact Pair objects into the tree. You can rename these two objects to Contact1 and Contact2, respectively. Then you select the surfaces for Master and Target Geometry properties.

"},{"location":"welsim/get_started/structural/structural_modal/#defining-analysis-settings","title":"Defining analysis settings","text":"

In the Properties View of Study Settings object, you can define the analysis details such as Number of Modes. Here, you can use the default settings as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/structural/structural_modal/#imposing-boundary-conditions","title":"Imposing boundary conditions","text":"

In this modal analysis, you impose a Constraint (Fixed Support) boundary condition, which can be processed by clicking the corresponding commands from the Toolbar and Structural Menu. In the Properties View of the Constraint object, select the left bottom surface for the Geometry property.

"},{"location":"welsim/get_started/structural/structural_modal/#solving-the-model","title":"Solving the model","text":"

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process.

"},{"location":"welsim/get_started/structural/structural_modal/#evaluating-results","title":"Evaluating results","text":"

To evaluate the deformation of the structure, you can add a Deformation object to the tree by clicking the Deformation item from the Toolbar, Structural Menu. A result object may provide multiple sub-result types. For example, a Deformation result object allows you to specify one deformation type from the candidates Deformation X, Y, Z, and Total.

After setting the Type property to Deformation Z, double-clicking on the result object displays the resulting contour in the Graphics window as shown in Figure\u00a0below. You also can click the Evaluate item from the Toolbar or FEM Menu to evaluate the result.

Info

This project file is located at examples/quick_structural_modal_solid_01.wsdb.

"},{"location":"welsim/get_started/structural/structural_static/","title":"Static structural analysis","text":"

This example shows you how to conduct a 3D static structural analysis for an assembly.

"},{"location":"welsim/get_started/structural/structural_static/#defining-materials","title":"Defining materials","text":"

In this multi-body analysis, we assign Structural Steel and Aluminum materials to different parts. Since a Structural Steel object is already added as you initialize a FEM Project, you only need to insert an aluminum material object by clicking Add Material from Toolbar or FEM Menu.

To edit the material properties, you can double-click the Material object, or right-click on the Material object and select the Edit command from the context menu. In the material editor, you select the Library tab > General Materials > Aluminum Alloy, then click Import button or double-click the Aluminum Alloy entry. The material properties are set as shown in Figure below. Click the OK to save and exit the material editing.

You can rename this new material object to Aluminum by press F2 key or right-clicking.

.

"},{"location":"welsim/get_started/structural/structural_static/#specifying-analysis","title":"Specifying analysis","text":"

Since the Static Structural analysis is the default settings at WELSIM application, you can keep the default settings as shown in Figure below.

"},{"location":"welsim/get_started/structural/structural_static/#preparing-geometry","title":"Preparing geometry","text":"

Next, you can import the geometry file \u201ch_section_multibody.step\u201d and assign the materials to the corresponding parts. As shown in Figure\u00a0below, three Part objects in the Geometry group represent three bodies in the Graphics window, respectively. You assign the Aluminum material to the Part2, which is the connection body in the middle, the rest bodies are assigned with Structural Steel material.

"},{"location":"welsim/get_started/structural/structural_static/#setting-mesh","title":"Setting mesh","text":"

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 5e-3, as shown in Figure\u00a0below.

Next, you add a Mesh Method object from the Toolbar or FEM Menu. In the property of this object, you select the left body for the Geometry property, and set Maximum Size value to 3e-3, , as shown in Figure\u00a0below.

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 21,117 nodes, and 12,427 Tet10 elements generated as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/structural/structural_static/#specifying-contacts","title":"Specifying contacts","text":"

Next, you need to define two Contact Pairs to bond the three parts into one uni-body for the analysis. Clicking the Add Contact command from the Toolbar or FEM Menu, you add two Contact Pair objects into the tree. You can rename these two objects to Contact1 and Contact2, respectively. Then you select the surfaces for Master and Target Geometry properties as shown in Figures\u00a0below.

"},{"location":"welsim/get_started/structural/structural_static/#imposing-conditions","title":"Imposing conditions","text":"

Next, you impose two boundary conditions, a Constraint (Fixed Support) and a Pressure by clicking the corresponding commands from the Toolbar and Structural Menu. In the Properties View of the Constraint object, select the left bottom surface for the Geometry property, as shown in Figure\u00a0below.

In the Properties View of Pressure object, set the Normal Pressure value to 1e7, and scope the right top surface for the Geometry property, as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/structural/structural_static/#solving-the-model","title":"Solving the model","text":"

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process. As shown in Figure\u00a0[fig:ch2_start_ex1_output_solver], this model is solved successfully.

"},{"location":"welsim/get_started/structural/structural_static/#evaluating-results","title":"Evaluating results","text":"

To evaluate the deformation of the structure, you can add a Deformation object to the tree by clicking the Deformation item from the Toolbar, Structural Menu. A result object may provide multiple sub-result types. For example, a Deformation result object allows you to specify one deformation type from the candidates Deformation X, Y, Z, and Total, as shown in Figure\u00a0below.

After setting the property Type to Total Deformation, double-clicking on the result object displays the resulting contour in the Graphics window. You can click the Evaluate item from the Toolbar or FEM Menu to evaluate the result.

Adding a stress result object is similar. Clicking the Stress result from Toolbar or Structural Menu, you insert a stress object to the tree. Evaluating the default von-Mises Stress Type, you obtain the von-Mises stress contour on bodies in the Graphics window. The Maximum and Minimum values of stress data are displayed in the Properties View, Tabular Data, and Chart windows.

Info

This project file is located at examples/quick_structural_static_solid_01.wsdb.

"},{"location":"welsim/get_started/structural/structural_transient/","title":"Transient structural analysis","text":"

This example shows you how to conduct a 3D transient structural analysis for an assembly.

"},{"location":"welsim/get_started/structural/structural_transient/#defining-materials","title":"Defining materials","text":"

In this multi-body analysis, we assign Structural Steel and Aluminum materials to different parts. Since a Structural Steel object is already added as you initialize a FEM Project, you only need to insert an aluminum material object by clicking Add Material from Toolbar or FEM Menu.

To edit the material properties, you can double-click the Material object, or right-click on the Material object and select the Edit command from the context menu. In the material editor, you select the Library tab > General Materials > Aluminum Alloy, then click Import button or double-click the Aluminum Alloy entry. The material properties are set as shown in Figure\u00a0below. Click the OK to save and exit the material editing.

You can rename this new material object to Aluminum by press F2 key or right-clicking.

"},{"location":"welsim/get_started/structural/structural_transient/#specifying-analysis","title":"Specifying analysis","text":"

In the Properties View of the FEM Project object, you set the Analysis Type property to Transient. A Transient Structural analysis is defined as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/structural/structural_transient/#preparing-geometry","title":"Preparing geometry","text":"

Next, you can import the geometry file \u201ch_section_multibody.step\u201d and assign the materials to the corresponding parts. As shown in Figure\u00a0below, three Part objects in the Geometry group represent three bodies in the Graphics window, respectively. You assign the Aluminum material to the Part2, which is the connection body in the middle, the rest bodies are assigned with Structural Steel material.

"},{"location":"welsim/get_started/structural/structural_transient/#setting-mesh","title":"Setting mesh","text":"

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 5e-3, as shown in Figure\u00a0below.

Next, you add a Mesh Method object from the Toolbar or FEM Menu. In the property of this object, you select the left body for the Geometry property, and set Maximum Size value to 3e-3, as shown in Figure\u00a0below.

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 21,117 nodes, and 12,427 Tet10 elements generated as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/structural/structural_transient/#specifying-contacts","title":"Specifying contacts","text":"

Next, you need to define two Contact Pairs to bond the three parts into one uni-body for the analysis. Clicking the Add Contact command from the Toolbar or FEM Menu, you add two Contact Pair objects into the tree. You can rename these two objects to Contact1 and Contact2, respectively. Then you select the surfaces for Master and Target Geometry properties as shown in Figures\u00a0below.

Note

Defining contacts is optional, adding a contact or not is up to your specific model.

"},{"location":"welsim/get_started/structural/structural_transient/#defining-analysis-settings","title":"Defining analysis settings","text":"

In this transient analysis, you define 18 steps and set the End Time for each step, as shown in Figure\u00a0below.

Next, you select the Study Settings object in the tree and set the Substeps property to 18, which determines the total number of substeps of the transient analysis. A screen capture of the defined properties is shown in Figure\u00a0below.

"},{"location":"welsim/get_started/structural/structural_transient/#imposing-conditions","title":"Imposing conditions","text":"

Next, you impose two boundary conditions, a Constraint (Fixed Support) and an Acceleration by clicking the corresponding commands from the Toolbar or Structural Menu. In the Properties View of the Constraint object, select the left bottom surface for the Geometry property, as shown in Figure\u00a0below.

In the Properties View of Acceleration object, set the Acceleration value for the current step, and repeat this value definition for each Step. After defining the acceleration values for all steps, you scope a surface on Part2 for the Geometry property, as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/structural/structural_transient/#solving-the-model","title":"Solving the model","text":"

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process. As shown in Figure\u00a0below, this model is solved successfully.

"},{"location":"welsim/get_started/structural/structural_transient/#evaluating-results","title":"Evaluating results","text":"

To evaluate the deformation of the structure, you can add a Deformation object to the tree by clicking the Deformation item from the Toolbar, Structural Menu. A result object may provide multiple sub-result types. For example, a Deformation result object allows you to specify one deformation type from the candidates Deformation X, Y, Z, and Total.

After setting the result Type to Deformation Z, double-clicking on the result object displays the resulting contour in the Graphics window as shown in Figure\u00a0below. You can click the Evaluate item from the Toolbar or FEM Menu to evaluate the result.

Adding a stress result object is similar. Clicking the Stress result from Toolbar or Structural Menu, you insert a stress object to the tree. Evaluating the default von-Mises Stress Type, you obtain the von-Mises stress contour on bodies in the Graphics window as shown in Figure\u00a0below. The Maximum and Minimum values of stress data are displayed in the Properties View, Tabular Data, and Chart windows.

Info

This project file is located at examples/quick_structural_transient_solid_01.wsdb.

"},{"location":"welsim/get_started/thermal/thermal_ss/","title":"Steady-state thermal analysis","text":"

This example shows you how to conduct a 3D static thermal analysis for an assembly.

"},{"location":"welsim/get_started/thermal/thermal_ss/#defining-materials","title":"Defining materials","text":"

In this multi-body analysis, we assign Structural Steel and Aluminum materials to different parts. Since a Structural Steel object is already added as you initialize a FEM Project, you only need to insert an aluminum material object by clicking Add Material from Toolbar or FEM Menu.

To edit the material properties, you can double-click the Material object, or right-click on the Material object and select the Edit command from the context menu. In the material editor, you select the Library tab > General Materials > Aluminum Alloy, then click Import button or double-click the Aluminum Alloy entry. The material properties are set as shown in Figure\u00a0below. Click the OK to save and exit the material editing.

You can rename this new material object to Aluminum by press F2 key or right-clicking.

"},{"location":"welsim/get_started/thermal/thermal_ss/#specifying-analysis","title":"Specifying analysis","text":"

In the Properties View of the FEM Project object, you set the Physics Type property to Thermal. A Steady-State Thermal analysis is defined as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/thermal/thermal_ss/#preparing-geometry","title":"Preparing geometry","text":"

Next, you can import the geometry file \u201ch_section_multibody.step\u201d and assign the materials to the corresponding parts. As shown in Figure, three Part objects in the Geometry group represent three bodies in the Graphics window, respectively. You assign the Aluminum material to the Part2, which is the connection body in the middle, the rest bodies are assigned with Structural Steel material.

"},{"location":"welsim/get_started/thermal/thermal_ss/#setting-mesh","title":"Setting mesh","text":"

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 3e-3.

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 42,329 nodes, and 25,920 Tet10 elements generated.

"},{"location":"welsim/get_started/thermal/thermal_ss/#specifying-contacts","title":"Specifying contacts","text":"

Next, you need to define two Contact Pairs to bond the three parts into one uni-body for the analysis. Clicking the Add Contact command from the Toolbar or FEM Menu, you add two Contact Pair objects into the tree. You can rename these two objects to Contact1 and Contact2, respectively. Then you select the surfaces for Master and Target Geometry properties.

"},{"location":"welsim/get_started/thermal/thermal_ss/#imposing-boundary-conditions","title":"Imposing boundary conditions","text":"

Next, you impose four boundary conditions, a Temperature, Heat Flux, Convection, and Radiation by clicking the corresponding commands from the Toolbar or Thermal Menu. In the Properties View of the Temperature object, select a left bottom surface for the Geometry property and set the Temperature value to 0, as shown in Figure\u00a0below.

In the Properties View of Heat Flux object, set the Heat Flux value to 5e3, and scope a surface for the Geometry property, as shown in Figure\u00a0below.

In the Properties View of Heat Radiation object, set the Radiation Coefficient value to 1e-6, Ambient Temperature value to 22.3, and scope a surface for the Geometry property, as shown in Figure\u00a0below.

In the Properties View of Heat Convection object, set the Convection Coefficient value to 1e3 and Ambient Temperature value to 22.3, and scope a surface for the Geometry property, as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/thermal/thermal_ss/#solving-the-model","title":"Solving the model","text":"

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process. As shown in Figure\u00a0below, this model is solved successfully.

"},{"location":"welsim/get_started/thermal/thermal_ss/#evaluating-results","title":"Evaluating results","text":"

To evaluate the deformation of the structure, you can add a Temperature object to the tree by clicking the Temperature item from the Toolbar or Thermal Menu. Next, double-clicking the result object or clicking the Evaluate item from the Toolbar or FEM Menu, you display the result contour in the Graphics window as shown in Figure\u00a0below.

Info

This project file is located at examples/quick_thermal_static_solid_01.wsdb.

"},{"location":"welsim/get_started/thermal/thermal_transient/","title":"Transient thermal analysis","text":"

This example shows you how to conduct a 3D transient thermal analysis for an assembly.

"},{"location":"welsim/get_started/thermal/thermal_transient/#defining-materials","title":"Defining materials","text":"

In this multi-body analysis, we assign Structural Steel and Aluminum materials to different parts. Since a Structural Steel object is already added as you initialize a FEM Project, you only need to insert an aluminum material object by clicking Add Material from Toolbar or FEM Menu.

To edit the material properties, you can double-click the Material object, or right-click on the Material object and select the Edit command from the context menu. In the material editor, you select the Library tab > General Materials > Aluminum Alloy, then click Import button or double-click the Aluminum Alloy entry. The material properties are set as shown in Figure\u00a0below. Click the OK to save and exit the material editing.

You can rename this new material object to Aluminum by press F2 key or right-clicking.

"},{"location":"welsim/get_started/thermal/thermal_transient/#specifying-analysis","title":"Specifying analysis","text":"

In the Properties View of the FEM Project object, you set the Physics Type property to Thermal and Analysis Type property to Transient. A Transient Thermal analysis is defined as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/thermal/thermal_transient/#preparing-geometry","title":"Preparing geometry","text":"

Next, you can import the geometry file \u201ch_section_multibody.step\u201d and assign the materials to the corresponding parts. As shown in Figure, three Part objects in the Geometry group represent three bodies in the Graphics window, respectively. You assign the Aluminum material to the Part2, which is the connection body in the middle, the rest bodies are assigned with Structural Steel material.

"},{"location":"welsim/get_started/thermal/thermal_transient/#setting-mesh","title":"Setting mesh","text":"

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 3e-3.

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 42,329 nodes, and 25,920 Tet10 elements generated.

"},{"location":"welsim/get_started/thermal/thermal_transient/#specifying-contacts","title":"Specifying contacts","text":"

Next, you need to define two Contact Pairs to bond the three parts into one uni-body for the analysis. Clicking the Add Contact command from the Toolbar or FEM Menu, you add two Contact Pair objects into the tree. You can rename these two objects to Contact1 and Contact2, respectively. Then you select the surfaces for Master and Target Geometry properties as shown in Figures\u00a0below.

"},{"location":"welsim/get_started/thermal/thermal_transient/#defining-analysis-settings","title":"Defining analysis settings","text":"

In this transient analysis, you define 1 step and set the Current End Time value to 600, as shown in Figure\u00a0below.

In the Properties View of Study Settings object in the tree, you can use the default settings as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/thermal/thermal_transient/#imposing-conditions","title":"Imposing conditions","text":"

Next, you can add an Initial Temperature object from the Toolbar or Thermal Menu. The initial temperature value is 300 as shown in Figure\u00a0below.

Next, you impose three boundary conditions, a Temperature, Heat Flux, and a Heat Convection by clicking the corresponding commands from the Toolbar and Thermal Menu. In the Properties View of the Temperature object, you select the bottom surface of Part1 for the Geometry property. Next set the Temperature value to 0, and define Initial Status to Equal to Step 1, as shown in Figure\u00a0below.

In the Properties View of Heat Flux object, set the Heat Flux value to -5000 and Initial Status to Equal to Step 1. Next, you scope a surface on Part1 for the Geometry property, as shown in Figure\u00a0below.

In the Properties View of Heat Convection object, set the Convection Coefficient value to 1000, Ambient Temperature value to 22.3, and Initial Status to Equal to Step 1. After defining these property values, you scope a surface on Part2 for the Geometry property, as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/thermal/thermal_transient/#solving-the-model","title":"Solving the model","text":"

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process. As shown messages in Output window, this model is solved successfully.

"},{"location":"welsim/get_started/thermal/thermal_transient/#evaluating-results","title":"Evaluating results","text":"

To evaluate the temperature of the model, you can add a Temperature object to the tree by clicking the Temperature item from the Toolbar, Thermal Menu.

After inserting the result object and settings the Set Number to 15, double-clicking on the result object displays the resulting contour in the Graphics window as shown in Figure\u00a0below. You can click the Evaluate item from the Toolbar or FEM Menu to evaluate the result.

Info

This project file is located at examples/quick_thermal_transient_solid_01.wsdb.

"},{"location":"welsim/material/mat_overview/","title":"Overview","text":"

Material Module serves as a database for material properties used in analysis projects. The module not only provides a material library but allow you to create a material using the given properties. The properties view of a Material object is the primary user interface designed to let you create, save, and retrieve material models. The well-defined material object can be saved and used in the subsequent projects.

Note

The WELSIM Material module and MatEditor share the same features. For the completed and latest content, you can refer to the manual of MatEditor.

"},{"location":"welsim/material/mat_overview/#graphical-user-interface","title":"Graphical user interface","text":"

The ease-of-use Material Module contains the following graphical user interface components:

"},{"location":"welsim/material/mat_overview/#predefined-materials","title":"Predefined materials","text":"

WELSIM also provide predefined materials, which covers most of commonly used materials. Users can choose these materials and apply to the successive finite element analysis.

Category Materials General Materials Structural Steel, Stainless Steel, Aluminum Alloy, Concrete, Copper Alloy, Gray Cast Iron, Titanium Alloy Nonlinear Materials Aluminum Alloy NL, Concrete NL, Copper Alloy NL, Stainless Steel NL, Structural Steel NL, Titanium Alloy NL Hyperelastic Materials Elastomer Mooney-Rivlin, Elastomer Neo-Hookean, Elastomer Ogden, Elastomer Yeoh, Neoprene Rubber Thermal Materials Brass, Bronze, Copper, Diamond, Ferrite, Nodular Cast Iron, Solder, Teflon, Tungsten, Wood Electromagnetic Materials SS416, Supermendure Other Materials Water Liquid, Argon, Ash"},{"location":"welsim/material/mat_overview/#material-properties","title":"Material properties","text":"

The supported material properties are listed in the table below.

Category Materials Basic Density, Isotropic Thermal Expansion, Isotropic Instantaneous Thermal Expansion, Orthotropic Thermal Expansion, Orthotropic Instantaneous Thermal Expansion, Constant Damping Coefficient Linear Elastic Isotropic Elasticity, Orthotropic Elasticity, Viscoelastic Hyperelastic Test Data Uniaxial Test Data, Biaxial Test Data, Shear Test Data, Volumetric Test Data, SimpleShear Test Data, Uniaxial Tension Test Data, Uniaxial Compression Test Data Hyperelastic Arruda-Boyce, Blatz-Ko, Gent, Mooney-Rivlin 2, Mooney-Rivlin 3, Mooney-Rivlin 5, Mooney-Rivlin 9, Neo-Hookean, Ogden 1st Order, Ogden 2nd Order, Ogden 3rd Order, Polynomial 1st Order, Polynomial 2nd Order, Polynomial 3rd Order, Yeoh 1st Order, Yeoh 2nd Order, Yeoh 3rd Order Plasticity Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening, Anand Viscoplasticity Creep Strain Hardening, Time Hardening, Generalized Exponential, Generalized Graham, Generalized Blackburn, Modified Time Hardening, Modified Strain Hardening, Generalized Garofalo, Exponential Form, Norton, Combined Time Hardening, Rational Polynomial, Generalized Time Hardening Visco-elastic Prony Shear Relaxation, Prony Volumetric Relaxation Other Mechanical Strain Life Parameters, Compressive Ultimate Strength, Compressive Yield Strength, LaRc0304 Constants, Orthotropic Strain Limits, Orthotropic Stress Limits, Puck Constants, Tensile Ultimate Strength, Tensile Yield Strength, Tsai-Wu Constants, Shape Memory Effect, Drucker-Prager Strength Piecewise, Drucker-Prager Strength Linear, Ideal Gas EOS, Crushable Foam, Nonlinear Elastic Model Damage, Plakin Special Hardening, Tensile Pressure Failure, Crack Softening Failure Thermal Enthalpy, Isotropic Thermal Conductivity, Orthotropic Thermal Conductivity, Specific Heat Electromagnetics B-H Curve, Isotropic Relative Permeability, Orthotropic Relative Permeability, Isotropic Resistivity, Orthotropic Resistivity"},{"location":"welsim/material/mat_overview/#working-with-material-data","title":"Working with material data","text":""},{"location":"welsim/material/mat_overview/#exporting","title":"Exporting","text":"

You can export the complete material data to an external XML file. The following format is supported for export:

"},{"location":"welsim/mesh/mesh_usage/","title":"Usage in WELSIM","text":""},{"location":"welsim/mesh/mesh_usage/#basic-meshing-process","title":"Basic meshing process","text":"

The following steps provide the fundamental workflow for using the Meshing module as part of a finite element analysis in WELSIM.

  1. Create a finite element project and set the appropriate project type in the Properties of FEM Project object, such as Static Structural.

  2. Define appropriate material data for your analysis. The system provide a Structural Steel material, and you can create a new material object. Double-click, or Right click the material object. The Material Editing workspace appears, where you can add or edit material data as necessary.

  3. Import geometry to your system or build new geometry. Assign the material to the geometry.

  4. Click on the Mesh object in the Tree to access Meshing application functionality and apply mesh controls.

  5. Define loads and boundary conditions. Set up your analysis using that application's tools and features.

  6. You can solve your analysis by clicking solve button.

  7. Review your analysis results.

Note

You should save your data periodically (File>Save Project). The data will be saved as a .wsdb file and associated folder.

"},{"location":"welsim/mesh/meshing/","title":"Meshing Overview","text":""},{"location":"welsim/mesh/meshing/#philosophy","title":"Philosophy","text":"

The goal of meshing in WELSIM is to provide easy-to-use and stable meshing utilities that will simplify the mesh generation process.

"},{"location":"welsim/mesh/meshing/#physics-based-meshing","title":"Physics-based meshing","text":"

The WELSIM mesh generation is set based on the physics and engineering preferences. Particularly, the mesh system targets on the mechanical, thermal and electromagnetics physics.

"},{"location":"welsim/mesh/meshing/#meshing-application-interface","title":"Meshing application interface","text":"

The intuitive Meshing applicaiton interface, shown in the figure below, faciliates your use of all meshing controls and settings.

The funcational elements of the interface are described in the following table.

Window Component Description Main Menu This menu includes all basic menus such as File and Mesh. Standard Toolbar This toolbar contains commonly used application commands. Graphics Toolbar This toolbar contains commands that control pointer mode or cause an action in the graphics browser. Tree Outline Outline view of the project. Always visible. Location in the outline sets the context for other controls. Provides access to object's context menus. Allows renaming of objects. Establishes what details display in the Details View. Property Details View The Details View corresponds to the Outline selection. Displays a details window on the lower left panel (by default) which contains details about each object in the Outline. Geometry Window (also sometimes called the Graphics window) Displays and manipulates the visual representation of the object selected in the Outline. This window may display: <\\br> 3D Geometry<\\br> 2D/3D Graph<\\br> Spreadsheet<\\br> HTML Pages<\\br> Scale ruler<\\br> Triad control<\\br> Legend<\\br>"},{"location":"welsim/theory/contact/","title":"Structures with contact","text":"

As contact occurs among multiple bodies, the contact force \\(\\mathbf{t}_{c}\\) is transmitted via the contact surface. The principle equation of the virtual work can be rewritten as follows

\\[ \\begin{align} \\label{eq:ch5_contact_gov1} \\intop_{^{t'}V}\\thinspace^{t'}\\sigma\\colon\\delta^{t'}\\mathbf{A}_{(L)}d^{t'}v=\\intop_{^{t'}S_{t}}\\thinspace^{t'}\\mathbf{t}\\cdot\\delta\\mathbf{u}d^{t'}s+\\intop_{V}\\thinspace^{t'}\\mathbf{b}\\cdot\\delta\\mathbf{u}d^{t'}v+\\intop_{^{t'}S\\text{c}}\\thinspace^{t'}\\mathbf{t}_{c}[\\delta\\mathbf{u}^{(1)}-\\delta\\mathbf{u}^{(2)}] \\end{align} \\]

where notation \\(s_{c}\\) represents the contact area, \\(\\mathbf{u}^{(1)}\\) and \\(\\mathbf{u}^{(2)}\\) denotes the displacement of the contact object 1 and 2, respectively.

In the contact analysis, the surfaces involve contact are paired. One of these surfaces is called the master surface, and another type of surface is target surface. We also assume

The governing equations with contact term can be reduced to the finite element formation

\\[ \\intop_{^{t'}S_{c}}\\thinspace^{t'}\\mathbf{t}_{c}[\\delta\\mathbf{u}^{(1)}-\\delta\\mathbf{u}^{(2)}]\\approx\\delta\\mathbf{UK}_{C}\\triangle\\mathbf{U}+\\delta\\mathbf{UF}_{C} \\]

where \\(\\mathbf{K}_{c}\\) and \\(\\mathbf{F}_{c}\\) are contact rigid matrix, and the contact forces, respectively.

Remember that we introduced total Lagrange and update Lagrange methods, those formulation can be extended with the consideration of contact factors. The total Lagrange and updated Lagrange formulation with contact terms are given below

\\[ \\delta\\mathbf{U}^{T}(_{0}^{t}\\mathbf{K}_{L}+_{0}^{t}\\mathbf{K}_{NL}+\\mathbf{K}_{c})\\triangle\\mathbf{U}=\\delta\\mathbf{U}^{T}\\thinspace_{0}^{t'}\\mathbf{F}-\\delta\\mathbf{U}^{T}\\thinspace_{0}^{t}\\mathbf{Q}+\\delta\\mathbf{U}^{T}\\mathbf{F}_{c} \\] \\[ \\delta\\mathbf{U}^{T}(_{t}^{t}\\mathbf{K}_{L}+_{t}^{t}\\mathbf{K}_{NL}+\\mathbf{K}_{c})\\triangle\\mathbf{U}=\\delta\\mathbf{U}^{T}\\thinspace_{t}^{t'}\\mathbf{F}-\\delta\\mathbf{U}^{T}\\thinspace_{t}^{t}\\mathbf{Q}+\\delta\\mathbf{U}^{T}\\mathbf{F}_{c} \\]"},{"location":"welsim/theory/electromagnetic/","title":"Electromagnetic analysis","text":"

This section discuss the electromagnetic theories that are applied in the WELSIM application.

"},{"location":"welsim/theory/electromagnetic/#electromagnetic-field-fundamentals","title":"Electromagnetic field fundamentals","text":"

The electromagnetic fields are governed by the well-known Maxwell's equations\u00a0\\(\\eqref{eq:ch4_theory_maxwell1}\\)-\\(\\eqref{eq:ch4_theory_maxwell4}\\)12.

\\[ \\begin{align} \\label{eq:ch4_theory_maxwell1} \\nabla\\times\\mathbf{H}=\\mathbf{J}+\\dfrac{\\partial\\mathbf{D}}{\\partial t}=\\mathbf{J}_{S}+\\mathbf{J}_{e}+\\mathbf{J}_{V}+\\dfrac{\\partial\\mathbf{D}}{\\partial t} \\end{align} \\] \\[ \\begin{align} \\label{eq:ch4_theory_maxwell2} \\nabla\\times\\mathbf{E}=-\\dfrac{\\partial\\mathbf{B}}{\\partial t} \\end{align} \\] \\[ \\begin{align} \\label{eq:ch4_theory_maxwell3} \\nabla\\cdot\\mathbf{B}=0 \\end{align} \\] \\[ \\begin{align} \\label{eq:ch4_theory_maxwell4} \\nabla\\cdot\\mathbf{D}=\\rho \\end{align} \\]

where \\(\\mathbf{H}\\) is the magnetic field intensity vector, \\(\\mathbf{J}\\) is total current density vector, \\(\\mathbf{J}_{s}\\) is the applied source current density vector, \\(\\mathbf{J}_{e}\\) is the induced eddy current density vector, and \\(\\mathbf{J}_{VS}\\) is the velocity current density vector, \\(\\mathbf{D}\\) is the electric flux density vector (this term is also called electric displacement), \\(\\mathbf{E}\\) is the electric field intensity vector, \\(\\mathbf{B}\\) is the magnetic flux density vector, and \\(\\rho\\) is the electric charge density.

The above field governing equations contian the constitutive relations:

\\[ \\mathbf{D}=\\epsilon\\mathbf{E}+\\mathbf{P} \\]

and

\\[ \\mathbf{B}=\\mu\\mathbf{H} \\]

where \\(\\mathbf{P}\\) is the polarization density, and \\(\\mathbf{M}\\) is t he magnetization. In many materials the polarization density can be approximated as a scalar multiple of the electric field. \\(\\mu\\) is the magnetic permeability matrix. For example, if the magnetic permeability is a function of temperature,

\\[ \\mu=\\mu_{0}\\left[\\begin{array}{ccc} \\mu_{rx} & 0 & 0\\\\ 0 & \\mu_{ry} & 0\\\\ 0 & 0 & \\mu_{rz} \\end{array}\\right] \\]

For the permanent magnets, the constitutive relation of magnetic field becomes

\\[ \\mathbf{B}=\\mu\\mathbf{H}+\\mu_{0}\\mathbf{M}_{0} \\]

where \\(\\mathbf{M}_{0}\\) is the remanet intrinsic magnetization vector.

Similarly, the consitutive relations for the related electric fields are:

\\[ \\mathbf{J}=\\sigma[\\mathbf{E}+\\mathbf{v}\\times\\mathbf{B}] \\] \\[ \\sigma=\\left[\\begin{array}{ccc} \\sigma_{xx} & 0 & 0\\\\ 0 & \\sigma_{yy} & 0\\\\ 0 & 0 & \\sigma_{zz} \\end{array}\\right] \\] \\[ \\epsilon=\\left[\\begin{array}{ccc} \\epsilon_{xx} & 0 & 0\\\\ 0 & \\epsilon_{yy} & 0\\\\ 0 & 0 & \\epsilon_{zz} \\end{array}\\right] \\]

where \\(\\sigma\\) is the electrical conductivity matrix, \\(\\epsilon\\) is the permittivity matrix, and \\(v\\) is the velocity vector.

"},{"location":"welsim/theory/electromagnetic/#electrostatics","title":"Electrostatics","text":"

The WELSIM application introduces electric scalar potential to solve the electrostatic problems. When the time-derivetive of magnetic flux density is neglected from the full Maxwell's equations. The governing equations are reduced to

\\[ \\begin{align} \\label{eq:ch4_theory_govern_eqn_electrostatic} \\nabla\\times\\mathbf{H}=\\mathbf{J}+\\dfrac{\\partial\\mathbf{D}}{\\partial t} \\end{align} \\] \\[ \\nabla\\times\\mathbf{E}=\\mathbf{0} \\] \\[ \\nabla\\cdot\\mathbf{B}=0 \\] \\[ \\nabla\\cdot\\mathbf{D}=\\rho \\]

Since the electric field \\(\\mathbf{E}\\) is irrotational and can be expressed as the function of electric scalar potential

\\[ \\mathbf{E}=-\\nabla \\varphi \\]

where \\(\\varphi\\) is the electric scalar potential and has units of Volts in the SI system. Inserting this definition into the Gauss's Law gives:

\\[ -\\nabla \\cdot \\epsilon\\nabla\\varphi = \\rho - \\nabla \\cdot \\mathbf{P} \\]

which is Poisson's equation for the electric potential , where we have assumed a linear constitutive relation between \\(\\mathbf{D}\\) and \\(\\mathbf{E}\\) of the form \\(\\mathbf{D}=\\epsilon\\mathbf{E}+\\mathbf{P}\\).

"},{"location":"welsim/theory/electromagnetic/#boundary-conditions","title":"Boundary Conditions","text":"

For an electric material interface, the continuious conditions for \\(\\mathbf{E}\\), \\(\\mathbf{D}\\), and \\(\\mathbf{J}\\) are

\\[ E_{t1}-E_{t2}=0 \\] \\[ J_{1n}+\\dfrac{\\partial D_{1n}}{\\partial t}=J_{2n}+\\dfrac{\\partial D_{2n}}{\\partial t} \\] \\[ D_{1n}-D_{2n}=\\rho_{s} \\]

where \\(E_{t}\\) is the tangential components of \\(\\mathbf{E}\\), \\(J_{n}\\) is the normal components of \\(\\mathbf{J}\\), \\(D_{n}\\) is the normal components of \\(\\mathbf{D}\\), and \\(\\rho_{s}\\) is the surface charge density.

Since the solutons to the governing equation are non-unique, we must impose a Dirichlet boundary condition at least at one node in the domain to get the physical solution. The Dirichlet condition could be a fixed piecewise voltage value on certain nodes. In addition, the normal derivative boundary condition \\(\\hat{n}\\cdot\\mathbf{D}\\) such as surface charge density can be imposed on the boundary.

"},{"location":"welsim/theory/electromagnetic/#matrix-forms","title":"Matrix Forms","text":"

The electric scalar potential algorithm is applied in the WELSIM application for solving electrostatic problems. The governing equations are reduced to the following:

\\[ -\\nabla\\cdot\\left(\\epsilon\\nabla V\\right)=\\rho \\]

The matrix equation for an electrostatic analysis is derived from Equation \\(\\eqref{eq:ch4_theory_govern_eqn_electrostatic}\\):

\\[ \\left[K^{VS}\\right]\\left\\{ V_{e}\\right\\} =\\left\\{ L_{e}\\right\\} \\]

where

\\[ \\left[K^{VS}\\right]=\\intop_{V}\\left(\\nabla\\left\\{ N\\right\\} ^{T}\\right)^{T}\\epsilon\\left(\\nabla\\left\\{ N\\right\\} ^{T}\\right)dV \\] \\[ \\left\\{ L_{e}\\right\\} =\\left\\{ L_{e}^{n}\\right\\} +\\left\\{ L_{e}^{c}\\right\\} +\\left\\{ L_{e}^{SC}\\right\\} \\] \\[ \\left\\{ L_{e}^{c}\\right\\} =\\int_{V}\\rho\\left\\{ N\\right\\} ^{T}dV \\] \\[ \\left\\{ L_{e}^{sc}\\right\\} =\\int_{V}\\rho_{s}\\left\\{ N\\right\\} ^{T}dV \\]"},{"location":"welsim/theory/electromagnetic/#vector-magnetic-potential","title":"Vector magnetic potential","text":"

The WELSIM application applies the vector magnetic potential method for the magentostatic analysis. Considering the neglected electric displacement currents, the full Maxwell's equations can be reduced to

\\[ \\nabla\\times\\mathbf{H}=\\mathbf{J} \\] \\[ \\nabla\\times\\mathbf{E}=-\\dfrac{\\partial\\mathbf{B}}{\\partial t} \\] \\[ \\nabla\\cdot\\mathbf{B}=0 \\]

A numerical solution can be achieved by introducing potentials to the governing equations. The proposed magnetic vector potential\u00a0\\(\\mathbf{A}\\) and electric scalar potential\u00a0\\(V\\) have the following characteristics:

\\[ \\mathbf{B}=\\nabla\\times\\mathbf{A} \\] \\[ \\mathbf{E}=-\\dfrac{\\partial\\mathbf{A}}{\\partial t}-\\nabla V \\]

In addition, the Coulomb gauge condition is introduced to ensure the uniqueness of the vector potential, as shown in the following equations.

\\[ \\nabla\\times\\mathbf{v}\\nabla\\times\\mathbf{A}-\\nabla v_{e}\\nabla\\cdot\\mathbf{A}+\\sigma\\left\\{ \\dfrac{\\partial\\mathbf{A}}{\\partial t}\\right\\} +\\sigma\\nabla V-\\mathbf{v}\\times\\sigma\\nabla\\times\\mathbf{A}=\\mathbf{0} \\] \\[ \\nabla\\cdot\\left(\\sigma\\left\\{ \\dfrac{\\partial\\mathbf{A}}{\\partial t}\\right\\} -\\sigma\\nabla V+\\mathbf{v}\\times\\sigma\\nabla\\times\\mathbf{A}\\right)=\\mathbf{0} \\] \\[ \\nabla\\times\\mathbf{v}\\nabla\\times\\mathbf{A}-\\nabla v_{e}\\nabla\\cdot\\mathbf{A}=\\mathbf{J}_s+\\nabla\\times\\dfrac{1}{\\mathbf{v}_{0}}\\mathbf{v}\\mathbf{M}_{0} \\]

where matrix invarient \\(v_{e}\\) is \\(v_{e}=\\frac{1}{3}\\mathrm{tr}(v)=\\frac{1}{3}(v_{11}+v_{22}+v_{33})\\).

"},{"location":"welsim/theory/electromagnetic/#edge-element-magnetic-vector-potential","title":"Edge-element magnetic vector potential","text":"

Due to the limitation of node-based vector magnetic potential algorithm2, WELSIM application uses the edge-based finite element for the magnetic vector potential algorithm.

The governing equation for the edge finite element method is given below.

\\[ \\nabla\\times\\mathbf{v}\\nabla\\times\\mathbf{A}+\\sigma\\left\\{ \\dfrac{\\partial\\mathbf{A}}{\\partial t}+\\nabla V\\right\\} +\\epsilon\\left(\\left\\{ \\dfrac{\\partial^{2}\\mathbf{A}}{\\partial t^{2}}\\right\\} +\\nabla\\left\\{ \\dfrac{\\partial V}{\\partial t}\\right\\} \\right)=\\mathbf{0} \\] \\[ \\nabla\\cdot\\left(\\sigma\\left(\\left\\{ \\dfrac{\\partial\\mathbf{A}}{\\partial t}\\right\\} +\\nabla V\\right)+\\epsilon\\left(\\left\\{ \\dfrac{\\partial^{2}\\mathbf{A}}{\\partial t^{2}}\\right\\} +\\nabla\\left\\{ \\dfrac{\\partial V}{\\partial t}\\right\\} \\right)\\right)=\\mathbf{0} \\] \\[ \\nabla\\times\\mathbf{v}\\nabla\\times\\mathbf{A}=\\mathbf{J}_{s}+\\nabla\\times\\dfrac{1}{\\mathbf{v}_{0}}\\mathbf{v}\\mathbf{M}_{0} \\]

The uniqueness of these equations is ensured by the tree gauging procedure, which sets the edge-flux degrees of freedom related to the spanning tree of the finite element mesh to zero.

  1. John D. Jackson, Classical Electrodynamics, 3rd edition, Wiley.\u00a0\u21a9

  2. Jian-Ming Jin, The Finite Element Method in Electromagnetics, 2nd edition, Wiley-IEEE Press.\u00a0\u21a9\u21a9

"},{"location":"welsim/theory/elements/","title":"Element library","text":"

The WELSIM application supports several types of finite elements. This section discuss the details of element that is used in the program.

Element type Finite element type Description Plane element (Shell) Tri3 Three node triangular element Plane element (Shell) Tri6 Six node triangular element(quadratic) Solid element Tet4 Four node tetrahedral element Solid element Tet10 Ten node tetrahedral element(quadratic)

The element groups shown in Table\u00a0[tab:ch4_theory_elem_types] can be used for engineering analysis. The schematic views and the surface definition of those elements are given in Figures\u00a0[fig:ch4_theory_elem_views], [fig:ch4_theory_elem_triangles], and [fig:ch4_theory_elem_tet].

Surface No. Linear Quadratic 1 1-2-3 [front] 1-6-2-4-3-5 [front] 2 3-2-1 [back] 3-4-2-6-1-5 [back]

Surface No. Linear Quadratic 1 1-2-3 1-7-2-5-3-6 2 1-2-4 1-7-2-9-4-8 3 2-3-4 2-5-3-10-4-9 4 3-1-4 3-6-1-10-4-8"},{"location":"welsim/theory/geometricnl/","title":"Structures with geometric nonlinearity","text":"

In the analysis of finite deformation problems, the principle equation of virtual work becomes a nonlinear equation regarding the displacement-strain relation. To solve the nonlinear equation, an iterative algorithm is generally applied. When implementing an incremental analysis for a finite deformation problem, whether to refer to the initial status as a reference layout, or refer to the starting point of the increments can be selected. The former is called the total Lagrange method, and the latter is called the updated Lagrange method. Both the total Lagrange and updated Lagrange methods are available in the program. This section discusses the various geometrically nonlinear options available, including the large strain.

"},{"location":"welsim/theory/geometricnl/#decomposition-of-increments-of-virtual-work-equation","title":"Decomposition of increments of virtual work equation","text":"

Given the solid deformation at time t is known, the status at time t'=t+\\triangle t is unknown. The equilibrium equation, dynamic boundary condition, and external boundary condition can be expressed as

\\[ \\begin{align} \\label{eq:ch5_nonlinear_gov1} \\nabla_{t'\\mathbf{x}}\\cdot^{t'}\\sigma+^{t'}\\mathbf{b}=0\\quad\\text{in}V \\end{align} \\] \\[ ^{t'}\\sigma\\cdot^{t'}\\mathbf{n}=^{t'}\\mathbf{t}\\quad\\mathrm{on}\\thinspace^{t'}S \\] \\[ ^{t'}\\mathbf{u}=^{t'}\\bar{\\mathbf{u}} \\]

where \\(^{t'}\\sigma\\), \\(^{t'}\\mathbf{b}\\), \\(^{t'}\\mathbf{n}\\), \\(^{t'}\\mathbf{t}\\), \\(^{t'}\\mathbf{u}\\) are the Cauchy stress, body force, outward normal vector of the object's surface, fixed surface force, and fixed displacement in each time t'.

"},{"location":"welsim/theory/geometricnl/#principle-of-virtual-work","title":"Principle of virtual work","text":"

The principle of virtual work to the equation \\(\\eqref{eq:ch5_nonlinear_gov1}\\) is

\\[ \\begin{align} \\label{eq:ch5_nonlinear_gov2} \\int_{^{t'}V}^{t'}\\sigma:\\delta^{t'}\\mathbf{A}_{(L)}d^{t'}v=\\int_{^{t'}S_{t}}^{t'}\\mathbf{t}\\cdot\\delta\\mathbf{u}d^{t'}s+\\int_{V}^{t'}\\mathbf{b}\\cdot\\delta\\mathbf{u}d^{t'}v \\end{align} \\]

where \\(^{t'}\\mathbf{A}_{(L)}\\) is the linear portion of the Almansi strain tensor and can be calculated by

\\[ ^{t'}\\mathbf{A}_{(L)}=\\dfrac{1}{2}\\{\\dfrac{\\partial^{t'}\\mathbf{u}}{\\partial^{t'}\\mathbf{x}}+(\\dfrac{\\partial^{t'}\\mathbf{u}}{\\partial^{t'}\\mathbf{x}})^{T}\\} \\]

The equation \\(\\eqref{eq:ch5_nonlinear_gov2}\\) needs to be solved referring to layout V at time 0, or layout \\(^{t}v\\) at time t. The following sections will introduce these two algorithms: total Lagrange method and updated Lagrange method, respectively.

"},{"location":"welsim/theory/geometricnl/#formulation-of-total-lagrange-algorithm","title":"Formulation of total lagrange algorithm","text":"

The principle equation of the virtual work at time t' assuming the initial layout of time 0 is the reference domain, which is shown below.

\\[ \\begin{align} \\label{eq:ch5_nonlinear_total_lag_gov1} \\intop_{V}\\thinspace_{0}^{t'}\\mathbf{S}:\\delta_{0}^{t'}\\mathbf{E}dV=^{t'}\\delta\\mathbf{R} \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_nonlinear_total_lag_gov2} ^{t'}\\delta\\mathbf{R}=\\intop_{S_{t}}\\thinspace_{0}^{t'}\\mathbf{t}\\cdot\\delta dS+\\intop_{V}\\thinspace_{0}^{t'}\\mathbf{b}\\cdot\\delta\\mathbf{u}dV \\end{align} \\]

where \\(_{0}^{t'}\\mathbf{S}\\) and \\(_{0}^{t'}\\mathbf{E}\\) are the 2nd order Piola-Kirchhoff stress tensor and the Green-Lagrange strain tensor at time t', respectively. The initial domain at time 0 is called the reference domain. The body force \\(_{0}^{t'}\\mathbf{b}\\) and nominal surface force vector \\(_{0}^{t'}\\mathbf{t}\\) are

\\[ _{0}^{t'}\\mathbf{t}=\\dfrac{d^{t'}s}{dS}\\thinspace^{t'}\\mathbf{t} \\] \\[ _{0}^{t'}\\mathbf{b}=\\dfrac{d^{t'}v}{dV}\\thinspace^{t'}\\mathbf{b} \\]

The Green-Lagrange strain tensor at time t is defined by

\\[ _{0}^{t}\\mathbf{E}=\\dfrac{1}{2}\\{\\dfrac{\\partial^{t}\\mathbf{u}}{\\partial\\mathbf{X}}+(\\dfrac{\\partial^{t}\\mathbf{u}}{\\partial\\mathbf{X}})^{T}+(\\dfrac{\\partial^{t}\\mathbf{u}}{\\partial\\mathbf{X}})^{T}\\cdot\\dfrac{\\partial^{t}\\mathbf{u}}{\\partial\\mathbf{X}}\\} \\]

Then the displacement \\(^{t'}\\mathbf{u}\\) and 2nd order Piola-Kirchhoff stress \\(_{0}^{t'}\\mathbf{S}\\) at time t' are

\\[ \\begin{align} \\label{eq:ch5_nonlinear_total_lag_gov3} ^{t'}\\mathbf{u}=^{t}\\mathbf{u}+\\triangle\\mathbf{u} \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_nonlinear_total_lag_gov4} _{0}^{t'}\\mathbf{S}=_{0}^{t}\\mathbf{S}+\\triangle\\mathbf{S} \\end{align} \\]

Similarly, the incremental Green-Lagrange strain can be defined as

\\[ \\begin{align} \\label{eq:ch5_nonlinear_total_lag_gov5} ^{t'}\\mathbf{E}=^{t}\\mathbf{E}+\\triangle\\mathbf{E} \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_nonlinear_total_lag_gov6} \\triangle\\mathbf{E}=\\triangle\\mathbf{E}_{L}+\\triangle\\mathbf{E}_{NL} \\end{align} \\]

where

\\[ \\triangle\\mathbf{E}_{L}=\\dfrac{1}{2}\\{\\dfrac{\\partial\\triangle\\mathbf{u}}{\\partial\\mathbf{X}}+(\\dfrac{\\partial\\triangle\\mathbf{u}}{\\partial\\mathbf{X}})^{T}+(\\dfrac{\\partial\\triangle\\mathbf{u}}{\\partial\\mathbf{X}})^{T}\\cdot\\dfrac{\\partial^{t}\\mathbf{u}}{\\partial\\mathbf{X}}+(\\dfrac{\\partial^{t}\\mathbf{u}}{\\partial\\mathbf{X}})^{T}\\cdot\\dfrac{\\partial\\triangle\\mathbf{u}}{\\partial\\mathbf{X}}\\} \\] \\[ \\triangle\\mathbf{E}_{NL}=\\dfrac{1}{2}(\\dfrac{\\partial\\triangle\\mathbf{u}}{\\partial\\mathbf{X}})^{T}\\cdot\\dfrac{\\partial\\triangle\\mathbf{u}}{\\partial\\mathbf{X}} \\]

Substituting equations \\(\\eqref{eq:ch5_nonlinear_total_lag_gov3}\\), \\(\\eqref{eq:ch5_nonlinear_total_lag_gov4}\\), \\(\\eqref{eq:ch5_nonlinear_total_lag_gov5}\\), and \\(\\eqref{eq:ch5_nonlinear_total_lag_gov6}\\) into governing equations \\(\\eqref{eq:ch5_nonlinear_total_lag_gov1}\\) and \\(\\eqref{eq:ch5_nonlinear_total_lag_gov2}\\), we have

\\[ \\intop_{v}\\triangle\\mathbf{S}:(\\delta\\triangle\\mathbf{E}_{L}+\\delta\\triangle\\mathbf{E}_{NL})dV+\\intop_{V}\\thinspace_{0}^{t}\\mathbf{S}\\colon\\delta\\triangle\\mathbf{E}_{NL}dV=^{t'}\\delta\\mathbf{R}-\\intop_{V}\\thinspace_{0}^{t}\\mathbf{S}:\\delta\\triangle\\mathbf{E}_{L}dV \\]

where \\(\\triangle\\mathbf{S}\\) is assumed to be

\\[ \\triangle\\mathbf{S}=_{0}^{t}\\mathbf{C}\\colon\\triangle\\mathbf{E}_{L} \\]

then we have

\\[ \\begin{align} \\label{eq:ch5_nonlinear_total_lag_gov7} \\intop_{v}(\\mathbf{C}\\colon\\triangle\\mathbf{E}):\\delta\\triangle\\mathbf{E}_{L}dV+\\intop_{V}\\thinspace_{0}^{t}\\mathbf{S}\\colon\\delta\\triangle\\mathbf{E}_{NL}dV=^{t'}\\delta\\mathbf{R}-\\intop_{V}\\thinspace_{0}^{t}\\mathbf{S}:\\delta\\triangle\\mathbf{E}_{L}dV \\end{align} \\]

Equation \\(\\eqref{eq:ch5_nonlinear_total_lag_gov7}\\) can be discreted to finite element formulation

\\[ \\delta\\mathbf{U}^{T}(_{0}^{t}\\mathbf{K}_{L}+{}_{0}^{t}\\mathbf{K}_{NL})\\triangle\\mathbf{U}=\\delta\\mathbf{U}^{T}\\thinspace_{0}^{t'}\\mathbf{F}-\\delta\\mathbf{\\mathbf{U}}^{T}\\thinspace_{0}^{t'}\\mathbf{Q} \\]

where \\(_{0}^{t}\\mathbf{K}_{L}\\), \\(_{0}^{t}\\mathbf{K}_{NL}\\), \\(_{0}^{t'}\\mathbf{F}\\), \\(_{0}^{t}\\mathbf{Q}\\) are the initial material stiffness matrix, initial geometric stiffness (stress) matrix, external force vector, and internal force vector, respectively. The recursive algorithm to calculate the deformation status at time t' from time t is given:

Step 1: i = 0

\\[ \\quad\\quad_{0}^{t'}\\mathbf{K}^{(0)}=_{0}^{t}\\mathbf{K}_{L}+_{0}^{t}\\mathbf{K}_{NL} \\] \\[ \\quad\\quad_{0}^{t'}\\mathbf{Q}^{(0)}=_{0}^{t}\\mathbf{Q} \\] \\[ \\quad\\quad^{t'}\\mathbf{U}^{(0)}=^{t}\\mathbf{U} \\]

Step 2:

\\[ \\quad\\quad_{0}^{t'}\\mathbf{K}^{(i)}\\triangle\\mathbf{U}^{(i)}=_{0}^{t'}\\mathbf{F}-_{0}^{t'}\\mathbf{Q}^{(i-1)} \\]

Step 3:

\\[ \\quad\\quad^{t'}\\mathbf{U}^{(i)}=^{t'}\\mathbf{U}^{(i-1)}+\\triangle\\mathbf{U}^{(i)} \\]"},{"location":"welsim/theory/geometricnl/#formulation-of-updated-lagrange-algorithm","title":"Formulation of updated lagrange algorithm","text":"

In addition to the total Lagrange algorithm, the updated Lagrange algorithm is also widely applied in the nonlinear structural model computation. The principle virtual work equation at time t' uses the current domain at time t as reference domain.

\\[ \\begin{align} \\label{eq:ch5_nonlinear_updated_lag_gov1} \\intop_{V}\\thinspace_{t}^{t'}\\mathbf{S}:\\delta_{t}^{t'}\\mathbf{E}dV=^{t'}\\delta\\mathbf{R} \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_nonlinear_updated_lag_gov2} ^{t'}\\delta\\mathbf{R}=\\intop_{S_{t}}\\thinspace_{t}^{t'}\\mathbf{t}\\cdot\\delta dS+\\intop_{V}\\thinspace_{t}^{t'}\\mathbf{b}\\cdot\\delta\\mathbf{u}dV \\end{align} \\]

where

\\[ _{t}^{t'}\\mathbf{t}=\\dfrac{d^{t'}s}{d^{t}s}\\thinspace^{t'}\\mathbf{t} \\] \\[ _{t}^{t'}\\mathbf{b}=\\dfrac{d^{t'}v}{d^{t}v}\\thinspace^{t'}\\mathbf{b} \\]

The tensors \\(_{t}^{t'}\\mathbf{S}\\), \\(_{t}^{t'}\\mathbf{E}\\) and vectors \\(_{t}^{t'}\\mathbf{t}\\), \\(_{t}^{t'}\\mathbf{b}\\) are using the current time domain t as the reference domain. Therefore, the Green-Lagrange strain does not contain the initial displacement (the displacement at the time t) \\(^{t}\\mathbf{u}\\);

\\[ \\begin{align} \\label{eq:ch5_nonlinear_updated_lag_gov3} _{t}^{t'}\\mathbf{E}=\\triangle_{t}\\mathbf{E}_{L}+\\triangle_{t}\\mathbf{E}_{NL} \\end{align} \\]

where

\\[ \\begin{align} \\label{eq:ch5_nonlinear_updated_lag_gov4} \\triangle_{t}\\mathbf{E}_{L}=\\dfrac{1}{2}\\{\\dfrac{\\partial\\triangle\\mathbf{u}}{\\partial^{t}x}+(\\dfrac{\\partial\\triangle\\mathbf{u}}{\\partial^{t}x})^{T}\\} \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_nonlinear_updated_lag_gov5} \\triangle_{t}\\mathbf{E}_{NL}=\\dfrac{1}{2}(\\dfrac{\\partial\\triangle\\mathbf{u}}{\\partial^{t}x})^{T}\\cdot\\dfrac{\\partial\\triangle\\mathbf{u}}{\\partial^{t}x} \\end{align} \\]

Similarly,

\\[ _{t}^{t'}\\mathbf{S}=_{t}^{t}\\mathbf{S}+\\triangle_{t}\\mathbf{S} \\]

Substituting equations \\(\\eqref{eq:ch5_nonlinear_updated_lag_gov3}\\) and \\(\\eqref{eq:ch5_nonlinear_updated_lag_gov2}\\) into governing equations \\(\\eqref{eq:ch5_nonlinear_updated_lag_gov1}\\), we have

\\[ \\intop_{^{t}v}\\triangle_{t}\\mathbf{S}:(\\delta\\triangle_{t}\\mathbf{E}_{L}+\\delta\\triangle_{t}\\mathbf{E}_{NL})d^{t}v+\\intop_{V}\\thinspace_{t}^{t}\\mathbf{S}\\colon\\delta\\triangle_{t}\\mathbf{E}_{NL}d^{t}v=^{t'}\\delta\\mathbf{R}-\\intop_{^{t}v}\\thinspace_{t}^{t}\\mathbf{S}:\\delta\\triangle_{t}\\mathbf{E}_{L}d^{t}v \\]

where \\(\\triangle_{t}\\mathbf{S}\\) is assumed to be

\\[ \\triangle_{t}\\mathbf{S}=_{t}^{t}\\mathbf{C}\\colon\\triangle_{t}\\mathbf{E}_{L} \\]

then we have

\\[ \\begin{align} \\label{eq:ch5_nonlinear_updated_lag_gov7} \\intop_{v}(\\mathbf{C}\\colon\\triangle t\\mathbf{E}_{L}):\\delta\\triangle_{t}\\mathbf{E}_{L}dV+\\intop_{V}\\thinspace_{t}^{t}\\mathbf{S}\\colon\\delta\\triangle_{t}\\mathbf{E}_{NL}dV=^{t'}\\delta\\mathbf{R}-\\intop_{V}\\thinspace_{t}^{t}\\mathbf{S}:\\delta\\triangle_{t}\\mathbf{E}_{L}dV \\end{align} \\]

Equation \\(\\eqref{eq:ch5_nonlinear_updated_lag_gov7}\\) can be discreted to finite element formulation

\\[ \\delta\\mathbf{U}^{T}(_{t}^{t}\\mathbf{K}_{L}+{}_{t}^{t}\\mathbf{K}_{NL})\\triangle\\mathbf{U}=\\delta\\mathbf{U}^{T}\\thinspace_{t}^{t'}\\mathbf{F}-\\delta\\mathbf{\\mathbf{U}}^{T}\\thinspace_{t}^{t'}\\mathbf{Q} \\]

where \\(_{t}^{t}\\mathbf{K}_{L}\\), \\(_{t}^{t}\\mathbf{K}_{NL}\\), \\(_{t}^{t'}\\mathbf{F}\\), \\(_{t}^{t}\\mathbf{Q}\\) are the initial material stiffness matrix, initial geometric stiffness (stress) matrix, external force vector, and internal force vector, respectively. The recursive algorithm to calculate the deformation status at time t' from time t is given:

Step 1: i = 0

\\[ \\quad\\quad_{t}^{t'}\\mathbf{K}^{(i)}=_{t}^{t}\\mathbf{K}_{L}+_{t}^{t}\\mathbf{K}_{NL} \\] \\[ \\quad\\quad_{t}^{t'}\\mathbf{Q}^{(i)}=_{t}^{t}\\mathbf{Q} \\] \\[ \\quad\\quad^{t'}\\mathbf{U}^{(i)}=^{t}\\mathbf{U} \\]

Step 2:

\\[ \\quad\\quad_{0}^{t'}\\mathbf{K}^{(i)}\\triangle\\mathbf{U}^{(i)}=_{0}^{t'}\\mathbf{F}-_{0}^{t'}\\mathbf{Q}^{(i-1)} \\]

Step 3:

\\[ \\quad\\quad^{t'}\\mathbf{U}^{(i)}=^{t'}\\mathbf{U}^{(i-1)}+\\triangle\\mathbf{U}^{(i)} \\]"},{"location":"welsim/theory/introduction/","title":"Introduction","text":"

This theory reference presents theoretical descriptions of all algorithms, as well as many procedures and elements used in these products. It is useful to any of our users who need to understand how the software program calculates the output based on the inputs.

"},{"location":"welsim/theory/materialnl/","title":"Structures with material nonlinearities","text":"

Material nonlinearities occur because of the nonlinear relationship between stress and strain; that is, the stress is a nonlinear function of the strain. The relationship is also path-dependent (except for the case of nonlinear elasticity and hyperelasticity), so that the stress depends on the strain history as well as the strain itself.

The program can account for many material nonlinearities, as follows:

  1. Rate-independent plasticity is characterized by the irreversible instantaneous straining that occurs in a material.

  2. Rate-dependent plasticity allows the plastic-strains to develop over a time interval. It is also termed viscoplasticity.

  3. Creep is also an irreversible straining that occurs in a material and is rate-dependent so that the strains develop over time. The time frame for creep is usually much larger than that for rate-dependent plasticity.

  4. Nonlinear elasticity allows a nonlinear stress-strain relationship to be specified. All straining is reversible.

  5. Hyperelasticity is defined by a strain-energy density potential that characterizes elastomeric and foam-type materials. All straining is reversible.

  6. Viscoelasticity is a rate-dependent material characterization that includes a viscous contribution to the elastic straining.

When the material applicable for analysis is an elastoplastic material, the updated Lagrange method is applied, and the total Lagrange method is applied for hyperelastic material. Moreover, the Newton-Raphson method is applied to the repetitive analysis method.

"},{"location":"welsim/theory/materialnl/#strain-definitions","title":"Strain definitions","text":"

For the case of nonlinear materials, the definition of elastic strain given in Equation\u00a0\\(\\eqref{eq:ch4_theory_stress_strain_relation}\\) expands to

\\[ \\begin{align} \\label{eq:ch4_guide_strain_full} \\{\\epsilon\\}=\\{\\epsilon^{el}\\}+\\{\\epsilon^{th}\\}+\\{e^{pl}\\}+\\{\\epsilon^{cr}\\}+\\{\\epsilon^{sw}\\} \\end{align} \\]

where \\(\\epsilon\\) is the total strain vector, \\(\\epsilon^{el}\\) is elastic strain vector, \\(\\epsilon^{th}\\) is the thermal strain vector, \\(\\epsilon^{pl}\\) is the plastic strain vector, \\(\\epsilon^{cr}\\) is the creep strain vector, and \\(\\epsilon^{sw}\\) is the swelling strain vector.

"},{"location":"welsim/theory/materialnl/#hyperelasticity","title":"Hyperelasticity","text":"

The elastic potential energy in hyperelastic material can be obtained from the initial state with no stress activation. Therefore, we have the main invariable terms of the right Cauchy-Green deformation tensor C(\\(I_{1}\\), \\(I_{2}\\), \\(I_{3}\\)), or the main invariable of the deformation tensor excluding the volume changes (\\(\\bar{I}_{1}\\), \\(\\bar{I}_{2}\\), \\(\\bar{I}_{3}\\)). The potential can be expressed as \\(\\mathbf{W}=\\mathbf{W}(I_{1},I_{2},I_{3})\\), or \\(\\mathbf{W}=\\mathbf{W}(\\bar{I}_{1},\\bar{I}_{2},\\bar{I}_{3})\\).

The nonlinear constitutive relation of hyperelastic material is defined by the relation between the second order Piola-Kirchhoff stress and the Green-Lagrange strain, the total Lagrange method is more efficient in solving such models.

When the elastic potential energy \\(W\\) of the hyperelasticity is known, the second Piola-Kirchhoff stress and strain-stress relationship can be calculated as follows

\\[ S=2\\dfrac{\\partial W}{\\partial C} \\] \\[ C=4\\dfrac{\\partial^{2}W}{\\partial C\\partial C} \\]"},{"location":"welsim/theory/materialnl/#arruda-boyce-model","title":"Arruda-Boyce model","text":"

The form of the strain-energy potential for Arruda-Boyce model is

\\[ \\begin{array}{ccc} W & = & [\\dfrac{1}{2}(\\bar{I}_{1}-3)+\\dfrac{1}{20\\lambda_{m}^{2}}(\\bar{I_{1}^{2}}-9)+\\dfrac{11}{1050\\lambda_{m}^{4}}(\\bar{I_{1}^{3}}-27)\\\\ & + & \\dfrac{19}{7000\\lambda_{m}^{6}}(\\bar{I_{1}^{4}}-81)+\\dfrac{519}{673750\\lambda_{m}^{8}}(\\bar{I_{1}^{5}}-243)]+\\dfrac{1}{D_1}(\\dfrac{J^{2}-1}{2}-\\mathrm{ln}J) \\end{array} \\]

where \\(\\lambda_{m}\\) is limiting network stretch, and \\(D_1\\) is the material incompressibility parameter.

The initial shear modulus is

\\[ \\mu=\\dfrac{\\mu_{0}}{1+\\dfrac{3}{5\\lambda_{m}^{2}}+\\dfrac{99}{175\\lambda_{m}^{4}}+\\dfrac{513}{875\\lambda_{m}^{6}}+\\dfrac{42039}{67375\\lambda_{m}^{8}}} \\]

The initial bulk modulus is

\\[ K=\\dfrac{2}{D_1} \\]

As the parameter \\(\\lambda_L\\) goes to infinity, the model is equivalent to neo-Hookean form.

"},{"location":"welsim/theory/materialnl/#blatz-ko-foam-model","title":"Blatz-Ko foam model","text":"

The form of strain-energy potential for the Blatz-Ko model is:

\\[ W=\\frac{\\mu}{2}\\left(\\frac{I_{2}}{I_{3}}+2\\sqrt{I_{3}}-5\\right) \\]

where \\(\\mu\\) is initla shear modulus of material. The initial bulk modulus is defined as :

\\[ K = \\frac{5}{3}\\mu \\]"},{"location":"welsim/theory/materialnl/#extended-tube-model","title":"Extended tube model","text":"

The elastic strain-energy potential for the extended tube model is:

\\[ \\begin{array}{ccc} W & = & \\frac{G_{c}}{2}\\left[\\frac{\\left(1-\\delta^{2}\\right)\\left(\\bar{I}_{1}-3\\right)}{1-\\delta^{2}\\left(\\bar{I}_{1}-3\\right)}+\\mathrm{ln}\\left(1-\\delta^{2}\\left(\\bar{I}_{1}-3\\right)\\right)\\right]\\\\ & + & \\frac{2G_{e}}{\\beta^{2}}\\sum_{i=1}^{3}\\left(\\bar{\\lambda}_{i}^{-\\beta}-1\\right)+\\frac{1}{D_1}\\left(J-1\\right)^{2} \\end{array} \\]

where the initial shear modulus is \\(G\\)=\\(G_c\\) + \\(G_e\\), and \\(G_e\\) is constraint contribution to modulus, \\(G_c\\) is crosslinked contribution to modulus, \\(\\delta\\) is extensibility parameter, \\(\\beta\\) is empirical parameter (0\\(\\leq \\beta \\leq\\)1), and \\(D_1\\) is material incompressibility parameter.

Extended tube model is equivalent ot a two-term Ogden model with the following parameters:

\\[ \\begin{array}{cccc} \\alpha_1 = 2 &, & \\alpha_2=-\\beta\\\\ \\mu_1=G_c &, & \\mu_2=-\\dfrac{2}{\\beta}G_e, & \\delta=0 \\end{array} \\]"},{"location":"welsim/theory/materialnl/#gent-model","title":"Gent model","text":"

The form of the strian-energy potential for the Gent model is:

\\[ W=-\\frac{\\mu J_{m}}{2}\\mathrm{ln}\\left(1-\\frac{\\bar{I}_{1}-3}{J_{m}}\\right)+\\frac{1}{D_1}\\left(\\frac{J^{2}-1}{2}-\\mathrm{ln}J\\right) \\]

where \\(\\mu\\) is initial shear modulus of material, \\(J_m\\) is limiting value of \\(\\bar{I}_1-3\\), \\(D_1\\) is material incompressibility parameter.

The initial bulk modulus is

\\[ K=\\dfrac{2}{D_1} \\]

When the parameter \\(J_m\\) goes to infinity, the Gent model is equivalent to neo-Hookean form.

"},{"location":"welsim/theory/materialnl/#mooney-rivlin-model","title":"Mooney-Rivlin model","text":"

This model includes two-, three-, five-, and nine-terma Mooney-Rivlin models. The form of the strain-energy potential for a two-parameter Mooney-Rivlin model is

\\[ W=C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right)+\\frac{1}{D_1}\\left(J-1\\right)^{2} \\]

where \\(C_{10}\\), \\(C_{01}\\), and \\(D_{1}\\) are the material constants.

The form of strain-energy potential for a three-parameter Mooney-Rivlin model is

\\[ W=C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right)+C_{11}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right)+\\frac{1}{D_1}\\left(J-1\\right)^{2} \\]

where \\(C_{10}\\), \\(C_{01}\\), \\(C_{11}\\), and \\(D_1\\) are material ocnstants.

The form of strain-energy potential for a five-parameter Mooney-Rivlin model is

\\[ \\begin{array}{ccc} W & = & C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right)+C_{20}\\left(\\bar{I}_{1}-3\\right)^{2}\\\\ & + & C_{11}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right)+C_{02}\\left(\\bar{I}_{2}-3\\right)^{2}+\\frac{1}{D_1}\\left(J-1\\right)^{2} \\end{array} \\]

where \\(C_{10}\\), \\(C_{01}\\), \\(C_{20}\\), \\(C_{11}\\), \\(C_{02}\\), and \\(D_1\\) are material ocnstants.

The form of strain-energy potential for a nine-parameter Mooney-Rivlin model is

\\[ \\begin{array}{ccc} W & = & C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right)+C_{20}\\left(\\bar{I}_{1}-3\\right)^{2}\\\\ & + & C_{11}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right)+C_{02}\\left(\\bar{I}_{2}-3\\right)^{2}+C_{30}\\left(\\bar{I}_{1}-3\\right)^{3}\\\\ & + & C_{21}\\left(\\bar{I}_{1}-3\\right)^{2}\\left(\\bar{I}_{2}-3\\right)+C_{12}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right)^{2}+C_{03}\\left(\\bar{I}_{2}-3\\right)^{3}+\\frac{1}{D_1}\\left(J-1\\right)^{2} \\end{array} \\]

where \\(C_{10}\\), \\(C_{01}\\), \\(C_{20}\\), \\(C_{11}\\), \\(C_{02}\\), \\(C_{30}\\), \\(C_{21}\\), \\(C_{12}\\), \\(C_{03}\\), and \\(D_1\\) are material ocnstants.

The initial shear modulus is given by:

\\[ \\mu=2(C_{10}+C_{01}) \\]

The initial bulk modulus is

\\[ K=\\dfrac{2}{D_1} \\]"},{"location":"welsim/theory/materialnl/#neo-hookean-model","title":"Neo-Hookean model","text":"

The Neo-Hookean model is a well-known hyperelastic model with an expanded linear rule (Hooke rule) having isotropy so that it can respond to finite deformation problems. The elastic potential is as follows.

\\[ W=\\frac{\\mu}{2}(\\bar{I}_{1}-3)+\\dfrac{1}{D_{1}}(J-1)^{2} \\]

where \\(\\mu\\) is initial shear modulus of materials, \\(D_{1}\\) is the material constant.

The initial bulk modulus is given by:

\\[ K=\\dfrac{2}{D_1} \\]"},{"location":"welsim/theory/materialnl/#ogden-compressible-foam-model","title":"Ogden compressible foam model","text":"

The strain-energy potential of the Ogden compressible foam model is based on the principal stretches of left Cauchy strain tensor, which has the form:

\\[ W=\\sum_{i=1}^{N}\\frac{\\mu_{i}}{\\alpha_{i}}\\left(J^{\\alpha_{i}/3}\\left(\\bar{\\lambda}_{1}^{\\alpha_{i}}+\\bar{\\lambda}_{2}^{\\alpha_{i}}+\\bar{\\lambda}_{3}^{\\alpha_{i}}\\right)-3\\right)+\\sum_{i=1}^{N}\\frac{\\mu_{i}}{\\alpha_{i}\\beta_{i}}\\left(J^{-\\alpha_{i}\\beta_{i}}-1\\right) \\]

where N determines the order of the polynomial, \\(\\mu_i\\), \\(\\alpha_i\\) are material constants, \\(D_k\\) is incompressiblity parameter. The reduced principal strench is defined by:

\\[ \\bar{\\lambda}_{p}=J^{-\\frac{1}{3}}\\lambda_p,\\; J=(\\lambda_{1}\\lambda_{2}\\lambda_{3})^{\\frac{1}{2}} \\]

The initial shear modulus is given by:

\\[ \\mu=\\dfrac{\\sum_{i=1}^{N}\\mu_{i}\\alpha_{i}}{2} \\]

The initial bulk modulus K is defined by

\\[ K = \\sum_{i=1}^{N}\\mu_{i}\\alpha_{i}\\left(\\dfrac{1}{3}+\\beta_{i}\\right) \\]

When parameters N=1, \\(\\alpha_1\\)=-2, \\(\\mu_1\\)=-\\(\\mu\\), and \\(\\beta\\)=0.5, the Ogden compressible model is converted to the Blatz-Ko model.

"},{"location":"welsim/theory/materialnl/#ogden-model","title":"Ogden model","text":"

The strain-energy potential of the Ogden compressible foam model is based on the principal stretches of left Cauchy strain tensor, which has the form:

\\[ W=\\sum_{i=1}^{N}\\frac{\\mu_{i}}{\\alpha_{i}}\\left(\\bar{\\lambda}_{1}^{\\alpha_{i}}+\\bar{\\lambda}_{2}^{\\alpha_{i}}+\\bar{\\lambda}_{3}^{\\alpha_{i}}-3\\right)+\\sum_{k=1}^{N}\\frac{1}{D_{k}}\\left(J-1\\right)^{2k} \\]

where N determines the order of the polynomial, \\(\\mu_i\\), \\(\\alpha_i\\) are material constants, \\(D_k\\) is incompressiblity parameter. The reduced principal strench is defined by:

\\[ \\bar{\\lambda}_{p}=J^{-\\frac{1}{3}}\\lambda_p,\\; J=(\\lambda_{1}\\lambda_{2}\\lambda_{3})^{\\frac{1}{2}} \\]

The initial shear modulus is given by:

\\[ \\mu=\\dfrac{\\sum_{i=1}^{N}\\mu_{i}\\alpha_{i}}{2} \\]

The initial bulk modulus K is defined by

\\[ K = \\dfrac{2}{D_1} \\]

When parameters N=1, \\(\\alpha_1\\)=2, the Ogden model is converted to the neo-Hookean model. When parameters N=2, \\(\\alpha_1\\)=2 and \\(\\alpha_2\\)=-2, the Ogden model is converted to the 2-parameter Mooney-Rivlin model.

"},{"location":"welsim/theory/materialnl/#polynomial-form","title":"Polynomial form","text":"

The polynomial form of strain-energy potential is:

\\[ W=\\sum_{i+j=1}^{N}c_{ij}\\left(\\bar{I}_{1}-3\\right)^{i}\\left(\\bar{I_{2}}-3\\right)^{j}+\\sum_{k=1}^{N}\\frac{1}{D_{k}}\\left(J-1\\right)^{2k} \\]

where \\(N\\) determines the order of polynomial, \\(c_{ij}\\), \\(D_k\\) are material constants.

The initial shear modulus is given by:

\\[ \\mu=2\\left(C_{10}+C_{01}\\right) \\]

The initial bulk modulus K is defined by

\\[ K = \\dfrac{2}{D_1} \\]

The Polynomial model is converted to following models with specific paramters:

Parameters of Polynomial model Equivalent model N=1, \\(C_{01}\\)=0 neo-Hookean N=1 2-parameter Mooney-Rivlin N=2 5-parameter Mooney-Rivlin N=3 9-parameter Mooney-Rivlin"},{"location":"welsim/theory/materialnl/#yeoh-model","title":"Yeoh model","text":"

The Yeoh model is also called the reduced polynomial form. The strain-energy potential is

\\[ W=\\sum_{i=1}^{N}c_{i0}\\left(\\bar{I}_{1}-3\\right)^{i}+\\sum_{k=1}^{N}\\frac{1}{D_{k}}\\left(J-1\\right)^{2k} \\]

where N denotes the order of polynomial, \\(C_{i0}\\) and \\(D_k\\) are material constants. When N=1, Yeoh becomes neo-Hookean model.

The initial shear modulus is defined:

\\[ \\mu=2c_{10} \\]

The initial bulk modulus is:

\\[ K=\\frac{2}{D_1} \\]"},{"location":"welsim/theory/materialnl/#rate-independent-plasticity","title":"Rate-independent plasticity","text":"

The elastoplasticity based on the flow rule is applied in this program. The constitutive relation between Jaumman rate and the deformation rate tensor of the Kirchhoff stress is numerically solved using the updated Lagrange method.

"},{"location":"welsim/theory/materialnl/#elastoplastic-constitutive-equation","title":"Elastoplastic constitutive equation","text":"

The yield criteria of an elasto-plastic solid can be written into math formulas. The initial yield criteria are

\\[ F(\\sigma,\\sigma_{y0})=0 \\]

The Consecutive yield criteria are

\\[ F(\\sigma,\\sigma_{y}(e^{-p}))=0 \\]

where \\(F\\) is the yield function, \\(\\sigma_{y0}\\) is initial yield stress, \\(\\sigma_{y}\\) is consecutive yield stress, \\(\\sigma\\) is stress tensor, \\(\\mathbf{e}\\) is the infinitesimal strain tensor, \\(\\mathbf{e}^{p}\\) is the plastic strain tensor, \\(\\bar{\\mathbf{e}}^{p}\\) is equivalent plastic strain.

The yield stress-equivalent plastic strain relationship is assumed to conform to the stress-plastic strain relation in a single axis state. The stress-plastic strain relation about one single axis state is:

\\[ \\sigma=H(e^{p}) \\] \\[ \\dfrac{d\\sigma}{de^{p}}=H' \\]

where \\(H'\\) is the strain hardening factor. The equivalent stress-equivalent plastic strain relation is :

\\[ \\bar{\\sigma}=H(\\bar{e}^{p}) \\] \\[ \\dot{\\bar{\\sigma}}=H'\\dot{\\bar{e^{p}}} \\]

The consecutive yield function is generally a function of temperature and plastic strain work. In this program, this function is assumed to be related to the equivalent plastic strain \\bar{e}^{p}. Since condition F=0 holds during the plastic deformation, we have

\\[ \\begin{align} \\label{eq:ch5_plastic_gov1} \\dot{F}=\\dfrac{\\partial F}{\\partial\\sigma}\\colon\\dot{\\sigma}+\\dfrac{\\partial F}{\\partial\\mathbf{e}^{p}}\\colon\\dot{\\mathbf{e}}^{p}=0 \\end{align} \\]

where \\(\\dot{F}\\) is the time derivative function of \\(F\\).

In this case, we assume the existence of the plastic potential \\(\\Theta\\), the plastic strain rate is

\\[ \\dot{\\mathbf{e}}^{p}=\\dot{\\lambda}\\dfrac{\\partial\\Theta}{\\partial\\sigma} \\]

where \\(\\dot{\\lambda}\\) is the factor. Moreover, assuming the plastic potential \\(\\Theta\\) is equivalent to yield function \\(F\\), the associated flow rule is assumed as

\\[ \\dot{\\mathbf{e}}^{p}=\\dot{\\lambda}\\dfrac{\\partial F}{\\partial\\sigma} \\]

which is substituted with equation \\(\\eqref{eq:ch5_plastic_gov1}\\), we have

\\[ \\dot{\\lambda}=\\dfrac{\\mathbf{a}^{T}\\colon\\mathbf{d}_{D}}{A+\\mathbf{a}^{T}\\colon\\mathbf{D}\\colon\\mathbf{a}}\\mathbf{\\dot{\\mathbf{e}}} \\]

where \\(\\mathbf{D}\\) is the elastic matrix, and

\\[ \\mathbf{a}^{T}=\\dfrac{\\partial F}{\\partial\\sigma}\\quad\\mathbf{d}_{D}=\\mathbf{D}\\mathbf{a}^{T}\\quad A=-\\dfrac{1}{\\dot{\\lambda}}\\dfrac{\\partial F}{\\partial\\mathbf{\\mathbf{e}}^{p}}\\colon\\dot{\\mathbf{e}}^{p} \\]

The stress-strain relation for elastoplasicity can be rewritten to

\\[ \\begin{align} \\label{eq:ch5_plastic_yield_func1} \\dot{\\sigma}=\\{\\mathbf{D}-\\dfrac{\\mathbf{d}_{D}\\otimes\\mathbf{d}_{D}^{T}}{A+\\mathbf{d}_{D}^{T}\\mathbf{a}}\\}\\colon\\dot{\\mathbf{e}} \\end{align} \\]

Here we give the explicit form of several yield functions that are applied in the program.

"},{"location":"welsim/theory/materialnl/#von-mises-yield-function","title":"Von-Mises yield function","text":"\\[ F=\\sqrt{3\\mathbf{J}_{2}}-\\sigma_{y} = 0 \\]"},{"location":"welsim/theory/materialnl/#mohr-coulomb-yield-function","title":"Mohr-Coulomb yield function","text":"\\[ F=\\sigma_{1}-\\sigma_{3}+(\\sigma_{1}+\\sigma_{3})\\mathrm{sin}\\phi-2c\\mathrm{cos}\\phi = 0 \\]"},{"location":"welsim/theory/materialnl/#drucker-prager-yield-function","title":"Drucker-Prager yield function","text":"\\[ F=\\sqrt{\\mathbf{J}_{2}}-\\alpha\\sigma\\colon\\mathbf{I}-\\sigma_{y}=0 \\]

where material constant \\(\\alpha\\) and \\(\\sigma_{y}\\) are calculated from the viscosity and friction angle of the material as shown below

\\[ \\alpha=\\dfrac{2\\mathrm{sin}\\phi}{3+\\mathrm{sin}\\phi},\\quad\\sigma_{y}=\\dfrac{6c\\mathrm{cos}\\phi}{3+\\mathrm{sin}\\phi} \\]"},{"location":"welsim/theory/materialnl/#viscoelasticity","title":"Viscoelasticity","text":"

A material is viscoelastic if the material has both elastic (recoverable) and viscous (nonrecoverable) parts. Upon loads, the elastic deformation is instantaneous while the viscous part occurs over time. A viscoelastic model can depicts the deformation behavior of glass or glass-like materials and simulate heating and cooling processing of such materials.

"},{"location":"welsim/theory/materialnl/#constitutive-equations","title":"Constitutive Equations","text":"

A generalized Maxwell model is applied for viscoelasticity in this program. The constitutive equation becomes a function of deviatoric strain \\(\\mathbf{e}\\) and deviatoric viscosity strain \\(\\mathbf{q}\\),

\\[ \\sigma(t)=K\\thinspace tr(\\epsilon\\mathbf{I})+2G(\\mu_{0}\\mathbf{e}+\\mu\\mathbf{q}) \\]

where

\\[ \\mu\\mathbf{q}=\\sum_{m=1}^{M}\\mu_{m}\\mathbf{q}^{(m)};\\quad\\sum_{m=0}^{M}\\mu_{m}=1 \\]

moveover, the deviatoric viscosity strain \\(\\mathbf{q}\\) can be calculated by

\\[ \\dot{\\mathbf{q}}\\thinspace^{(m)}+\\dfrac{1}{\\tau_{m}}\\mathbf{q}^{(m)}=\\dot{\\mathbf{e}} \\]

where \\(\\tau_{m}\\) is the relaxation time. The shear and volumetric relaxation coefficient \\(G\\) is represented by the following Prony series:

\\[ G(t)=G[\\mu_{0}^{G}+\\sum_{i=1}^{M}\\mu_{i}^{G}e^{-(t/\\tau_{i}^{G})}] \\] \\[ K(t)=K[\\mu_{0}^{K}+\\sum_{i=1}^{M}\\mu_{i}^{K} e^{-\\frac{t}{\\tau_{i}^{K}}}] \\]

where \\(\\tau_{i}^{G}\\) and \\(\\tau_{i}^{K}\\) are relaxation times for each Prony component, \\(G_i\\) and \\(K_i\\) are shear and volumetric moduli, respectively.

"},{"location":"welsim/theory/materialnl/#themorheological-simplicity","title":"Themorheological Simplicity","text":"

Viscous material depends strongly on temperature. For instance, A glass-like material turninto viscous fluids at high temperatures and behave like a solid material at low temperatures. The thermorheological simplicity is proposed to assumes that material response to a load at a high temperature over a short duration is identical to that at lower temperature but over a longer duration. Essentially, the relaxation times in Prony components oby the scaling law:

\\[ \\tau_{i}^{G}(T) = \\dfrac{\\tau_{i}^{G}(T_r)}{A(T,T_r)} ,\\qquad \\tau_{i}^{K}(T) = \\dfrac{\\tau_{i}^{K}(T_r)}{A(T,T_r)} \\]

where \\(A(T,T_r)\\) is called the shift function.

"},{"location":"welsim/theory/materialnl/#shift-functions","title":"Shift Functions","text":"

WELSIM offers the following forms of the shift function:

"},{"location":"welsim/theory/materialnl/#williams-landel-ferry-shift-function","title":"Williams-Landel-Ferry Shift Function","text":"

The Williams-Landel-Ferry (WLF) shift function is defined by

\\[ log_{10}(A) = \\dfrac{C1(T-T_r)}{C2+T-T_r} \\]

where T is temperature, \\(T_r\\) is reference temperature, \\(C_1\\) and \\(C_2\\) are the WLF constants.

"},{"location":"welsim/theory/materialnl/#rate-dependent-plasticity-including-creep-and-viscoplasticity","title":"Rate-dependent plasticity (including creep and viscoplasticity)","text":"

The creep is a deformation phenomenon that the displacement depends on the time even under constant stress condition. The viscoelasticity can be viewed as linear creep. Several nonlinear creep are described in this section. In the mathematical theory, we define creep strain \\(\\epsilon^{c}\\) and creep strain rate \\(\\dot{\\epsilon}^{c}\\)

\\[ \\begin{align} \\label{eq:ch5_creep_gov1} \\dot{\\epsilon}^{c}=\\dfrac{\\partial\\epsilon^{c}}{\\partial t}=\\beta(\\sigma,\\epsilon^{c}) \\end{align} \\]

In this case, if the instantaneous strain is assumed as the elasticity strain \\(\\epsilon^{e}\\), the total strain can be expressed as the summary of elastic and creep strains

\\[ \\epsilon=\\epsilon^{e}+\\epsilon^{c} \\]

where the elastic strain can be calculated by

\\[ \\epsilon^{e}=\\mathbf{c}^{e-1}\\colon\\sigma \\]

When the creep occurs in the deformation, the stress becomes

\\[ \\sigma_{n+1}=\\mathbf{c}\\colon(\\epsilon_{n+1}-\\epsilon_{n+1}^{c}) \\] \\[ \\epsilon_{n+1}^{c}=\\epsilon_{n}^{c}+\\triangle t\\beta_{n+\\theta} \\]

where \\(\\beta_{n+\\theta}\\) becomes

\\[ \\beta_{n+\\theta}=(1+\\theta)\\beta_{n}+\\theta\\beta_{n+1} \\]

The incremental creep strain \\(\\triangle\\epsilon^{c}\\) can be simplified to a nonlinear equation

\\[ \\mathbf{R}_{n+1}=\\epsilon_{n+1}-\\mathbf{c}^{-1}\\colon\\sigma_{n+1}-\\epsilon_{n}^{c}-\\triangle t\\beta_{n+\\theta}=0 \\]

The Newton-Raphson method is applied to solve the nonlinear conditions. The iterative scheme in the finite element framework is

\\[ \\begin{align} \\label{eq:ch5_creep_gov2} \\mathbf{R}_{n+1}^{(k+1)}=0=\\mathbf{R}_{n+1}^{(k)}-(\\mathbf{c}^{-1}+\\triangle t\\mathbf{c}_{n+1}^{c})d\\sigma_{n+1}^{(k)} \\end{align} \\]

which yields

\\[ \\begin{align} \\label{eq:ch5_creep_gov3} \\mathbf{c}_{n+1}^{c}=\\dfrac{\\partial\\beta}{\\partial\\sigma}\\mid_{n+\\theta}=\\theta\\dfrac{\\partial\\beta}{\\partial\\sigma}\\mid_{n+1} \\end{align} \\]

The above equations \\(\\eqref{eq:ch5_creep_gov2}\\) and \\(\\eqref{eq:ch5_creep_gov3}\\) are used in the iterative scheme. As the residual \\(\\mathbf{R}\\) gets close to zero, the stress \\(\\sigma_{n+1}\\) and tangent tensile modulus are

\\[ \\mathbf{c}_{n+1}^{*}=[\\mathbf{c}^{-1}+\\triangle t\\mathbf{c}_{n+1}^{c}]^{-1} \\]

To solve the equation \\(\\eqref{eq:ch5_creep_gov1}\\), the following Norton model is applied in the program. The equivalent clip strain \\(\\dot{\\epsilon}^{cr}\\) is defined to be the function of Mises stress \\(q\\) and time \\(t\\).

\\[ \\dot{\\epsilon}^{cr}=Aq^{n}t^{m} \\]

where \\(A\\), \\(m\\), \\(n\\) are the material coefficients.

"},{"location":"welsim/theory/materialnl/#creep","title":"Creep","text":"

Creep is the inelastic, irreversible deformation of structures during time. It is a life limiting factor and depends on stress, strain, temperature and time. This dependency can be modeled as followed:

\\[ \\dot{\\epsilon}^{cr}=f(\\sigma,\\epsilon,T,t) \\]

Creep can occur in all crystalline materials, such as metal or glass, has various impacts on the behavior of the material.

"},{"location":"welsim/theory/materialnl/#three-types-of-creep","title":"Three types of creep","text":"

Creep can be divided in three different stages: primary creep, secondary creep and irradiation induced creep.

Primary creep (0<m<1) starts rapidly with an infinite creep rate at the initialization. Here is m the time index. It occurs after a certain amount of time and slows down constantly. It occurs in the first hour after applying the load and is essential in calculating the relaxation over time.

Secondary creep (m=1) follows right after the primary creep stage. The strain rate is now constant over a long period of time.

The strain rate in the irradiation induced creep stage is growing rapidly until failure. This happens in a short period of time and is not of great interest. Therefore only primary and secondary creep are modeled in WelSim.

"},{"location":"welsim/theory/materialnl/#creep-models","title":"Creep models","text":"

WELSIM supports implicit creep models including Strain Hardening, Time Hardening, Generalized Exponentia, Generalized Graham, Generalized Blackburn, Modified Time Hardening, Modified Strain Hardening, Generalized Garofalo, Exponential form, Norton, Combined Time Hardening, Rational polynomial, and Generalized Time Hardening. The details of these models are given in the table below.

Creep Model(index) Name Equations Parameters Type 1 Strain Hardening \\(\\dot{\\epsilon}_{cr}=C_{1}\\sigma^{C_2}\\epsilon_{cr}^{C_3}e^{-C_4/T}\\) \\(C_1>0\\) Primary 2 Time Hardening \\(\\dot{\\epsilon}_{cr}=C_{1}\\sigma^{C_2}t^{C_3}e^{-C_4/T}\\) \\(C_1>0\\) Primary 3 Generalized Exponential \\(\\dot{\\epsilon}_{cr}=C_{1}\\sigma^{C_2}re^{-rt}\\), \\(r=C_{5}\\sigma^{C_3}e^{-C4/T}\\) \\(C_1>0\\)\\(C_5>0\\) Primary 4 Generalized Graham \\(\\dot{\\epsilon}_{cr}=C_{1}\\sigma^{C_2}\\left( t^{C_3} + C_{4}t^{C_5} + C_{6}t^{C_7} \\right) e^{-C_8/T}\\) \\(C_1>0\\) Primary 5 Generalized Blackburn \\(\\dot{\\epsilon}_{cr} = f\\left(1-e^{-rt}\\right)+gt\\)\\(f=C_{1}e^{C_2\\sigma}\\), \\(r=C_3\\left(\\sigma/C_4\\right)^{C_5}\\), \\(g=C_{6}e^{C_{7}\\sigma}\\) \\(C_1>0\\)\\(C_3>0\\)\\(C_6>0\\) Primary 6 Modified Time Hardening \\(\\dot{\\epsilon}_{cr}=\\dfrac{C_{1}}{C_3+1}\\sigma^{C_2}t^{C_3+1}e^{-C_4/T}\\) \\(C_1>0\\) Primary 7 Modified Strain Hardening \\(\\dot{\\epsilon}_{cr}= \\{ C_{1} \\sigma^{C_2} \\left[\\left( C_3+1\\right)\\epsilon_{cr} \\right]^{C_3} \\}^{1/(C_3+1)} e^{-C_4/T}\\) \\(C_1>0\\) Primary 8 Generalized Garofalo \\(\\dot{\\epsilon}_{cr}=C_1\\left[ sinh(C_2\\sigma)\\right]^{C_3} e^{-C_4/T}\\) \\(C_1>0\\) Secondary 9 Exponential form \\(\\dot{\\epsilon}_{cr}=C_1 e^{\\sigma/C_2} e^{-C_3/T}\\) \\(C_1>0\\) Secondary 10 Norton \\(\\dot{\\epsilon}_{cr}=C_1 \\sigma^{C_2} e^{-C_3/T}\\) \\(C_1>0\\) Secondary 11 Combined Time Hardening \\(\\dot{\\epsilon}_{cr}=\\dfrac{C_1}{C_3+1} \\sigma^{C_2} t^{C_3+1} e^{-C_4/T} + C_5 \\sigma^{C_6}te^{-C_7/T}\\) \\(C_1>0\\), \\(C_5>0\\) Primary + Secondary 12 Rational Polynomial \\(\\dot{\\epsilon}_{cr}=C_1 \\dfrac{\\partial\\epsilon_c}{\\partial t}\\), \\(\\epsilon_{c}=\\dfrac{cpt}{1+pt}+\\dot{\\epsilon}_m t\\) \\(\\dot{\\epsilon}_m=C_2(10)^{C_3\\sigma}\\sigma^{C_4}\\) \\(c=C_7\\dot{\\epsilon}_m^{C_8}\\sigma^{C_9}\\), \\(p=C_{10}\\dot{\\epsilon}_{m}^{C_{11}}\\sigma^{C_{12}}\\) \\(C_2>0\\) Primary + Secondary 13 Generalized Time Hardening \\(\\dot{\\epsilon}_{cr}=ft^r e^{-C_6/T}\\) \\(f=C_1\\sigma+C_2\\sigma^2+C_3\\sigma^3\\) \\(r=C_4 + C_5\\sigma\\) - Primary

where \\(\\epsilon_{cr}\\) is equivalent creep strain, \\(\\dot{\\epsilon}_{cr}\\) is the change in equivalent creep strain with respect to time, \\(\\sigma\\) is equivalent stress. \\(T\\) is temperature. \\(C_1\\) through \\(C_{12}\\) are creep constants. \\(t\\) is time at end of substep. \\(e\\) is natural logarithm base.

"},{"location":"welsim/theory/modal/","title":"Modal analysis","text":""},{"location":"welsim/theory/modal/#generalized-eigenvalue-problem","title":"Generalized eigenvalue problem","text":"

When conducting a free oscillation analysis of the continuum, assuming no damping in the free vibration. The governing eqatuion is

\\[ \\begin{align} \\label{eq:ch5_modal_gov} \\mathbf{M}\\ddot{\\mathbf{u}}+\\mathbf{Ku}=0 \\end{align} \\]

where \\(\\mathbf{u}\\) is the generated displacement vector, \\(\\mathbf{M}\\) is the mass matrix and \\(\\mathbf{K}\\) is the stiffness matrix. The solution is assumed to

\\[ \\begin{align} \\label{eq:ch5_eigenvalue_vector} \\mathbf{u}(t)=(asin\\omega t+bcos\\omega t)\\mathbf{x} \\end{align} \\]

where \\(\\omega\\) is the natural angular frequency, \\(a\\) and \\(b\\) are the arbitrary constants. Herein, the second order differential of equation \\(\\eqref{eq:ch5_eigenvalue_vector}\\) is

\\[ \\begin{align} \\label{eq:ch5_modal_acceleration} \\ddot{\\mathbf{u}}(t)=\\omega(asin\\omega t-bsin\\omega t)\\mathbf{x} \\end{align} \\]

Combining equations \\(\\eqref{eq:ch5_modal_gov}\\), \\(\\eqref{eq:ch5_eigenvalue_vector}\\), and \\(\\eqref{eq:ch5_modal_acceleration}\\), we have

\\[ \\begin{align} \\label{eq:ch5_modal_gov3} \\mathbf{M}\\ddot{\\mathbf{u}}+\\mathbf{Ku}=(a\\mathrm{sin}\\omega t+b\\mathrm{cos}\\omega t)(-\\omega^{2}\\mathbf{M}+\\mathbf{K}\\mathbf{x})=(-\\lambda\\mathbf{M}\\mathbf{x}+\\mathbf{K}\\mathbf{x})=0 \\end{align} \\]

which simplifies

\\[ \\mathbf{K}\\mathbf{x}=\\lambda\\mathbf{M}\\mathbf{x} \\]

which indicates that if factor \\(\\lambda(=\\omega^{2})\\) and vector \\(\\mathbf{x}\\) satisfies equation \\(\\eqref{eq:ch5_modal_gov3}\\), function \\(\\mathbf{u}(t)\\) becomes the solution of equation \\(\\eqref{eq:ch5_modal_gov}\\). The factor \\(\\lambda\\) is called the eigenvalue, vector \\(\\mathbf{x}\\) is called the eigenvector.

"},{"location":"welsim/theory/modal/#problem-settings","title":"Problem settings","text":"

Equation \\(\\eqref{eq:ch5_modal_acceleration}\\) can be expanded to calculate arbitrary order frequencies, which may appear at real engineering practices. To solve various physical problems, we assume the system is Hermitian(Matrix Symmetrical). Thus, a complex matrix can be transposed into a conjugate complex number and a real symmetric matrix. The relationship can be expressed by the equation below

\\[ k_{ij}=\\bar{k}_{ji} \\]

In this manual, the matrix in modal analysis is assumed to be symmetrical and positive definite. A positively definite matrix always yields to positive eigenvalues. Thus a matrix in the modal system always satisfies the following equation

\\[ \\mathbf{x}^{T}\\mathbf{Ax}>0 \\]"},{"location":"welsim/theory/modal/#shifted-inverse-iteration-method","title":"Shifted inverse iteration method","text":"

In the practical structural modal analysis, not all eigen values are required. There are many cases that some low order eigenvalues are sufficient for the engineering analysis. In the large scale problem that contains large sparse matrix, efficiently calculate the eigenvalues of the low order modes becomes important.

When the lower limit of the eigenvalue is given, the equation \\(\\eqref{eq:ch5_modal_gov3}\\) can be derived to:

\\[ \\begin{align} \\label{eq:ch5_modal_gov4} (\\mathbf{K}-\\sigma\\mathbf{M})^{-1}\\mathbf{M}\\mathbf{x}=[1/(\\lambda-\\sigma)]\\mathbf{x} \\end{align} \\]

this formation of the equations has following advantages in numerical calculation:

In the computing practice, the maximum eigenvalue may be calculated by first. For this reason, we use the equation \\(\\eqref{eq:ch5_modal_gov4}\\) rather than equation \\(\\eqref{eq:ch5_modal_gov3}\\) to calculate the eigenvalues around \\sigma. This scheme is called the shifted inverse iteration.

"},{"location":"welsim/theory/modal/#lanczos-method","title":"Lanczos method","text":"

In the WELSIM application, the Lanczos method is applied to solve the eigenvalues. Lanczos method is a numerical method performing tridiagonalization of matrices. It has capabilities of :

The Lanczos method calculates the base of partial spaces by creating orthogonal vectors from the initial vectors. This method has advantages of computation speed over the subspace method. However, Lanczos method is easily affected by numerical errors. It is essential to check the solution with the numerical errors.

"},{"location":"welsim/theory/modal/#geometric-meaning-in-the-lanczos-method","title":"Geometric meaning in the lanczos method","text":"

Based on equation \\(\\eqref{eq:ch5_modal_gov4}\\), we define

\\[ \\begin{align} \\label{eq:ch5_modal_gov5} \\begin{cases} \\mathbf{A}=(\\mathbf{K}-\\sigma\\mathbf{M})^{-1}\\\\{} [1/(\\lambda-\\sigma)]=\\zeta \\end{cases} \\end{align} \\]

which can be rewritten to the following equation

\\[ \\mathbf{Ax}=\\zeta\\mathbf{x} \\]

The algorithm of the Lanczos method is the Gram-Schmidt orthogonalization for column vectors. Those column vectors are also called the columns of Krylov, and the space created by this scheme is called the Krylov subspace. When the Gram-Schmidt orthogonalization is performed in this space, the vectors can be acquired using the two nearest vectors. This is called the principle of Lanczos.

"},{"location":"welsim/theory/shapefunction/","title":"Shape functions","text":"

This chapter describes the shape functions for the finite elements.

"},{"location":"welsim/theory/shapefunction/#understanding-shape-function-notations","title":"Understanding shape function notations","text":"

The notations used in shape functions are listed below:

"},{"location":"welsim/theory/shapefunction/#3d-shell-elements","title":"3D shell elements","text":"

This section describes the shape functions for 3D shell elements that are applied in the WELSIM application.

"},{"location":"welsim/theory/shapefunction/#3-node-triangle","title":"3-Node triangle","text":"

The shape functions for the 3-node triangular shell elements are:

\\[ u=u_{0}L_{0}+u_{1}L_{1}+u_{2}L_{2} \\] \\[ v=v_{0}L_{0}+v_{1}L_{1}+v_{2}L_{2} \\] \\[ w=w_{0}L_{0}+w_{1}L_{1}+w_{2}L_{2} \\] \\[ A_{x}=A_{x0}L_{0}+A_{x1}L_{1}+A_{x2}L_{2} \\] \\[ A_{y}=A_{y0}L_{0}+A_{y1}L_{1}+A_{y2}L_{2} \\] \\[ A_{z}=A_{z0}L_{0}+A_{z1}L_{1}+A_{z2}L_{2} \\] \\[ T=T_{0}L_{0}+T_{1}L_{1}+T_{2}L_{2} \\] \\[ V=V_{0}L_{0}+V_{1}L_{1}+V_{2}L_{2} \\]"},{"location":"welsim/theory/shapefunction/#6-node-triangle","title":"6-Node triangle","text":"

The shape functions for the 6-node triangular shell elements are:

\\[ u=u_{0}(2L_{0}-1)L_{0}+u_{1}(2L_{1}-1)L_{1}+u_{2}(2L_{2}-1)L_{2}+u_{3}(4L_{0}L_{1})+u_{4}(4L_{1}L_{2})+u_{5}(4L_{2}L_{0}) \\] \\[ v=v_{0}(2L_{0}-1)L_{0}+v_{1}(2L_{1}-1)L_{1}+v_{2}(2L_{2}-1)L_{2}+v_{3}(4L_{0}L_{1})+v_{4}(4L_{1}L_{2})+v_{5}(4L_{2}L_{0}) \\] \\[ w=w_{0}(2L_{0}-1)L_{0}+w_{1}(2L_{1}-1)L_{1}+w_{2}(2L_{2}-1)L_{2}+w_{3}(4L_{0}L_{1})+w_{4}(4L_{1}L_{2})+w_{5}(4L_{2}L_{0}) \\]"},{"location":"welsim/theory/shapefunction/#3d-solid-elements","title":"3D solid elements","text":"

This section describes the shape functions for the 3D solid elements that are applied in the WELSIM application.

"},{"location":"welsim/theory/shapefunction/#4-node-tetrahedra","title":"4-Node tetrahedra","text":"

The 4-node tetrahedra is also called liner tetrahedra element. The shape functions are:

\\[ u=u_{0}L_{0}+u_{1}L_{1}+u_{2}L_{2}+u_{3}L_{3} \\] \\[ v=v_{0}L_{0}+v_{1}L_{1}+v_{2}L_{2}+v_{3}L_{3} \\] \\[ w=w_{0}L_{0}+w_{1}L_{1}+w_{2}L_{2}+w_{3}L_{3} \\]"},{"location":"welsim/theory/shapefunction/#10-node-tetrahedra","title":"10-Node tetrahedra","text":"

The 10-node tetrahedra is also called bilinear tetrahedra element. The shape functions are:

\\[ u=u_{0}(2L_{0}-1)L_{0}+u_{1}(2L_{1}-1)L_{1}+u_{2}(2L_{2}-1)L_{2}+u_{3}(2L_{3}-1)L_{3}+4u_{4}L_{0}L_{1}+u_{5}L_{1}L_{2}+u_{6}L_{0}L_{2}+u_{7}L_{0}L_{3}+u_{8}L_{1}L_{3}+u_{9}L_{2}L_{3} \\] \\[ v=...\\text{(analogous to u)} \\] \\[ w=...\\text{(analogous to u)} \\]"},{"location":"welsim/theory/structures/","title":"Structures","text":"

This section describes the mathematical and numerical theories used in this finite element analysis program. In the stress analysis of solids, the infinitesimal deformation linear elasticity static analysis method is discussed by first. The geometric nonlinearity and elastoplasticity are introduced to describe the finite deformation in solids.

"},{"location":"welsim/theory/structures/#infinitesimal-deformation-linear-elasticity-static-analysis","title":"Infinitesimal deformation linear elasticity static analysis","text":"

The infinitesimal deformation theory is the essential formulation for the linear elasticity, which assumes the stress-strain constitutive relation is linear. The equilibrium equation of solid mechanics, boundary conditions are given by the following equation.

\\[ \\begin{align} \\label{eq:ch5_equilibrium_eqn1} \\nabla\\cdot\\mathbf{\\sigma}+\\mathbf{b}=0\\quad\\mathrm{in}V \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_equilibrium_eqn2} \\sigma\\cdot\\mathbf{n}=\\mathbf{t}\\quad\\mathrm{on}\\thinspace S_{t} \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_equilibrium_eqn3} \\mathbf{u}=\\mathbf{u}_{0}\\quad\\mathrm{on}\\thinspace S_{u} \\end{align} \\]

where \\(\\sigma\\) is the stress, \\(\\mathbf{t}\\) is the surface force, \\(\\mathbf{b}\\) is the body force, and S_{t} expresses the dynamic boundary and the \\(S_{u}\\) expresses the geometric boundary. The strain and displacement relation in the infinitesimal deformation is given

\\[ \\epsilon=\\nabla_{s}\\mathbf{u} \\]

The stress and strain constitutive relation in the linear elastic body is given

\\[ \\sigma=\\mathbf{C}\\colon\\epsilon \\]

where \\(\\mathbf{C}\\) is the fourth order elasticity tensor.

"},{"location":"welsim/theory/structures/#principle-of-virtual-work","title":"Principle of virtual work","text":"

The principle of the virtual work regarding the equilibrium equations \\(\\eqref{eq:ch5_equilibrium_eqn1}\\), \\(\\eqref{eq:ch5_equilibrium_eqn2}\\), and \\(\\eqref{eq:ch5_equilibrium_eqn3}\\) is

\\[ \\begin{align} \\label{eq:ch5_equilibrium_virtual1} \\int_{V}\\sigma\\colon\\delta\\epsilon dV=\\int_{S_{t}}\\mathbf{t}\\cdot\\delta\\mathbf{u}dS+\\int_{V}\\mathbf{b}\\cdot\\delta\\mathbf{u}dV \\end{align} \\] \\[ \\delta\\mathbf{u}=0\\quad\\mathrm{on}\\quad S_{u} \\]

which can be rewritten into

\\[ \\begin{align} \\label{eq:ch5_equilibrium_virtual2} \\int_{V}(\\mathbf{C}\\colon\\epsilon)\\colon\\delta\\epsilon dV=\\int_{S_{t}}\\mathbf{t}\\cdot\\delta\\mathbf{u}dS+\\int_{V}\\mathbf{b}\\cdot\\delta\\mathbf{u}dV \\end{align} \\]

where \\(\\epsilon\\) is the strain tensor, \\(\\sigma\\) is the stress tensor, and \\(\\mathbf{C}\\) is the fourth order elasticity tensor. The strain tensor \\(\\epsilon\\) and stress tensor \\(\\sigma\\) can be rewritten into vector forms \\(\\hat{\\epsilon}\\) and \\(\\hat{\\sigma}\\), respectively. Then we have

\\[ \\begin{align} \\label{eq:ch4_theory_stress_strain_relation} \\hat{\\sigma}=\\mathbf{D}\\hat{\\epsilon} \\end{align} \\]

where \\(\\mathbf{D}\\) is the elasticity matrix. Given the strain and stress in the vector form, we can rewrite the governing equation ([eq:ch5_equilibrium_virtual1]) into

\\[ \\begin{align} \\label{eq:ch5_equilibrium_virtual3} \\int_{V}\\hat{\\epsilon}^{T}\\mathbf{D}\\delta\\hat{\\epsilon}dV=\\int_{S_{t}}\\delta\\mathbf{u^{T}}\\mathbf{t}dS+\\int_{V}\\delta\\mathbf{u}^{T}\\mathbf{b}dV \\end{align} \\]

Equation ([eq:ch5_equilibrium_virtual3]) is the principles of the virtual work applied in this software program.

"},{"location":"welsim/theory/structures/#finite-element-formulation","title":"Finite element formulation","text":"

The principle governing equation ([eq:ch5_equilibrium_virtual3]) of the virtual work can be discreted for each finite element:

\\[ \\begin{align} \\label{eq:ch5_equilibrium_fe_form1} \\sum_{e}\\int_{V^{e}}\\hat{\\epsilon}^{T}\\mathbf{D}\\delta\\hat{\\epsilon}dV=\\sum_{e}\\int_{S_{t}^{e}}\\delta\\mathbf{u}^{T}\\mathbf{t}dS+\\sum_{e}\\int_{V^{e}}\\delta\\mathbf{u}^{T}\\mathbf{b}dV \\end{align} \\]

where the displacement field is interpolated for each element

\\[ \\begin{align} \\label{eq:ch5_equilibrium_fe_form2} \\mathbf{u}=\\sum_{i=1}^{m}N_{i}\\mathbf{u}_{i}=\\mathbf{NU} \\end{align} \\]

Similarly, the strain component can be expressed as

\\[ \\begin{align} \\label{eq:ch5_equilibrium_fe_form3} \\hat{\\epsilon}=\\mathbf{BU} \\end{align} \\]

Substituting equations \\(\\eqref{eq:ch5_equilibrium_fe_form2}\\) and \\(\\eqref{eq:ch5_equilibrium_fe_form3}\\) into \\(\\eqref{eq:ch5_equilibrium_fe_form1}\\), we have

\\[ \\begin{align} \\label{eq:ch5_equilibrium_fe_form4} \\sum_{e}\\delta\\mathbf{U}^{T}(\\int_{V^{e}}\\mathbf{B}^{T}\\mathbf{DB}dV)\\mathbf{U}=\\sum_{e}\\delta\\mathbf{U}^{T}\\cdot\\int_{S_{t}^{e}}\\mathbf{N}^{T}\\mathbf{t}dS+\\sum_{e}\\delta\\mathbf{U}^{T}\\int_{V^{e}}\\mathbf{N}^{T}\\mathbf{b}dV \\end{align} \\]

The equation above can be summarized as

\\[ \\begin{align} \\label{eq:ch5_equilibrium_fe_form5} \\delta\\mathbf{U}^{T}\\mathbf{KU}=\\delta\\mathbf{U}^{T}\\mathbf{F} \\end{align} \\]

where

\\[ \\begin{align} \\label{eq:ch5_equilibrium_fe_form6} \\mathbf{K}=\\sum_{e}\\int_{V^{e}}\\mathbf{B}^{T}\\mathbf{DB}dV \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_equilibrium_fe_form7} \\mathbf{F}=\\sum\\int_{S_{t}^{e}}\\mathbf{N}^{T}\\mathbf{t}dS+\\int_{V^{e}}\\mathbf{N}^{T}\\mathbf{b}dV \\end{align} \\]

The components of the matrix and vectors defined by equations \\(\\eqref{eq:ch5_equilibrium_fe_form6}\\) and \\(\\eqref{eq:ch5_equilibrium_fe_form7}\\) can be calculated for each finite element. For arbitrary virtual displacement \\(\\delta\\mathbf{U}\\), equation \\(\\eqref{eq:ch5_equilibrium_fe_form5}\\) can be rewritten into

\\[ \\mathbf{KU=F} \\]"},{"location":"welsim/theory/thermal/","title":"Thermal analysis","text":"

This section discuss the theories used in the WESLIM thermal analysis.

"},{"location":"welsim/theory/thermal/#governing-equations","title":"Governing equations","text":"

The governing equations applied in thermal analysis are:

\\[ \\begin{align} \\label{eq:ch5_thermal_gov} \\rho c\\frac{\\partial T}{\\partial t}=\\nabla\\cdot(k\\nabla T) \\end{align} \\]

where \\(\\rho=\\rho(x)\\) is mass density, \\(c=c(x,T)\\) is the specific heat, \\(T=T(x,t)\\) is the temperature, \\(K=k(x,T)\\) is the thermal conductivity, \\(Q=Q(x,T,t)\\) is the calorific value. \\(x\\) is the position in the modeling domain, \\(T\\) is the temperature and \\(t\\) is the time.

The modeling domain is represented by S, and the boundary is represented by \\(\\varGamma\\). When assuming the boundary conditions of either the Dirichlet or Neumann type, those boundary conditions can be mathematically expressed as

\\[ T=T_{1}(x,t) \\qquad X\\in\\Gamma_{1} \\] \\[ k\\frac{\\partial T}{\\partial n}=q(x,T,t) \\qquad X\\in\\Gamma_{2} \\]

where the term \\(T_{1}\\), \\(q\\) is already known. \\(q\\) is the heat flux outflow from the boundary. Three types of heat flux can be considered in WELSIM thermal module.

\\[ q=-q_{s}+q_{c}+q_{r} \\] \\[ q_{s}=q_{s}(x,t) \\] \\[ q_{c}=hc(T-T_{c}) \\] \\[ q_{r}=hc(T^{4}-T_{r}^{4}) \\]

where \\(q_{s}\\) is the distributed heat flux, \\(q_{c}\\) is the heat flux by the convective heat transfer, and \\(q_{r}\\) is the heat flux by the radiant heat transfer. The other quantities are

"},{"location":"welsim/theory/thermal/#derivation-of-heat-flow-matrices","title":"Derivation of heat flow matrices","text":"

When equation \\(\\eqref{eq:ch5_thermal_gov}\\) is discreted by the Galerkin approximation, it becomes as follows,

\\[ \\begin{align} \\label{eq:ch5_thermal_gov2} [\\mathbf{K}]\\{T\\}+[\\mathbf{M}]\\frac{\\partial T}{\\partial t}=\\{F\\} \\end{align} \\]

where the matrices and vectors are

\\[ \\begin{array}{ccc} [\\mathbf{K}] & = & \\int(k_{xx}\\dfrac{\\partial\\{N\\}^{T}}{\\partial x}\\dfrac{\\partial\\{N\\}}{\\partial x}+k_{yy}\\dfrac{\\partial\\{N\\}^{T}}{\\partial y}\\dfrac{\\partial\\{N\\}}{\\partial y}+k_{zz}\\dfrac{\\partial\\{N\\}^{T}}{\\partial z}\\dfrac{\\partial\\{N\\}}{\\partial z})dV\\\\ & + & \\int h_{c}\\{N\\}^{T}\\{N\\}ds+\\int h_{r}\\{N\\}^{T}\\{N\\}ds \\end{array} \\] \\[ [\\mathbf{M}]=\\int\\rho c\\{N\\}^{T}\\{N\\}dV \\] \\[ \\{F\\}=\\int Q\\{N\\}^{T}dV-\\int q_{s}\\{N\\}^{T}dS+\\int h_{c}T_{c}\\{N\\}^{T}dS+\\int h_{r}T_{r}(T+T_{r})(T^{2}+T_{r}^{2})\\{N\\}^{T}dS \\]

where shape function

\\[ \\{N\\}=(N^{1},N^{2},.......),\\thinspace N_{i}=N_{i}(x) \\]

Equation \\(\\eqref{eq:ch5_thermal_gov2}\\) is nonlinear and unsteady. When the time is discretized by the backward Euler's rule and the temperature at time t=t_{0} is known, the temperature at t=t_{0+\\triangle t} is calculated using the following equation.

\\[ \\begin{align} \\label{eq:ch5_thermal_gov_disc1} [\\mathbf{K}]_{t=t_{0+\\triangle t}}\\{T\\}_{t=t_{0+\\triangle t}}+[\\mathbf{M}]_{t=t_{0+\\triangle t}}\\dfrac{\\{T\\}_{t=t_{0+\\triangle t}}-\\{T\\}_{t=t_{0}}}{\\triangle t}=\\{F\\}_{t=t_{0+\\triangle t}} \\end{align} \\]

The temperature vector can be expressed as

\\[ \\begin{align} \\label{eq:ch5_thermal_gov_disc2} \\{T\\}_{t=t_{0}+\\triangle t}=\\{T\\}_{t=t_{0}+\\triangle t}^{(i)}+\\{\\triangle T\\}_{t=t_{0}+\\triangle t}^{(i)} \\end{align} \\]

The product of the heat conduction matrix and temperature vector, mass matrix and etc. are expressed in approximation as in the following equation.

\\[ \\begin{align} \\label{eq:ch5_thermal_gov_disc3} [\\mathbf{K}]_{t=t_{0+\\triangle t}}\\{T\\}_{t=t_{0+\\triangle t}}\\cong[\\mathbf{K}]_{t=t_{0+\\triangle t}}^{(i)}\\{T\\}_{t=t_{0+\\triangle t}}^{(i)}+\\dfrac{\\partial[\\mathbf{K}]_{t=t_{0+\\triangle t}}^{(i)}\\{T\\}_{t=t_{0+\\triangle t}}^{(i)}}{\\partial\\{T\\}_{t=t_{0+\\triangle t}}^{(i)}}\\{\\triangle T\\}_{t=t_{0+\\triangle t}}^{(i)} \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_thermal_gov_disc4} [M]_{t=t_{0+\\triangle t}}\\cong[M]_{t=t_{0}+\\triangle t}^{(i)}+\\dfrac{\\partial[M]_{t=t_{0}+\\triangle t}^{(i)}}{\\partial\\{T\\}_{t=t_{0+\\triangle t}}^{\\{i\\}}}\\{\\triangle T\\}_{t=t_{0+\\triangle t}}^{(i)} \\end{align} \\]

Substituting equations \\(\\eqref{eq:ch5_thermal_gov_disc2}\\), \\(\\eqref{eq:ch5_thermal_gov_disc3}\\), and \\(\\eqref{eq:ch5_thermal_gov_disc4}\\) into equation \\(\\eqref{eq:ch5_thermal_gov_disc1}\\) and skipping the high order polynomial terms, we have

\\[ (\\dfrac{[\\mathbf{M}]_{t=t_{0+\\triangle t}}^{(i)}}{\\triangle t}+\\dfrac{\\partial[\\mathbf{M}]_{t=t_{0+\\triangle t}}^{(i)}\\{T\\}_{t=t_{0}+\\text{\\triangle t}}^{(i)}}{\\partial\\{T\\}_{t=t_{0}+\\triangle t}^{(i)}}\\dfrac{\\{T\\}_{t=t_{0}+\\triangle t}^{(i)}-\\{T\\}_{t=t0}}{\\triangle t}+\\dfrac{\\partial[\\mathbf{K}]_{t=t_{0}+\\triangle t}^{(i)}\\{T\\}_{t=t_{0}+\\triangle t}^{(i)}}{\\partial\\{T\\}_{t=t_{0}+\\triangle t}^{(i)}})\\{\\triangle T\\}_{t=t_{0}+\\triangle t}^{(i)}\\\\=\\{F\\}_{t=t_{0}+\\triangle t}-[\\mathbf{M}]_{t=t_{0}+\\triangle t}^{(i)}\\dfrac{\\{T\\}_{t=t_{0}+\\triangle t}^{(i)}-\\{T\\}_{t=t_{0}}}{\\triangle t}-[\\mathbf{K}]_{t=t_{0}+\\triangle t}^{(i)}\\{T\\}_{t=t_{0}+\\triangle t}^{(i)} \\]

Furthermore, an approximation evaluation for the left hand side factor is given below,

\\[ [\\mathbf{K}^{*}]^{(i)}=\\dfrac{[M]_{t=t_{0}+\\triangle t}^{(i)}}{\\triangle t}+\\dfrac{\\partial[\\mathbf{K}]_{t=t_{0}+\\triangle t}^{(t)}}{\\partial\\{T\\}_{t=t_{0}+\\triangle t}^{(i)}}\\{T\\}_{t=t_{0}+\\triangle t}^{(i)}=\\dfrac{[M]_{t=t_{0}+\\triangle t}^{(i)}}{\\triangle t}+[\\mathbf{K}_{T}]_{t=t_{0}+\\triangle t}^{(i)} \\]

where \\([\\mathbf{K}_{T}]_{t=t_{0}+\\triangle t}^{(i)}\\) tangent stiffness matrix.

Eventually, the temperature at time \\(t=t_{0}+\\triangle t\\) can be calculated by iterative solver using the following scheme:

\\[ \\begin{array}{cc} [\\mathbf{K}^{*}]^{(i)}\\{T\\}_{t=t_{0}+\\triangle t}^{(i)}=\\{F\\}_{t=t_{0}+\\triangle t}-[\\mathbf{M}]_{t=t_{0}+\\triangle t}^{(i)}\\dfrac{\\{T\\}_{t=t_{0}+\\triangle t}^{(i)}-\\{T\\}_{t=t_{0}}}{\\triangle t}-[\\mathbf{K}]_{t=t_{0}+\\triangle t}^{(i)}\\\\ \\{T\\}_{t=t_{0}+\\triangle t}^{(i+1)}=\\{T\\}_{t=t_{0}+\\triangle t}^{(i)}+\\{\\triangle T\\}_{t=t_{0}+\\triangle t}^{(i)} \\end{array} \\]

For the steady state analysis, the iteration algorithm is given below

\\[ \\begin{array}{cc} [\\mathbf{K}_{T}]^{(i)}\\{\\triangle T\\}_{t=\\infty}^{(i)}=\\{F\\}_{t=\\infty}-[\\mathbf{K}_{T}]^{(i)}\\{\\triangle T\\}_{t=\\infty}^{(i)}\\\\ \\{T\\}_{t=\\infty}^{(i+1)}=\\{T\\}_{t=\\infty}^{(i)}+\\{\\triangle T\\}_{t=\\infty}^{(i)} \\end{array} \\]

Since the implicit time solver is applied in the program, the selection of incremental time \\(\\triangle t\\) is relatively flexible. However, if the magnitude of \\(\\triangle t\\) is too large, the convergence frequency will be decreased in the iterative computation. The program contains automatic incremental functions to monitor the size of the residual vectors during the iterations. As the convergence rate becomes slow, the incremental time \\(\\triangle t\\) is automatically reduced. When the convergence rate becomes high, the program increases the incremental time \\(\\triangle t\\). Doing this automatic scheme can improve the numerical performance and saving computational time.

"},{"location":"welsim/theory/transient/","title":"Structures with transient analysis","text":"

The time integration method applied in structural transient analysis is described in the section.

"},{"location":"welsim/theory/transient/#formulation-of-implicit-method","title":"Formulation of implicit method","text":"

In the direct time integration, the equation of motion can be expressed as follows

\\[ \\begin{align} \\label{eq:ch5_time_solver_imp1} \\mathbf{M}(t+\\triangle t)\\ddot{\\mathbf{U}}(t+\\triangle t)+\\mathbf{C}(t+\\triangle t)\\dot{\\mathbf{U}}(t+\\triangle t)+\\mathbf{Q}(t+\\triangle t)=\\mathbf{F}(t+\\triangle t) \\end{align} \\]

where \\(\\mathbf{M}\\) and \\(\\mathbf{C}\\) is the mass matrix and damping matrix, respectively. The \\(\\mathbf{Q}\\) and \\(\\mathbf{F}\\) are the internal force vector, and external force vector, respectively. Note that, the mass density is consistent in the structural analysis, thus the mass matrix keep constants regardless of the deformation in non-linearity.

In the Newmark-\\(\\beta\\) method, the displacement, velocity, and acceleration at the each time incremental \\(\\triangle t\\) are

\\[ \\begin{align} \\label{eq:ch5_time_solver_imp2} \\dot{\\mathbf{U}}(t+\\triangle t)=\\dfrac{\\gamma}{\\beta\\triangle t}\\triangle\\mathbf{U}(t+\\triangle t)-\\dfrac{\\gamma-\\beta}{\\beta}\\dot{\\mathbf{U}}(t)-\\triangle t\\dfrac{\\gamma-2\\beta}{2\\beta}\\ddot{\\mathbf{U}}(t) \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_time_solver_imp3} \\ddot{\\mathbf{U}}(t+\\triangle t)=\\dfrac{\\text{1}}{\\beta\\triangle t^{2}}\\triangle\\mathbf{U}(t+\\triangle t)-\\dfrac{1}{\\beta\\triangle t}\\dot{\\mathbf{U}}(t)-\\dfrac{1-2\\beta}{2\\beta}\\ddot{\\mathbf{U}}(t) \\end{align} \\]

where \\(\\gamma\\) and \\(\\beta\\) are time solver parameters. Given the specific values, the numerical algorithm becomes linear acceleration method, or the trapezoid rule.

\\[ \\gamma=\\frac{1}{2},\\thinspace\\beta=\\frac{1}{6},\\quad\\mathrm{Linear}\\thinspace\\mathrm{acceleration\\thinspace\\mathrm{method}} \\] \\[ \\gamma=\\frac{1}{2},\\thinspace\\beta=\\frac{1}{4},\\quad\\mathrm{Trapezoid}\\thinspace\\mathrm{rule} \\]

substituting equations \\(\\eqref{eq:ch5_time_solver_imp2}\\) and \\(\\eqref{eq:ch5_time_solver_imp3}\\) into equation \\(\\eqref{eq:ch5_time_solver_imp1}\\), the following equation can be acquired

\\[ \\begin{array}{ccc} (\\dfrac{1}{\\beta\\triangle t^{2}}\\mathbf{M}+\\dfrac{\\gamma}{\\beta\\triangle t}\\mathbf{C}+\\mathbf{K})\\triangle\\mathbf{U}(t+\\triangle t) & = & \\mathbf{F}(t+\\triangle t)-\\mathbf{Q}(t+\\triangle t)\\\\ & + & \\dfrac{1}{\\beta\\triangle t}\\mathbf{\\mathbf{M}\\dot{\\mathbf{U}}}(t)+\\dfrac{1-2\\beta}{2\\beta}\\mathbf{M}\\ddot{\\mathbf{U}}(t)+\\dfrac{\\gamma-\\beta}{\\beta}\\mathbf{C}\\dot{\\mathbf{U}}(t)\\\\ & + & \\triangle t\\dfrac{\\gamma-2\\beta}{2\\beta}\\mathbf{C}\\ddot{\\mathbf{U}}(t) \\end{array} \\]

when we use linear stiffness matrix \\(\\mathbf{K}_{L}\\) for a linear problem, the equation above becomes \\(\\mathbf{Q}(t+\\triangle t)=\\mathbf{K}_{L}\\mathbf{U}(t+\\triangle t)\\). Substituting this term into the equation (), we have

\\[ \\begin{array}{ccc} \\{\\mathbf{M}(-\\dfrac{1}{(\\triangle t)^{2}\\beta}\\mathbf{U}(t)-\\dfrac{1}{(\\triangle t)\\beta}\\dot{\\mathbf{U}}(t)-\\dfrac{1-2\\beta}{2\\beta}\\ddot{\\mathbf{U}}(t))\\\\ +\\mathbf{C}(-\\dfrac{\\gamma}{(\\triangle t)\\beta}\\mathbf{U}(t)+(1-\\dfrac{\\gamma}{\\beta})\\dot{\\mathbf{U}}(t)+\\triangle t\\dfrac{2\\beta-\\gamma}{2\\beta}\\ddot{\\mathbf{U}}(t))\\}\\\\ +\\{\\dfrac{1}{(\\triangle t)^{2}\\beta}\\mathbf{M}+\\dfrac{\\gamma}{(\\triangle t)\\beta}\\mathbf{C}+\\mathbf{K}_{L}\\}\\mathbf{U}(t+\\triangle t) & = & \\mathbf{F}(t+\\triangle t) \\end{array} \\]

In the analysis practice, the acceleration and velocity boundary conditions are imposed. Then the displacement of the following equation can be derived from equation \\(\\eqref{eq:ch5_time_solver_imp1}\\).

\\[ u_{is}(t+\\triangle t)=u_{is}(t)+\\triangle t\\dot{u}_{is}(t)+(\\triangle t)^{2}(\\frac{1}{2}-\\beta)\\ddot{u}_{is}(t+\\triangle t) \\]

where \\(u_{is}(t+\\triangle t)\\) is the nodal displacement at time \\(t+\\triangle t\\), \\(\\dot{u}{}_{is}(t+\\triangle t)\\) is the nodal velocity, \\(\\ddot{u}{}_{is}(t+\\triangle t)\\) is the nodal acceleration, i is the degree of freedom per node, s is the node number.

The mass and damping terms are treated as follows

  1. The lumped mass matrix is used at most of cases in this program.
  2. The damping matrix is treated using Rayleigh algorithm \\(\\mathbf{C}=R_{m}\\mathbf{M}+R_{k}\\mathbf{K}_{L}\\).
"},{"location":"welsim/theory/transient/#formulation-of-explicit-method","title":"Formulation of explicit method","text":"

This section discuss how the explicit time solver is formulation to solve the governing equation below

\\[ \\begin{align} \\label{eq:ch5_time_solver_exp1} \\mathbf{M}\\ddot{\\mathbf{U}}(t)+\\mathbf{C}\\text{(t)}\\dot{\\mathbf{U}(t)+\\mathbf{Q}(t)=\\mathbf{F}(t)} \\end{align} \\]

where the displacement at the time \\(t+\\triangle t\\) and \\(t-\\triangle t\\) can be expressed by the Taylor's expansion at time t with the second order truncation.

\\[ \\begin{align} \\label{eq:ch5_time_solver_exp2} \\mathbf{U}(t+\\triangle t)=\\mathbf{U}(t)+\\dot{\\mathbf{U}}(t)(\\triangle t)+\\dfrac{1}{2!}\\ddot{\\mathbf{U}}(t)(\\triangle t)^{2} \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_time_solver_exp3} \\mathbf{U}(t-\\triangle t)=\\mathbf{U}(t)-\\dot{\\mathbf{U}}(t)(\\triangle t)+\\dfrac{1}{2!}\\ddot{\\mathbf{U}}(t)(\\triangle t)^{2} \\end{align} \\]

Differentiating equations \\(\\eqref{eq:ch5_time_solver_exp2}\\) and \\(\\eqref{eq:ch5_time_solver_exp3}\\), we have

\\[ \\begin{align} \\label{eq:ch5_time_solver_exp4} \\dot{\\mathbf{U}}(t)=\\dfrac{1}{2\\triangle t}(\\mathbf{U}(t+\\triangle t)-\\mathbf{U}(t-\\triangle t)) \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_time_solver_exp5} \\ddot{\\mathbf{U}}(t)=\\dfrac{1}{(\\triangle t)^{2}}(\\mathbf{U}(t+\\triangle t)-2\\mathbf{U}(t)+\\mathbf{U}(t-\\triangle t)) \\end{align} \\]

Substituting equations \\(\\eqref{eq:ch5_time_solver_exp4}\\) and \\(\\eqref{eq:ch5_time_solver_exp5}\\) into \\(\\eqref{eq:ch5_time_solver_exp1}\\), we have

\\[ (\\dfrac{1}{\\triangle t^{2}}\\mathbf{M}+\\dfrac{1}{2\\triangle t}\\mathbf{C})\\mathbf{U}(t+\\triangle t)=\\mathbf{F}(t)-\\mathbf{Q}(t)-\\dfrac{1}{\\triangle t^{2}}\\mathbf{M}[2\\mathbf{U}(t)-\\mathbf{U}(t-\\triangle t)]-\\dfrac{1}{2\\triangle t}\\mathbf{CU}(t-\\triangle t) \\]

For the linear problem, we also have condition \\(\\mathbf{Q}(t)=\\mathbf{K}_{L}\\mathbf{U}(t)\\) for equation. Finally, the displacement at \\(t+\\triangle t\\) is:

\\[ \\mathbf{U}(t+\\triangle t)=\\dfrac{1}{(\\frac{1}{\\triangle t^{2}}\\mathbf{M}+\\frac{1}{2\\triangle t}\\mathbf{C})}\\{\\mathbf{F}(t)-\\mathbf{Q}(t)-\\dfrac{1}{\\triangle t^{2}}\\mathbf{M}[2\\mathbf{U}(t)-\\mathbf{U}(t-\\triangle t)]-\\dfrac{1}{2\\triangle t}\\mathbf{C}(t-\\triangle t)\\mathbf{U}\\} \\]"},{"location":"welsim/users/analysistypes/","title":"Physics and analysis types","text":"

WELSIM supports several types of finite element analyses. This section describes those analysis types that you can perform in the WELSIM user interface.

"},{"location":"welsim/users/analysistypes/#static-structural-analysis","title":"Static structural analysis","text":"

As one of the most widely used analysis types, a static structural analysis discloses the structural displacements, stresses, strains, and forces caused by loads or other mechanical effects. In this static analysis, the constant loading and response are assumed.

The static structural analysis can be either linear or nonlinear. The non-linearity can be introduced by the large deformations, in-elasticity, contact, hyperelasticity, etc. For the nonlinear problem, it is recommended to set multiple substeps in the Study Settings.

"},{"location":"welsim/users/analysistypes/#conducting-a-static-structural-analysis","title":"Conducting a static structural analysis","text":"

The following lists the general and specifics steps in conducting static structural analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Structural and Analysis Type to Static. Since the static structural analysis is the default analysis type, you do not need to change these properties if the analysis is newly created. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, the default setting is Solid. You need to change this property value accordingly if the geometry is Shell or other types. See Defining Part Behaviors for details.

  5. Setting bonnections: Optional. Contacts are supported in a static structural analysis. See Setting Connections for details.

  6. Applying mesh: It is recommended to generate Tet10 elements for Solid analysis and the Tri6 element for the Shell analysis. See Applying Mesh for details.

  7. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analyses such as nonlinear models, the analysis controls you can tune: Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  8. Setting up boundary conditions: For a static structural analysis, the applicable boundary conditions are Fixed Supported, Fixed Rotation, Displacement, Force, and Pressure. The following body conditions are supported: Body Force, Acceleration, Earth Gravity, and Rotational Velocity. See Setting up Boundary Conditions for details.

  9. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  10. Evaluating results: For a static structural analysis, the applicable results are Deformations, Stresses, Strains, Rotations, Reaction Forces, and Reaction Moments. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

"},{"location":"welsim/users/analysistypes/#transient-structural-analysis","title":"Transient structural analysis","text":"

In the transient structural analysis, the dynamic response is updated and is a function of time. You can impose general time-dependent boundary conditions on the model and obtain the time-varying responded to these transient loads or constraints. The inertia or damping effects play important roles in this analysis type, if the inertia and damping effects are minimal, you could use the static analysis instead.

The transient structural analysis can be either linear or nonlinear. The non-linearity can be introduced by the large deformations, inelasticity, contact, hyperelasticity, etc. For the nonlinear problem, it is recommended to set multiple substeps for each load step in the Study Settings.

"},{"location":"welsim/users/analysistypes/#conducting-a-transient-structural-analysis","title":"Conducting a transient structural analysis","text":"

The following lists the general and specifics steps in conducting transient structural analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Structural and Analysis Type to Transient. You can choose either Implicit or Explicit time integration solver. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. You need to change this property value accordingly if the geometry is Shell or other types. See Defining Part Behaviors for details.

  5. Setting connections: Optional. Contacts are supported in a transient structural analysis. See Setting Connections for details.

  6. Applying mesh: It is recommended to generate Tet10 elements for Solid analysis and the Tri6 element for the Shell analysis. See Applying Mesh for details.

  7. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analyses such as nonlinear models, the analysis controls you can tune are Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  8. Defining initial conditions: Optional. In the transient structural analysis, you can define the initial status of boundary and body conditions. The Initial Status property provides two options: None and Equal to Step 1. The default option None set the initial value to zero, the option Equal to Step 1 set the initial value to that of step 1. See Defining Initial Conditions for details.

  9. Setting up boundary conditions: For the transient structural analysis, the applicable boundary conditions are Fixed Supported, Fixed Rotation, Displacement, Force, Pressure, Velocity, and Acceleration. The following body conditions are supported: Body Force, Acceleration, Earth Gravity, and Rotational Velocity. See Setting up Boundary Conditions for details.

  10. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  11. Evaluating results: For the transient structural analysis, the applicable results are: Deformations, Stresses, Strains, Rotations, Reaction Forces, Reaction Moments, Velocity, and Acceleration. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

"},{"location":"welsim/users/analysistypes/#modal-analysis","title":"Modal analysis","text":"

The modal analysis investigates the vibration characteristics of a structure or component. You can obtain the natural frequencies and mode shapes, which serve as a starting pointing for dynamic analysis of the target structure.

"},{"location":"welsim/users/analysistypes/#conducting-a-modal-structural-analysis","title":"Conducting a modal structural analysis","text":"

The following lists the general and specifics steps in conducting modal structural analysis:

  1. Creating analysis environment: From the properties view of FEM Project object, set the Physics Type to Structural and Analysis Type to Modal. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. However, the nonlinearity in the modal analysis is ignored due to the characteristics of eigen solver algorithms. You must define the sufficient properties that are required in the solving process. For example, the mass density parameter must be defined. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. You need to change this property value accordingly if the geometry is Shell or other types. See Defining Part Behaviors for details.

  5. Setting connections: Optional. The Bonded Contacts are supported in a modal structural analysis. See Setting Connections for details.

  6. Applying mesh: It is recommended to generate the Tet10 elements for Solid analysis and the Tri6 element for the Shell analysis. See Applying Mesh for details.

  7. Configuring study settings: You typically do not need to change these settings for simple modal analyses. The default number of modes is 6, increasing this value yields to calculate more natural frequency modes, while it requires more computational resources. See Configuring Study Settings for details.

  8. Setting up boundary conditions: For the modal structural analysis, the applicable boundary conditions are Fixed Supported, Fixed Rotation, zero Displacement. The following body conditions are supported: Body Force, Acceleration, Earth Gravity, and Rotational Velocity. Note that only constraint-type boundaries are applicable in modal analysis. See Setting up Boundary Conditions for details.

  9. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  10. Evaluating results: For the modal structural analysis, the applicable results are Deformations, and Frequencies. Note that deformation results here are just relative quantities intended to show the shape modes. The Tabular Data and Chart windows display the frequencies and related mode numbers. See Evaluating Results for details.

"},{"location":"welsim/users/analysistypes/#steady-state-thermal-analysis","title":"Steady-state thermal analysis","text":"

In the steady-state thermal analysis, you can determine the temperatures in objects that are impacted by the time-invariant thermal loads. Users are recommended to perform a steady-state analysis before conducting a transient study in a complex model.

The static thermal analysis can be either linear or nonlinear. The nonlinearity can be introduced by the temperature-depend material properties, or radiation and convection coefficient. For the nonlinear problem, it is recommended to set multiple substeps in the Study Settings.

"},{"location":"welsim/users/analysistypes/#conducting-a-static-structural-analysis_1","title":"Conducting a static structural analysis","text":"

The following lists the general and specifics steps in conducting static structural analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Thermal and Analysis Type to Static. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. You need to change this property value accordingly if the geometry is Shell or other types. See Defining Part Behaviors for details.

  5. Setting connections: Optional. The steady-state thermal analysis supports the Bonded Contact. See Setting Connections for details.

  6. Applying mesh: It is recommended to generate the Tet10 elements for Solid analysis, and the Tri6 element for the Shell analysis. See Applying Mesh for details.

  7. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analysis such as nonlinear models, the analysis controls you can tune are Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  8. Setting up boundary conditions: In the steady-state thermal analysis, the applicable boundary conditions are: Temperature, Heat Flux, Convection, and Radiation. See Setting up Boundary Conditions for details.

  9. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  10. Evaluating results: In steady-state thermal analysis, the applicable results are Temperature. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

"},{"location":"welsim/users/analysistypes/#transient-thermal-analysis","title":"Transient thermal analysis","text":"

In the transient thermal analysis, you can obtain the temperatures of objects that vary over time. Many heat transfer applications such as coiling or quenching problems, and so on involve transient thermal analysis. The transient thermal analysis can be either linear or nonlinear. The nonlinearity can be introduced by the temperature-dependent material properties or convection and radiation boundary conditions. For the nonlinear problem, it is recommended to define multiple substeps for each load step in the Study Settings.

"},{"location":"welsim/users/analysistypes/#conducting-a-transient-thermal-analysis","title":"Conducting a transient thermal analysis","text":"

The following lists the general and specifics steps in conducting transient thermal analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Thermal and Analysis Type to Transient. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. You need to change this property value accordingly if the geometry is Shell or other types. See Defining Part Behaviors for details.

  5. Setting connections: Optional. In the transient thermal analysis, the Bonded Contact is supported. See Setting Connections for details.

  6. Applying mesh: It is recommended to generate the Tet10 elements for Solid analysis and the Tri6 element for the Shell analysis. See Applying Mesh for details.

  7. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analysis such as nonlinear models, the analysis controls you can tune are Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  8. Setting up boundary conditions: In the transient thermal analysis, the applicable boundary conditions are: Temperature, Heat Flux, Convection, and Radiation. See Setting up Boundary Conditions for details.

  9. Defining initial conditions: You can define the global initial temperature condition for the analysis. In the transient thermal analysis, you can define the initial status of boundary and body conditions. The Initial Status property provides two options: None and Equal to Step 1. The default option None set the initial value to zero, the option Equal to Step 1 set the initial value to that of step 1. See Defining Initial Conditions for details.

  10. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  11. Evaluating results: In the transient thermal analysis, the applicable results are Temperature. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

"},{"location":"welsim/users/analysistypes/#electrostatic-analysis","title":"ElectroStatic Analysis","text":"

The electrostatic analysis can be applied to determine the distribution of electric potential in a conducting body under voltage or current conditions. You can obtain the solution results such as voltage, electric field, etc. The electrostatic analysis supports the single body analysis.

An electrostatic analysis could be either linear or nonlinear. The electric field dependent material properties can introduce the nonlinearity. For the nonlinear problem, it is recommended to set multiple substeps in the Study Settings.

"},{"location":"welsim/users/analysistypes/#conducting-an-electrostatic-analysis","title":"Conducting an electrostatic analysis","text":"

The following lists the general and specifics steps in conducting electrostatic analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Electromagnetic and Analysis Type to ElectroStatic. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. An electrostatic analysis only supports the Solid geometry type. See Defining Part Behaviors for details.

  5. Applying mesh: It is recommended to generate Tet10 elements for Solid analysis. See Applying Mesh for details.

  6. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analysis such as nonlinear models, the analysis controls you can tune are Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  7. Setting up boundary conditions: In the electrostatic analysis, the applicable boundary conditions are Ground, Voltage, Symmetry, Zero Charge, Surface Charge Density, and Electric Displacement. See Setting up Boundary Conditions for details.

  8. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  9. Evaluating results: In the electrostatic analysis, the applicable results are Voltage, Electric Field, Electric Displacement, and Energy Density. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

"},{"location":"welsim/users/analysistypes/#magnetostatic-analysis","title":"MagnetoStatic analysis","text":"

The magnetostatic analysis determines the magnetic field in and around a magnetic body.

A magnetostatic analysis requires the medium such as air surrounding the geometry be included as part of the entire simulation domain. In many cases, the full model can be reduced to the symmetric model by applying a symmetric boundary condition on the symmetric surface.

"},{"location":"welsim/users/analysistypes/#conducting-a-magnetostatic-analysis","title":"Conducting a magnetostatic analysis","text":"

The following lists the general and specifics steps in conducting magnetostatic analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Electromagnetic and Analysis Type to MagnetoStatic. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. A magnetostatic analysis only supports the Solid geometry type. See Defining Part Behaviors for details.

  5. Applying mesh: It is recommended to generate the Tet10 elements for magnetostatic analysis. See Applying Mesh for details.

  6. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analysis such as nonlinear models, the analysis controls you can tune are Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  7. Setting up boundary conditions: In the magnetostatic analysis, the applicable boundary conditions are Insulating, Symmetry, Magnetic Potential, and Magnetic Flux Density. See Setting up Boundary Conditions for details.

  8. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  9. Evaluating results: In the magnetostatic analysis, the applicable results are Magnetic Potential, Magnetic Field, Magnetic Induction Field, and Energy Density. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

The following describes the widget components in the material editor interface:

"},{"location":"welsim/users/analysistypes/#library-outline-tab","title":"Library outline tab","text":"

The Library Outline Tab shows an outline of the contents of the selectable material sources. You can directly load a material data from this pre-defined source by one of the methods below:

"},{"location":"welsim/users/bcs/","title":"Setting up boundary conditions","text":"

Boundary or Body conditions are essential conditions for the most analyses. A boundary condition is imposed on the boundary of the geometry. For example, a displacement condition imposed on the face of the 3D solid geometry. A body condition is imposed on the entire body. For example, the rotational velocity imposed on the body.

Each analysis type has its boundary and body conditions. These boundary and body conditions will be described separately regarding structural, thermal, and electromagnetic analyses.

Note

The boundary condition here includes both boundary and body conditions.

"},{"location":"welsim/users/bcs/#add-boundary-condition","title":"Add boundary condition","text":"

Adding boundary and body conditions in WELSIM application is straightforward. The following describes the adding method and its behaviors.

"},{"location":"welsim/users/bcs/#scoping-method","title":"Scoping method","text":"

The scoping method supports the geometry selection, and you can select the target geometry entities and set to the properties. A voltage boundary condition scoping is illustrated in Figure\u00a0below. You can select multiple geometry entities such as bodies, faces, edges, or vertices to a Geometry property, but all these entities must be the same type.

"},{"location":"welsim/users/bcs/#tips-in-geometry-selection","title":"Tips in geometry selection","text":"

The following describes the tips in selecting geometries for boundary and body conditions:

"},{"location":"welsim/users/bcs/#types-of-boundary-conditions","title":"Types of boundary conditions","text":"

This section describes the boundary conditions that are provided in the WELSIM application.

"},{"location":"welsim/users/bcs/#displacement","title":"Displacement","text":"

Displacement determines the spatial motion of one or more faces, edges, or vertices for their original location. This boundary condition is available for all structural analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application","title":"Boundary condition application","text":"

To apply Displacement:

  1. On the menu or toolbar of the Structural, click Displacement button. Or, right-click the Study object in the tree and select Impose Conditions > Displacement.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Displacement components on X, Y, and Z directions.
"},{"location":"welsim/users/bcs/#properties-view","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#displacement-example","title":"Displacement example","text":"

Displacement boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#fixed-support","title":"Fixed support","text":"

Fixed Support is a special case of Displacement boundary condition. It essentially sets the displacement to zero at the scoped geometries. This boundary condition is available for all structural analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_1","title":"Boundary condition application","text":"

To apply the Fixed Support:

  1. On the menu or toolbar of the Structural, click Fixed Support button. Or, right-click the Study object in the tree and select Impose Conditions > Fixed Support.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Determine the constraint status on X, Y, and Z directions.
"},{"location":"welsim/users/bcs/#properties-view_1","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#fixed-support-example","title":"Fixed support example","text":"

Fixed support boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#fixed-rotation","title":"Fixed rotation","text":"

Fixed Rotation constrains the rotation of the scoped geometry entities. This boundary condition is only available for Shell structural analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_2","title":"Boundary condition application","text":"

To apply Fixed Rotation: 1. On the menu or toolbar of the Structural, click Fixed Rotation button. Or, right-click the Study object in the tree and select Impose Conditions > Fixed Rotation. 2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window. 3. Determine the constraint status on X, Y, and Z directions.

"},{"location":"welsim/users/bcs/#properties-view_2","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#fixed-rotation-example","title":"Fixed Rotation example","text":"

Fixed Rotation boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#pressure","title":"Pressure","text":"

A pressure boundary condition imposes a constant normal pressure to one or more surfaces. A positive pressure acts into the surface, which compresses the scoped body. Similarly, a negative pressure pulling away from the scoped surface. This boundary condition is available for all structural analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_3","title":"Boundary condition application","text":"

To apply Pressure:

  1. On the menu or toolbar of the Structural, click Pressure button. Or, right-click the Study object in the tree and select Impose Conditions > Pressure.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Input the magnitude of normal pressure. A positive pressure acts into the surface, and a negative pressure pulls away from the surface.
"},{"location":"welsim/users/bcs/#properties-view_3","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#pressure-example","title":"Pressure example","text":"

Pressure boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#force","title":"Force","text":"

A force boundary condition imposes a constant force to one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for all structural analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_4","title":"Boundary condition application","text":"

To apply Force:

  1. On the menu or toolbar of the Structural, click Force button. Or, right-click the Study object in the tree and select Impose Conditions>Force.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Force components on X, Y, and Z directions.
"},{"location":"welsim/users/bcs/#properties-view_4","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#force-example","title":"Force example","text":"

Force boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#velocity","title":"Velocity","text":"

A velocity boundary condition imposes a constant velocity to one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for transient structural analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_5","title":"Boundary condition application","text":"

To apply Velocity:

  1. On the menu or toolbar of the Structural, click Velocity button. Or, right-click the Study object in the tree and select Impose Conditions > Velocity.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Velocity components on X, Y, and Z directions.
"},{"location":"welsim/users/bcs/#properties-view_5","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#velocity-example","title":"Velocity example","text":"

Velocity boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#acceleration","title":"Acceleration","text":"

An acceleration boundary condition imposes a constant acceleration to one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for transient structural analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_6","title":"Boundary condition application","text":"

To apply Acceleration:

  1. On the menu or toolbar of the Structural, click Acceleration button. Or, right-click the Study object in the tree and select Impose Conditions>Acceleration.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Acceleration components on X, Y, and Z directions.
"},{"location":"welsim/users/bcs/#properties-view_6","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#acceleration-example","title":"Acceleration example","text":"

Acceleration boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#temperature","title":"Temperature","text":"

A temperature boundary condition imposes a constant temperature to one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for all thermal analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_7","title":"Boundary condition application","text":"

To apply Temperature:

  1. On the menu or toolbar of the Thermal, click Temperature button. Or, right-click the Study object in the tree and select Impose Conditions>Temperature.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Temperature scalar value.
"},{"location":"welsim/users/bcs/#properties-view_7","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#temperature-example","title":"Temperature example","text":"

Temperature boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#heat-flux","title":"Heat flux","text":"

A Heat Flux boundary condition imposes a constant flux to one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for all thermal analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_8","title":"Boundary condition application","text":"

To apply Heat Flux:

  1. On the menu or toolbar of the Thermal, click Heat Flux button. Or, right-click the Study object in the tree and select Impose Conditions>Heat Flux.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Heat Flux scalar value.
"},{"location":"welsim/users/bcs/#properties-view_8","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#heat-flux-example","title":"Heat flux example","text":"

Heat Flux boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#heat-convection","title":"Heat convection","text":"

A heat convection boundary condition imposes a constant convection onto one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for all thermal analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_9","title":"Boundary condition application","text":"

To apply Heat Convection:

  1. On the menu or toolbar of the Thermal, click Heat Convection button. Or, right-click the Study object in the tree and select Impose Conditions > Heat Convection.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Convection Coefficient and Ambient Temperature scalar values.
"},{"location":"welsim/users/bcs/#properties-view_9","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#heat-convection-example","title":"Heat convection example","text":"

Heat Convection boundary condition is applied in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#heat-radiation","title":"Heat radiation","text":"

A heat radiation boundary condition imposes a constant radiation onto one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for all thermal analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_10","title":"Boundary condition application","text":"

To apply Heat Radiation:

  1. On the menu or toolbar of the Thermal, click Heat Radiation button. Or, right-click the Study object in the tree and select Impose Conditions>Heat Radiation.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Radiation Coefficient and Ambient Temperature scalar values.
"},{"location":"welsim/users/bcs/#properties-view_10","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#heat-radiation-example","title":"Heat radiation example","text":"

Heat Radiation boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#initial-temperature","title":"Initial temperature","text":""},{"location":"welsim/users/bcs/#boundary-condition-application_11","title":"Boundary condition application","text":"

To apply Initial Temperature:

  1. On the Menu or Toolbar of the Thermal, click Initial Temperature button. Or, right-click the Study object in the tree and select Impose Conditions > Heat Radiation.
  2. Set the Initial Temperature value or use the default value.
"},{"location":"welsim/users/bcs/#properties-view_11","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#initial-temperature-example","title":"Initial temperature example","text":"

Initial Temperature boundary condition is applied as shown in Figure\u00a0below.

Note

Initial Temperature should be added before any other boundary conditions in all kinds of thermal analyses.

"},{"location":"welsim/users/bcs/#heat-flow","title":"Heat flow","text":""},{"location":"welsim/users/bcs/#boundary-condition-application_12","title":"Boundary condition application","text":"

To apply Heat Flow:

  1. On the Menu or Toolbar of the Thermal, click Heat Flow button. Or, right-click the Study object in the tree and select Impose Conditions > Heat Flow.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Set the Heat Flow value.
"},{"location":"welsim/users/bcs/#properties-view_12","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#heat-flow-example","title":"Heat flow example","text":"

Heat Flow boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#perfectly-insulated","title":"Perfectly insulated","text":""},{"location":"welsim/users/bcs/#boundary-condition-application_13","title":"Boundary condition application","text":"

To apply Perfectly Insulated:

  1. On the Menu or Toolbar of the Thermal, click Heat Flow button. Or, right-click the Study object in the tree and select Impose Conditions > Heat Flow.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
"},{"location":"welsim/users/bcs/#properties-view_13","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#perfectly-insulated-example","title":"Perfectly insulated example","text":"

Perfectly Insulated boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#voltage","title":"Voltage","text":"

Voltage determines the electric potential to one or more faces or edges, or vertices. This boundary condition is available for the electrostatic analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_14","title":"Boundary condition application","text":"

To apply Voltage:

  1. On the menu or toolbar of the Electromagnetic, click Voltage button. Or, right-click the Study object in the tree and select Impose Conditions>Voltage.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Voltage value.
"},{"location":"welsim/users/bcs/#properties-view_14","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#voltage-example","title":"Voltage example","text":"

Voltage boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#ground","title":"Ground","text":"

A Ground boundary condition is a special case of Voltage boundary condition. It essentially sets the voltage to zero at the scoped geometries. This boundary condition is available for the electrostatic analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_15","title":"Boundary condition application","text":"

To apply Ground:

  1. On the menu or toolbar of the Electromagnetic, click Ground command. Or, right-click the Study object in the tree and select Impose Conditions>Ground.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
"},{"location":"welsim/users/bcs/#properties-view_15","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#ground-example","title":"Ground example","text":"

Ground boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#symmetry","title":"Symmetry","text":"

A Symmetry boundary condition defines the symmetric boundary for the scoped geometry. This boundary condition is available for electromagnetic analyses.

"},{"location":"welsim/users/bcs/#boundary-condition-application_16","title":"Boundary condition application","text":"

To apply Symmetry:

  1. On the menu or toolbar of the Electromagnetic, click Symmetry button. Or, right-click the Study object in the tree and select Impose Conditions>Symmetry.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
"},{"location":"welsim/users/bcs/#properties-view_16","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#symmetry-example","title":"Symmetry example","text":"

Symmetry boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#zero-charge","title":"Zero charge","text":"

A Zero Charge boundary condition defines the zero surface charge for the scoped geometry. This boundary condition is available for electrostatic analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_17","title":"Boundary condition application","text":"

To apply Zero Charge:

  1. On the menu or toolbar of the Electromagnetic, click Zero Charge button. Or, right-click the Study object in the tree and select Impose Conditions>Zero Charge.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
"},{"location":"welsim/users/bcs/#properties-view_17","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#zero-charge-example","title":"Zero charge example","text":"

Zero Charge boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#surface-charge-density","title":"Surface charge density","text":"

A Surface Change Density boundary condition defines the surface charge density for the scoped geometry. This boundary condition is available for electrostatic analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_18","title":"Boundary condition application","text":"

To apply Surface Charge Density:

  1. On the menu or toolbar of the Electromagnetic, click Surface Charge Density button. Or, right-click the Study object in the tree and select Impose Conditions>Surface Charge Density.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
"},{"location":"welsim/users/bcs/#properties-view_18","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#surface-charge-density-example","title":"Surface charge density example","text":"

Surface Charge Density boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#electric-displacement","title":"Electric displacement","text":"

An Electric Displacement boundary condition defines the electric displacement vector for the scoped geometry. This boundary condition is available for electrostatic analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_19","title":"Boundary condition application","text":"

To apply Electric Displacement:

  1. On the menu or toolbar of the Electromagnetic, click Electric Displacement button. Or, right-click the Study object in the tree and select Impose Conditions>Electric Displacement.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Determine the values of Electric Displacement.
"},{"location":"welsim/users/bcs/#properties-view_19","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#electric-displacement-example","title":"Electric displacement example","text":"

Electric Displacement boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#insulating","title":"Insulating","text":"

An Insulating boundary condition defines the zero magnetic field for the scoped geometry. This boundary condition is available for the magnetic analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_20","title":"Boundary condition application","text":"

To apply Insulating:

  1. On the menu or toolbar of the Electromagnetic, click Insulating command. Or, right-click the Study object in the tree and select Impose Conditions>Insulating.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
"},{"location":"welsim/users/bcs/#properties-view_20","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#insulating-example","title":"Insulating example","text":"

Insulating boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#vector-magnetic-potential","title":"Vector magnetic potential","text":"

A Vector Magnetic Potential boundary condition defines the magnetic potential vector for the scoped geometry. This boundary condition is available for magnetic analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_21","title":"Boundary condition application","text":"

To apply Vector Magnetic Potential:

  1. On the menu or toolbar of the Electromagnetic, click Magnetic Potential button. Or, right-click the Study object in the tree and select Impose Conditions>Magnetic Potential.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Determine the value of Vector Magnetic Potential.
"},{"location":"welsim/users/bcs/#properties-view_21","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#magnetic-potential-example","title":"Magnetic potential example","text":"

Magnetic Potential boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#magnetic-flux-density","title":"Magnetic flux density","text":"

A Magnetic Flux Density boundary condition defines the magnetic flux density for the scoped geometry. This boundary condition is available for magnetic analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_22","title":"Boundary condition application","text":"

To apply Magnetic Flux Density:

  1. On the menu or toolbar of the Electromagnetic, click Magnetic Flux Density button. Or, right-click the Study object in the tree and select Impose Conditions>Magnetic Flux Density.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
"},{"location":"welsim/users/bcs/#properties-view_22","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#magnetic-flux-density-example","title":"Magnetic flux density example","text":"

Magnetic Flux Density boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#types-of-body-conditions","title":"Types of body conditions","text":"

This section describes the Body Conditions that are provided in the WELSIM application.

"},{"location":"welsim/users/bcs/#acceleration_1","title":"Acceleration","text":"

The Acceleration body condition defines a linear acceleration of a structure in a particular direction. This body condition is available for all structural analysis.

If desired, acceleration body condition can be used to mimic the Earth Gravity. For example, the standard earth gravity is 9.80665 m/s\\(^{2}\\) toward the ground, you can add an acceleration body condition object and apply to all or the target bodies to represent the earth gravity.

"},{"location":"welsim/users/bcs/#body-condition-application","title":"Body condition application","text":"

To apply Acceleration:

  1. On the menu or toolbar of the Structural, click Acceleration button. Or, right-click the Study object in the tree and select Impose Conditions>Acceleration.
  2. Keep the All bodies Scoping Method, or choose the Geometry Selection and scope the geometric entities from Graphics window.
  3. Define the Acceleration magnitude on X, Y, and Z directions.
"},{"location":"welsim/users/bcs/#properties-view_23","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#acceleration-example_1","title":"Acceleration example","text":"

Acceleration is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#earth-gravity","title":"Earth gravity","text":"

The earth gravity condition defines gravitational effects on structure bodies. This body condition is available for all structural analysis. This condition is equivalent to the Acceleration body condition.

"},{"location":"welsim/users/bcs/#body-condition-application_1","title":"Body condition application","text":"

To apply Acceleration:

  1. On the menu or toolbar of the Structural, click Earth Gravity button. Or, right-click the Study object in the tree and select Impose Conditions>Earth Gravity.
  2. Keep the All bodies Scoping Method, or choose the Geometry Selection and scope the geometric entities from Graphics window.
  3. Define the Earth Gravity magnitude on X, Y, and Z directions.
"},{"location":"welsim/users/bcs/#properties-view_24","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#earth-gravity-example","title":"Earth gravity example","text":"

The Earth Gravity body condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#body-force","title":"Body force","text":"

The body force condition defines a linear force acting structure bodies. This body condition is available for all structural analysis. The contribution of body force to the governing equation can be seen at Infinitesimal deformation linear elasticity static analysis.

"},{"location":"welsim/users/bcs/#body-condition-application_2","title":"Body condition application","text":"

To apply Body Force:

  1. On the menu or toolbar of the Structural, click Body Force button. Or, right-click the Study object in the tree and select Impose Conditions>Body Force.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Body Force magnitude on X, Y, and Z directions.
"},{"location":"welsim/users/bcs/#properties-view_25","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#body-force-example","title":"Body force example","text":"

The Body Force is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#rotational-velocity","title":"Rotational velocity","text":"

The Rotational Velocity condition determines the centrifugal force generated from a part spinning at a constant rate. This body condition is available for all structural analysis.

"},{"location":"welsim/users/bcs/#body-condition-application_3","title":"Body condition application","text":"

To apply Rotational Velocity:

  1. On the menu or toolbar of the Structural, click Rotational Velocity button. Or, right-click the Study object in the tree and select Impose Conditions>Rotational Velocity.
  2. Keep the All bodies Scoping Method, or choose the Geometry Selection and scope the geometric entities from Graphics window.
  3. Define the coefficients of Angular Velocity, Rotating Axis.
"},{"location":"welsim/users/bcs/#properties-view_26","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#rotational-velocity-example","title":"Rotational velocity example","text":"

The Rotational Velocity is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#internal-heat-generation","title":"Internal heat generation","text":"

The Internal Heat Generation condition determines the heat flow generated from the body. This body condition is available for all thermal analysis.

"},{"location":"welsim/users/bcs/#internal-heat-generation-application","title":"Internal heat generation application","text":"

To apply Internal Heat Generation:

  1. On the menu or toolbar of the Thermal, click Internal Heat Generation button. Or, right-click the Study object in the tree and select Impose Conditions > Internal Heat Generation.
  2. Keep the All bodies Scoping Method, or choose the Geometry Selection and scope the geometric entities from Graphics window.
  3. Define the coefficients of Heat Flow value.
"},{"location":"welsim/users/bcs/#properties-view_27","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#internal-heat-generation-example","title":"Internal heat generation example","text":"

The Internal Heat Generation is applied as shown in Figure below.

"},{"location":"welsim/users/connections/","title":"Setting connections","text":"

The Connections object acts as a group folder includes all connecting related settings, such as Contact Pair.

"},{"location":"welsim/users/connections/#connections-group","title":"Connections group","text":"

The Connections group is a unique container in WELSIM application for all types of connection objects. As illustrated in Figure\u00a0below, the Connections object includes multiple Contact Pair objects.

"},{"location":"welsim/users/connections/#contact-pairs","title":"Contact pairs","text":"

Contact Pairs are applied when two separate parts (solid, surface, and line bodies) in an assembly touch one another (they are mutually tangent). The contact bodies/surfaces:

As shown in Figure\u00a0below, the Contact for structure analysis support three types of contact: Bonded, Frictionless, and Frictional. For the Frictionless and Frictional types, the contact pairs (surfaces, edges) are free to separate and move away from one another, which is called to have status-changing nonlinearity. The stiffness matrice in the solving change dramatically as the parts are touching or separated.

"},{"location":"welsim/users/connections/#formulation-of-contact","title":"Formulation of contact","text":"

Since the contact algorithms are complicated, it is recommended to use the default formulation method for your contact analysis. This section describes the theory of contact formulations: Lagrange and Augmented Lagrange methods. Those methods only exist in the structural analysis.

"},{"location":"welsim/users/connections/#bonded","title":"Bonded","text":"

For the Non-Separated Bonded contact, the MPC algorithm is applied internally to add constraint equations to the tied nodes on the contact entities (surfaces, edges). The bonded contact has no penetration, no separation behaviors during the motion.

"},{"location":"welsim/users/connections/#lagrange-method","title":"Lagrange method","text":"

This formulation adds an extra contact pressure term to satisfy the contact compatibility. Thus the contact force is solved explicitly as an unknown degree of freedom.

"},{"location":"welsim/users/connections/#augmented-lagrange-method","title":"Augmented lagrange method","text":"

Augmented Lagrange method is a penalty-based contact formulation. The finite contact force is

\\[ F_{Normal}=k_{Normal}x_{Penetration}+\\lambda \\]

where \\(k_{Normal}\\) is the contact stiffness, \\(x_{Penetration}\\) is the penetration depth along the normal direction. The smaller the penetration depth, the more accurate numerical solutions. The exist of term \\(\\lambda\\) is the difference between the traditional penalty method and the augmented Lagrange method.

"},{"location":"welsim/users/connections/#contact-settings","title":"Contact settings","text":"

When you select a Contact Pair object in the tree, the contact settings become available in the Properties view. The Target Geometry and Master Geometry properties allow you to scope the contact pairs from the Graphics window. Note that the valid Target and Master Geometries show in different colors. You can change the highlight color in the Display tab of the contact Properties View.

When you choose the Frictionless or Frictional option in the Contact Type property, the following properties shows:

"},{"location":"welsim/users/connections/#supported-contact-types","title":"Supported contact types","text":"

The Table below identifies the supported formulations for the various contact geometries.

Contact Geometry Face (Master) Edge (Master) Vertex (Master) Face (Target) Yes Yes Not Supported for solving Edge (Target) Yes Yes Not Supported for solving Vertex (Target) Not Supported for solving Not Supported for solving Not Supported for solving"},{"location":"welsim/users/connections/#ease-of-use-contact","title":"Ease of use contact","text":""},{"location":"welsim/users/connections/#flipping-master-and-target-scoping-geometries","title":"Flipping master and target scoping geometries","text":"

This feature provides you a command to quickly swap master and target geometries that are already scoped in the Properties View. You can achieve this by right clicking on the specific Contact Pair, and choosing Switch Target/Master Contacts from the context menu as shown in Figure\u00a0below.

Note

This feature is not applicable to Face to Edge contact where faces and edges are always designated as targets and masters, respectively.

"},{"location":"welsim/users/geometry/","title":"Specifying geometry","text":""},{"location":"welsim/users/geometry/#geometry-fundamentals","title":"Geometry fundamentals","text":"

Part is the fundamental object carries the geometry data. An assembly model may contain one or multiple parts. There is no limit of parts in WELSIM application, and large assemblie require more hardware resources to process the geometric operations. All parts object are grouped in the Geometry Group object.

"},{"location":"welsim/users/geometry/#working-with-parts","title":"Working with parts","text":"

The part has these attributes:

"},{"location":"welsim/users/geometry/#color-scheme-of-parts","title":"Color scheme of parts","text":"

The geometry is assigned with predefined random color. However, you can define the color of part to visually identify different components in an assembly. Click the Display tab from the Properties view of the Part Object, and click the Color By property to determine the color scheme. The following lists the available color schemes:

You can reset the colors back to the default color scheme by right click on the Geometry object in the tree and selecting Reset Body Colors.

"},{"location":"welsim/users/geometry/#overview","title":"Overview","text":"

The WELSIM geometry module's interface is similar to that most other features. The graphical user interface of geometry commands is consist of three regions:

  1. Toolbars: Located at the top of the interface, there is a toolbar.
  2. Geometry Menu: Located at the Menu, the Geometry Menu provides all geometry related commands.
  3. Context Menu: Popped up at Geometry tree objects, the context menu provides geometry related commands as shown in Figure\u00a0below.

"},{"location":"welsim/users/geometry/#creating-primitive-geometry","title":"Creating primitive geometry","text":"

The system provides built-in commands to allow you to create primitive geometries. The following describes the supported geometries: Box, Cylinder, Plate, and Line.

"},{"location":"welsim/users/geometry/#box","title":"Box","text":"

An example of a created box shape is shown in Figure\u00a0[fig:ch3_guide_geom_box].

"},{"location":"welsim/users/geometry/#cylinder","title":"Cylinder","text":"

An example of a created cylinder shape is shown in Figure\u00a0[fig:ch3_guide_geom_cylinder].

"},{"location":"welsim/users/geometry/#plate","title":"Plate","text":"

An example of a created plate shape is shown in Figure\u00a0[fig:ch3_guide_geom_plate].

"},{"location":"welsim/users/geometry/#line","title":"Line","text":"

An example of a created Line shape is shown in Figure\u00a0[fig:ch3_guide_geom_line].

"},{"location":"welsim/users/geometry/#importing-and-exporting-geometry","title":"Importing and exporting geometry","text":""},{"location":"welsim/users/geometry/#importing","title":"Importing","text":"

The geometry importing feature supports the STEP and IGES format files, and the STEP file is recommended. The following lists the behaviors of importing geometry:

"},{"location":"welsim/users/geometry/#exporting","title":"Exporting","text":"

The geometries in the tree can be exported to an external STEP file. The following methods show you how to export:

"},{"location":"welsim/users/geometry/#boolean-operations","title":"Boolean operations","text":"

The WELSIM geometry module supports fundamental Boolean operations, which allow users to manipulate the shape of geometries. The available operations are Union, Intersection, and Difference. You can select multiple geometry objects from the tree list and press the Boolean commands to implement the operations. You can hold Ctrl or Shift keys to select multiple geometry objects from the project tree.

"},{"location":"welsim/users/geometry/#union","title":"Union","text":"

The union operation consolidates two or more geometry into one geometry. An example of Union geometry of a box and cylinder shape is shown in Figure\u00a0below.

"},{"location":"welsim/users/geometry/#intersection","title":"Intersection","text":"

The intersection operation keeps the commonly shared portions of two or more geometries. An example of Intersection geometry of a box and cylinder shape is shown in Figure\u00a0below.

"},{"location":"welsim/users/geometry/#difference","title":"Difference","text":"

The Difference operation subtracts the secondly selected geometry from the first selected geometry. Thus the selection order plays an important role in the final generated geometry. You can see the results of two different selection orders in Figures\u00a0below.

"},{"location":"welsim/users/geometry/#geometry-commands","title":"Geometry commands","text":"

In addition to the fundamental geometry commands, the following lists the commands that may be applied in the geometry modeling:

"},{"location":"welsim/users/geometry/#generate-solid","title":"Generate solid","text":"

In the most of analysis, the model needs to be solid to generate the 3D solid finite element. If the imported geometry only contains the surface data, the mesher cannot generate solid elements. In this scenario, you need to convert a surface geometry to solid geometry. The Generate Solid command provides you with a tool to complete this conversion.

To convert a surface to solid geometry, you can follow the steps below:

  1. Select the surface geometry objects from the tree.
  2. Click the Generate Solid command from the Geometry Menu, or right click on the selected geometry objects, and select the Generate Solid command from the context menu.
"},{"location":"welsim/users/geometry/#part-structure-types","title":"Part structure types","text":""},{"location":"welsim/users/geometry/#solid-bodies","title":"Solid bodies","text":"

The solid bodies including parts and assembly support all simulation features of WELSIM application.

"},{"location":"welsim/users/geometry/#surface-bodies","title":"Surface bodies","text":"

The surface bodies are treated as Shell structure in the structural and thermal analyses. In the Properties View of the Shell part, you need to specify the thickness of the shell, as shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/","title":"Application user interface","text":"

This section describes the fundamental components of the WELSIM application interface, their usage, and behaviors.

"},{"location":"welsim/users/gui/#welsim-application-window","title":"WELSIM application window","text":"

The functional components of the graphical user interface include the following as listed in Table\u00a0below.

Window Component Description Main Menus This menu includes all application level actions such as File and About Standard Toolbar This toolbar contains commonly used actions such as Mesh and Solve Graphics Toolbar This toolbar contains graphics related actions such as Zoom and Selection Project Explorer (Tree) Window This window contains a list of simulation objects that represents the modeling settings. Since it contains the branches and trunk, this windows is also called tree outline. The context menu for each object could vary. The object can be renamed, deleted, duplicated, copied and pasted Properties Window This window displays the properties of each object in the tree list. The user can view or edit the property values Graphics View This window shows and manipulates the visual content of the simulation entities. This window can display: 3D geometry, mesh, annotation, coordinate system symbol, spreadsheet, etc Output Window This window display the messages from the system or solvers Tabular Data Window This window lists the data that is input from user or output from the solvers. The listed data is always consistent with the curves in the Chart window Chart Window This window plots the graphics that is input from user or output from the solvers. The curves are always consistent with the table data in the Tabular Data window Context Menu This menu shows up as user right mouse button click on objects, graphics, toolbars, etc. Different entities may show different context Status Bar This widget shows the message and status on the bottom area of the application interface"},{"location":"welsim/users/gui/#windows-management","title":"Windows management","text":"

The WELSIM window owns panes that can carry project objects, properties, graphics, output, tabular data, and chart views.Window management functionalities enable you to dock, hide, show, move, and resize the windows.

"},{"location":"welsim/users/gui/#hiding-and-showing","title":"Hiding and showing","text":"

The windows can be hidden or shown by setting the view controller. As shown in Figure\u00a0[tab:ch3_guide_gui_windows], there are two ways to control the window views:

  1. Browse the View Menu > Windows, toggle the windows that you would show or hide.
  2. Right mouse button clicks on the Toolbar, you can toggle the windows.

You also can click the cross button on the title bar to hide the window.

"},{"location":"welsim/users/gui/#docking-and-undocking","title":"Docking and undocking","text":"

You can drag a window's title bar to move a window pane. Once you start to drag the window, the activated window is moving with your mouse. You can release the button on the target area to settle the new docking area. You can double-click a window's title bar to move it around the screen. The size of the window can be adjusted easily by dragging the borders or corners. You also can click the undocking button on the title bar to undock the window.

"},{"location":"welsim/users/gui/#moving-and-resizing","title":"Moving and resizing","text":"

You can drag a window's title bar to move and undock a window pane. Once you start to drag the window, the potential dock target area appears in the allowed space. At this moment, you can release the button to dock the window on the target area.

"},{"location":"welsim/users/gui/#main-windows","title":"Main windows","text":"

Besides the menu and toolbar widgets of the user interface, some other widgets are available. Those windows appear by default or when specific options are activated. The availability of those windows is controlled by the VIEW\u202f>\u202fWindows menu. This section discusses the following windows:

As the user selects a tree object in the Project Explorer window, all attributes for the selected object in Properties View, Tabular Data, and Chart Window are displayed or updated. The Properties window contains two tabs, and the Data tab shows the attributes about the object data, the Display tab lists the specifications about the graphics. The Graphics window shows the three-dimensional geometry model, depending on the tree object selection, shows information about the object details, highlighted areas, and annotations. The Output window displays the messages from the system or solvers. The Spreadsheet window shows the worksheet data for specific tree objects.

Those user interface components are described in the following sections:

"},{"location":"welsim/users/gui/#project-explorer","title":"Project explorer","text":"

The object Tree list represents the logical steps of the conducted simulation study. All branches relate to the parenting object. For instance, a key object called Study contains Study Settings and boundary condition objects. The user can right click on an object to activate a context menu that relates to the clicked object. The objects can be copied, pasted, duplicated, and renamed.

An example of the Project Explorer window is shown in Figure\u00a0below.

Note

The tree outline contains all elements that applied in the simulation study. The root object displays the number of projects in the solution. The Material project node includes all material specification. The FEM project contains the analysis settings, multiple FEM projects are allowed in the solution.

"},{"location":"welsim/users/gui/#knowing-the-tree-objects","title":"Knowing the tree objects","text":"

The tree objects in the Project Explorer window have the following conventions:

"},{"location":"welsim/users/gui/#object-status-symbols","title":"Object status symbols","text":"

The status icons are smaller than the tree object icon and located to the right bottom corner of the object icon. These symbols are intend to provide a quick visual reference to the status of the object. The details of the status symbols are described in Table\u00a0below.

Status Name Symbol Icon Description Underdefined A study object or its child objects requires user input values Error A fixed supported object may stop the simulation due to the confliction with other settings, user needs to resolve the confliction to continue the modeling OK A mesh settings object is well defined or any action about this object is succeed Suppressed An object is suppressed, such object becomes deactivated and won't participate the simulation. User can unsuppress the object Needs to be Updated An answers object or its child objects are not evaluated. Waiting for user to update"},{"location":"welsim/users/gui/#suppressingunsuppressing-objects","title":"Suppressing/Unsuppressing objects","text":"

Most of the objects in the Project Explorer window can be suppressed or unsuppressed by users. A suppressed object means that it is excluded from the further analysis. For example, suppressing a boundary condition excludes the boundary condition from the study and the further solutions. You also can unsuppress the object with the restored object attributes.

There are two ways to suppress/unsuppress an object:

"},{"location":"welsim/users/gui/#properties-view","title":"Properties view","text":"

The Properties View is located in the bottom left corner of the main user interface by default, and the user can change the location by dragging the window pane. This view window provides the user with details and information that relate to the selected object in the Project Explorer. Some properties are read-only that cannot be changed by the users, and some properties allow users to input values. An example of Properties View of the object is shown in Figures\u00a0below.

"},{"location":"welsim/users/gui/#features","title":"Features","text":"

The features of the Properties View include:

"},{"location":"welsim/users/gui/#group-property","title":"Group property","text":"

The Group Property is a read-only and occupy the entire row of the Properties pane, as shown in Figure below.

The group provides you better user experience by organizing the properties into distinct categories.

"},{"location":"welsim/users/gui/#undefined-or-invalid-properties","title":"Undefined or invalid properties","text":"

In the Properties View, the undefined or invalid fields are highlighted in yellow as shown in Figure\u00a0below.

Once the property is well defined and becomes valid, highlight yellow color disappears.

"},{"location":"welsim/users/gui/#drop-down-list","title":"Drop-down list","text":"

The combo property shows the drop-down list as user clicks the attribute as shown in Figure below.

Note

You can adjust the width of the columns by dragging the separator between the columns.

"},{"location":"welsim/users/gui/#text-entry","title":"Text entry","text":"

In the text entry field, you can input strings, numbers, or integers, depending on the type of the cell as shown in Figure\u00a0below.

The invalid value for the specific cell will be discarded, or the cell shows red background.

"},{"location":"welsim/users/gui/#geometry-selection","title":"Geometry selection","text":"

Geometry Selection allows users to scope topological entities from the graphics window. An example of Geometry Selection property is shown in Figure\u00a0below.

After selecting appropriate geometry entities, you can click the OK button to set the current selection into the field. Clicking the Cancel button does not change the pre-existing selection.

"},{"location":"welsim/users/gui/#graphics-window","title":"Graphics window","text":"

The Graphics window displays the geometry, annotation, mesh, result, etc. The components in the graphics window could be:

An example view of the Grpahics window is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#tabular-data-window","title":"Tabular data window","text":"

Tabular Data window is designed in better reviewing the input and output data. When you select the following objects in the tree window, both Tabular Data and Chart windows display data on the interface.

The listed data in Tabular Data window is consistent with the curves in the Chart window. As an example shown in Figure below, you can see the maximum and minimum values at all time steps are consistent between those two windows.

"},{"location":"welsim/users/gui/#chart-window","title":"Chart window","text":"

The Chart window displays the curves for the selected tree object. The curves are consistent with the data in the Tabular Data window. An example of Chart window drawing the maximum and minimum values along time is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#spreadsheet-window","title":"Spreadsheet window","text":"

The spreadsheet window provides object data in the form of tables, charts, or text to you. This widget usually contains the summarized data for a collection of properties. Note that not all objects contain a spreadsheet window, only the object that has large data may own a spreadsheet window. The behaviors of the spreadsheet window are:

  1. A spreadsheet designed to show large data on one field does not automatically display the data. You can open the spreadsheet window by double-clicking specific objects, such as Material and Study Setting objects.
  2. A new tab shows up as the spreadsheet window is open. You can close the window by clicking the cross button on the tab, or by pressing the OK button on the spreadsheet.

An example of the spreadsheet window is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#output-window","title":"Output window","text":"

The output window prompts you with feedback concerning the results of your actions in using WELSIM. In the current version, the output window mainly displays the message from the solvers. An example of output window displaying the solver messages is shown in Figure\u00a0below.

The Output window pane contains several buttons, there are:

"},{"location":"welsim/users/gui/#main-menus","title":"Main menus","text":"

The main menus contain the following items as shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#file-menu","title":"File menu","text":"

The FILE menu includes the following actions:

The items of the File menu is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#view-menu","title":"View menu","text":"

The VIEW menu includes the following actions:

The items of the View menu is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#material-menu","title":"Material menu","text":"

The MATERIAL menu includes the following actions:

The items of the Material Menu is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#geometry-menu","title":"Geometry menu","text":"

The GEOMETRY menu includes the following actions:

The items of the Geometry Menu is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#fem-menu","title":"FEM menu","text":"

The FEM Menu includes the following actions:

The items of the FEM Menu is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#structural-menu","title":"Structural menu","text":"

The STRUCTURAL menu includes the following actions:

The items of the Structural menu is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#thermal-menu","title":"Thermal menu","text":"

The THERMAL menu includes the following actions:

The items on the Thermal menu is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#electromagnetic-menu","title":"Electromagnetic menu","text":"

The ELECTROMAGNETIC menu includes the following actions:

The items of the Electromagnetic menu is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#tools-menu","title":"Tools menu","text":"

The TOOLS menu includes the following actions:

The items of the Tools menu is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#help-menu","title":"Help menu","text":"

The HELP menu includes the following actions:

The items of the Help menu is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#toolbars","title":"Toolbars","text":"

Toolbars are displayed across the top of the main user interface. Toolbars are dockable, and you can drag the toolbar to your preferred field.

"},{"location":"welsim/users/gui/#file-toolbar","title":"File toolbar","text":"

The File toolbar contains application-level commands as shown in Figure\u00a0below. Each icon button and its description follows:

"},{"location":"welsim/users/gui/#material-toolbar","title":"Material toolbar","text":"

The Material toolbar contains material-related simulation commands as shown in Figure\u00a0below. Each icon button and its description follows:

"},{"location":"welsim/users/gui/#geometry-toolbar","title":"Geometry toolbar","text":"

The Geometry toolbar contains geometry-related commands as shown in Figure below. Each icon button and its description follows:

"},{"location":"welsim/users/gui/#fem-toolbar","title":"FEM toolbar","text":"

The FEM toolbar contains finite element analysis commands as shown in Figure\u00a0below. Each icon button and its description follows:

"},{"location":"welsim/users/gui/#structural-toolbar","title":"Structural toolbar","text":"

The Structural toolbar contains structural analysis commands as shown in Figure\u00a0below. Each icon button and its description follows:

"},{"location":"welsim/users/gui/#thermal-toolbar","title":"Thermal toolbar","text":"

The Thermal toolbar contains thermal analysis commands as shown in Figure\u00a0below. Each icon button and its description follows:

"},{"location":"welsim/users/gui/#electromagnetic-toolbar","title":"Electromagnetic toolbar","text":"

The Electromagnetic toolbar contains electric and magnetic analyses commands as shown in Figure\u00a0below. Each icon button and its description follows:

"},{"location":"welsim/users/gui/#tool-toolbar","title":"Tool toolbar","text":"

The Tool toolbar contains assistance commands as shown in Figure below. Each icon button and its description follows:

To be added ...\n
"},{"location":"welsim/users/gui/#help-toolbar","title":"Help toolbar","text":"

The Help toolbar contains assistance commands as shown in Figure\u00a0below. Each icon button and its description follows:

"},{"location":"welsim/users/gui/#graphics-toolbar","title":"Graphics toolbar","text":"

The Graphics toolbar contains graphical operation commands as shown in Figure\u00a0below. Each icon button and its description follows:

"},{"location":"welsim/users/gui/#working-with-graphics","title":"Working with graphics","text":"

The following lists the tips for working with WELSIM graphics:

"},{"location":"welsim/users/gui/#preselecting-geometry","title":"PreSelecting geometry","text":"

This section discusses the pre-selection features in the Graphics window.

"},{"location":"welsim/users/gui/#highlighting","title":"Highlighting","text":"

As you hover the cursor over a geometry entity, the graphics highlights the selection and shows the location of the pointer. The pre-selection is controlled by the selection filter, and only the allowed entity types can be pre-selected and highlighted.

As shown in Figure\u00a0below, the face are highlighted in green color at pre-selection mode.

"},{"location":"welsim/users/gui/#selecting-geometry","title":"Selecting geometry","text":"

This section discusses how to select and pick geometry in the Graphics window.

"},{"location":"welsim/users/gui/#picking","title":"Picking","text":"

You can pick visible geometries by left clicking on the entities. A valid picking sets the geometry selection property for specific objects, such as boundary conditions.

You can hold the Ctrl or Shift key down to add or remove multiple selections from the current selections. A pick in the free space clears the current selection.

"},{"location":"welsim/users/gui/#selection-filters","title":"Selection filters","text":"

The selection filters control the user selection mode and provide an easy interface for users to pick or select the geometry entities. A pressed button in the selection filter toolbar denotes a selectable geometry type. The following describes the filters.

"},{"location":"welsim/users/gui/#controlling-graphical-view","title":"Controlling graphical view","text":"

The section describes the controlling and manipulating the graphical view with mouse and keys.

"},{"location":"welsim/users/gui/#view-annotations","title":"View annotations","text":"

Graphics window may contain these types of annotations:

"},{"location":"welsim/users/objects/","title":"Objects reference","text":"

This reference provides a specification for the objects in the tree.

"},{"location":"welsim/users/objects/#answers","title":"Answers","text":"

The Answers object customizes the solution properties and contains all result-level objects. The Properties View of the Answers object is shown in Figure\u00a0below.

"},{"location":"welsim/users/objects/#tree-dependencies","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options","title":"Insertion options","text":"

Appears by default when you create a new FEM project.

"},{"location":"welsim/users/objects/#object-properties","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Solver Method A drop-down field allows you to select a solver from the options: CG(Conjugate Gradient), BiCGStab, GMRES, GPBiCG, MUMPS, Direct, DIRECTmkl, where MUMPS, Direct, and DIRECTmkl are direct solvers, and the rest are iterative solvers. The default solver is MUMPS Number of Iterations A number field defines the maximum number of the linear algebra solver iterations. The default is 10000 Residual Threshold A number field defines the residual threshold for the linear algebra solver. The default is 1e-7 Output Time Log A Boolean field outputs the log for each time step. The default is False Output Iteration Log A Boolean field outputs the log each iteration step. The default is False Generate Result Files A Boolean field generates ASCII format result file. The default is False Output Frequency A number field determines the frequency of the result data output. The default value is 1, which outputs result data every step."},{"location":"welsim/users/objects/#body-conditions","title":"Body conditions","text":"

Body condition type objects enable you to impose the body condition onto the geometry bodies.

"},{"location":"welsim/users/objects/#application-objects","title":"Application objects","text":"

Body Force, Acceleration, Earth Gravity, Rotational Velocity

"},{"location":"welsim/users/objects/#tree-dependencies_1","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_1","title":"Insertion options","text":"

You can use any of the following methods to insert body conditions:

"},{"location":"welsim/users/objects/#object-properties_1","title":"Object properties","text":"

The properties may vary for different body conditions. See the Setting Up Boundary Conditions section for more information about body conditions.

"},{"location":"welsim/users/objects/#boundary-conditions","title":"Boundary conditions","text":"

Boundary condition type objects enable you to impose the boundary condition onto the geometry entities, such as faces, edges, and vertices.

"},{"location":"welsim/users/objects/#application-objects_1","title":"Application objects","text":"

Displacement, Fixed Support, Fixed Rotation, Pressure, Force, Velocity, Acceleration, Temperature, Heat Flux, Convection, Radiation, Voltage, Ground, Symmetry, Zero Charge, Surface Charge Density, Electric Displacement, Insulating, Magnetic Potential, Magnetic Flux Density

"},{"location":"welsim/users/objects/#tree-dependencies_2","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_2","title":"Insertion options","text":"

You can use any of the following methods to insert boundary condition:

"},{"location":"welsim/users/objects/#object-properties_2","title":"Object properties","text":"

The properties may vary for different body conditions. See the Setting up Boundary Conditions section for more information about Boundary Conditions.

"},{"location":"welsim/users/objects/#box","title":"Box","text":"

The Box object defines a shape that is generated by the built-in modeler. An example of Box object and properties are illustrated in Figure\u00a0below.

"},{"location":"welsim/users/objects/#tree-dependencies_3","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_3","title":"Insertion options","text":"

Appears when you create a box shape. You can use any of the following methods to insert a Box:

"},{"location":"welsim/users/objects/#object-properties_3","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Suppressed Include (False - default) or exclude (True) the geometry from the analysis Length A vector component field to determine the length, width, and height of the box. The default value is 10 Origin A vector component field to determine the location of origin. The default vector is 0 Material A drop-down field to assign the material for the selected part. The available material candidates are defined in the Material Project Source A read-only field indicates the shape is generated internally"},{"location":"welsim/users/objects/#connections","title":"Connections","text":"

The Connections object is a group-type object that may contain the connection objects between two or more parts. The currently supported children object types are Contact Pair.

"},{"location":"welsim/users/objects/#tree-dependencies_4","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_4","title":"Insertion options","text":"

Connections object is automatically inserted as you add a contact pair object to the tree.

"},{"location":"welsim/users/objects/#object-properties_4","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Suppressed A Boolean field to include (False - Default) or exclude (True) the object in the analysis"},{"location":"welsim/users/objects/#contact-pair","title":"Contact pair","text":"

This object defines a contact pair between parts.

"},{"location":"welsim/users/objects/#tree-dependencies_5","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_5","title":"Insertion options","text":"

You can use any of the following methods to insert contact pairs:

"},{"location":"welsim/users/objects/#object-properties_5","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Suppressed A Boolean field to include (False - Default) or exclude (True) the object in the analysis Master Geometry A Geometry Selection field to scope geometry entities, such as faces, edges Target Geometry A Geometry Selection field to scope geometry entities, such as faces, edges Contact Type A drop-down enumeration field to select a type from three options: Bonded, Frictionless, and Frictional Formulation A drop-down enumeration field to selection contact formulation from two options: Lagrange and Augmented Lagrange. This property is only available for Frictionless or Frictional contact type Finite Sliding A Boolean field to turn on (True) or off (False - default) the finite sliding algorithm. This property is only available for Frictionless or Frictional contact type Normal Direction Tolerance A number field to determine the distance tolerance in the normal direction. The default value is 1e-5 Tangential Direction Tolerance A number field to determine the distance tolerance in the tangential direction. The default value is 1e-5 Normal Direction Penalty A number field to determine the penalty value in the normal direction. The default value is 1e3 Tangential Direction Penalty A number field to determine the penalty value in the tangential direction. The default value is 1e3"},{"location":"welsim/users/objects/#cylinder","title":"Cylinder","text":"

The Cylinder object defines a shape that is generated by the built-in modeler. An example of Cylinder object and properties are illustrated in Figure\u00a0below.

"},{"location":"welsim/users/objects/#tree-dependencies_6","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_6","title":"Insertion options","text":"

Appears when you create a Cylinder shape. You can use any of the following methods to insert a Cylinder:

"},{"location":"welsim/users/objects/#object-properties_6","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Suppressed Include (False - default) or exclude (True) the geometry from the analysis Normal A vector component field to determine the direction of the cylinder. The default value is (0,0,1) Radius A number component field to determine the radius of the cylinder base. The default value is 10 Height A number component field to determine the height of the cylinder. The default value is 30 Angle A number component field to determine the sweeping angle of the cylinder circle. The default value 360 gives a full cylinder Origin A vector component field to determine the location of origin. The default vector is 0 Material A drop-down field to assign the material for the selected part. The available material candidates are defined in the Material Project Source A read-only field indicates the shape is generated internally"},{"location":"welsim/users/objects/#fem-project","title":"FEM project","text":"

The FEM Project object represents an independent analysis, which contains Geometry, Mesh, Study, and Answers objects. The Connections object is not created until you add a contact pair object. An example of FEM Project and properties are illustrated in Figure\u00a0[fig:ch3_guide_obj_fem_proj].

"},{"location":"welsim/users/objects/#tree-dependencies_7","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_7","title":"Insertion options","text":"

Appears by default when you create a new FEM project.

"},{"location":"welsim/users/objects/#object-properties_7","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Numerical Method A read-only field to indicate the Finite Element Method applied in this project Dimension A read-only field to indicate a 3D analysis of this project Physics Type A drop-down enumeration field for you to select the physics type. The available options are Structural, Thermal, and Electromagnetic. The default is Structural. Note that change this property may change the validation of existing objects and display of object's properties Analysis Type A drop-down enumeration field for you to select the analysis type. Depending on the Physics Type, the available options vary. For the Structural analysis, the options are Static, Transient, and Modal. For the Thermal analysis, the options are Steady-State and Transient. For the Electromagnetic analysis, the options are ElectroStatic and MagnetoStatic Ambient Temperature A number field to determine the environment temperature for the analysis, the default value is 22.3"},{"location":"welsim/users/objects/#geometry-group","title":"Geometry group","text":"

Geometry Group object contains the geometries in the form of a part or assembly. All imported and created geometries are included in this group-level object as shown in Figure\u00a0below.

"},{"location":"welsim/users/objects/#tree-dependencies_8","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_8","title":"Insertion options","text":"

Appears by default when you create a new FEM project.

"},{"location":"welsim/users/objects/#object-properties_8","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name"},{"location":"welsim/users/objects/#initial-temperature","title":"Initial temperature","text":"

Initial Temperature defines the temperature status at the beginning of the simulation for transient thermal analysis. An example of Initial Temperature and its properties are shown in Figure\u00a0below.

"},{"location":"welsim/users/objects/#tree-dependencies_9","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_9","title":"Insertion options","text":"

You can use any of the following methods to insert initial temperature:

Note

Inserting initial condition command is only applicable when the Physics Type and Analysis Type properties of FEM Project object are Thermal and Transient, respectively.

"},{"location":"welsim/users/objects/#object-properties_9","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Suppressed A Boolean field to include (False - Default) or exclude (True) the object in the analysis Scoping Method A read-only field shows All Initial Temperature A number field to define the temperature value. The default is 22.3"},{"location":"welsim/users/objects/#line","title":"Line","text":"

The Line object defines a shape that is generated by the built-in modeler. An example of Line object and properties are illustrated in Figure\u00a0below.

"},{"location":"welsim/users/objects/#tree-dependencies_10","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_10","title":"Insertion options","text":"

Appears when you create a line shape. You can use any of the following methods to insert a Line:

"},{"location":"welsim/users/objects/#object-properties_10","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Suppressed Include (False - default) or exclude (True) the geometry from the analysis Start Point A vector component field to determine one point of a line. The default value is 0 End Point A vector component field to determine another point of a line. The default value is (10, 10, 0) Material A drop-down field to assign the material for the selected part. The available material candidates are defined in the Material Project Source A read-only field indicates the shape is generated internally"},{"location":"welsim/users/objects/#material","title":"Material","text":"

A Material object defines a material data using the associated properties and spreadsheet data. You can define multiple material objects in the WELSIM application. An example of a Material object and its properties and spreadsheet are shown in Figure\u00a0below.

"},{"location":"welsim/users/objects/#tree-dependencies_11","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_11","title":"Insertion options","text":"

You can use any of the following methods to insert material:

"},{"location":"welsim/users/objects/#object-properties_11","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Suppressed A Boolean field to include (False - Default) or exclude (True) the object in the analysis"},{"location":"welsim/users/objects/#spreadsheet","title":"Spreadsheet","text":"

The Material object is able to display the Spreadsheet window, which provides a friendly user interface for defining all material properties as shown in Figure\u00a0below. You can double click or right click on the Material object and select the Edit command to display the spreadsheet window.

"},{"location":"welsim/users/objects/#material-project","title":"Material project","text":"

The Material Project object holds all material definition objects.

"},{"location":"welsim/users/objects/#tree-dependencies_12","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_12","title":"Insertion options","text":"

Appears by default when you create a new FEM project.

"},{"location":"welsim/users/objects/#object-properties_12","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name"},{"location":"welsim/users/objects/#mesh-group","title":"Mesh group","text":"

Mesh Group manages all meshing features and tools for the project. An example of mesh object and properties is shown in Figure\u00a0below.

"},{"location":"welsim/users/objects/#tree-dependencies_13","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_13","title":"Insertion options","text":"

Appears by default when you create a new FEM project.

"},{"location":"welsim/users/objects/#object-properties_13","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Number of Nodes A read-only output field to show the number of generated nodes. The value is automatically updated as the mesh is completed Number of Elements A read-only output field to show the number of generated elements. The value is automatically updated as the mesh is completed Number of Tetrahedrons A read-only output field to show the number of generated tetrahedrons. The value is automatically updated as the mesh is completed Number of Triangles A read-only output field to show the number of generated triangles. The value is automatically updated as the mesh is completed"},{"location":"welsim/users/objects/#mesh-method","title":"Mesh method","text":"

In the multi-body analysis, different parts may need different mesh density due to the various sizes of geometries. Mesh Method object helps you fine tuning the mesh for the specifically scoped geometries. An example of Mesh Method object is shown in Figure\u00a0below.

"},{"location":"welsim/users/objects/#tree-dependencies_14","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_14","title":"Insertion options","text":"

You can use any of the following methods to insert Mesh Method:

"},{"location":"welsim/users/objects/#object-properties_14","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Scoping Method A read-only field indicates the scoping method Geometry A geometry selection field to scope the geometry entities (volume/body only) Maximum Size A number field determines the maximum size of the generated finite element Quadratic A read-only field to show the order of the generated element. This property is determined by the Quadratic property in the global Mesh Settings object Mesh Density A drop-down enumeration field to determine the mesh density for the scoped geometries. The options are Very Coarse, Coarse, Regular, Fine, Very Fine, and User Defined. The default is Regular. If you select User Defined, additional properties Growth Rate, Segments per Edge, and Segments per Radius are shown Growth Rate A number field determines the change of mesh density in spatial. The default value is 0.3 Segments per Edge A number field determines the number of element segments per edge. The default value is 1. The higher value, the more dense mesh Segments per Radius A number field determines the number of element segments per radius. The default value is 2. The higher value, the more dense mesh Number of Nodes A read-only output field to show the number of generated nodes. The value is updated as the mesh is completed Number of Elements A read-only output field to show the number of generated elements. The value is updated as the mesh is completed Number of Tetrahedrons A read-only output field to show the number of generated tetrahedrons. The value is updated as the mesh is completed Number of Triangles A read-only output field to show the number of generated triangles. The value is updated as the mesh is completed"},{"location":"welsim/users/objects/#mesh-settings","title":"Mesh settings","text":"

The Mesh Settings object is a global setting for the meshing operations. You change the global mesh settings by tuning the properties of this object. An example of Mesh Settings object is shown in Figure\u00a0[fig:ch3_guide_obj_mesh_settings].

"},{"location":"welsim/users/objects/#tree-dependencies_15","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_15","title":"Insertion options","text":"

Appears by default when you create a new FEM project.

"},{"location":"welsim/users/objects/#object-properties_15","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Maximum Size A number field to determine the maximum size of the generated finite element Quadratic A Boolean field to determine the linear element (False) or bilinear element (True) Mesh Density A drop-down enumeration field to determine the mesh density for the scoped geometries. The options are Very Coarse, Coarse, Regular, Fine, Very Fine, and User Defined. The default is Regular. If you select User Defined, additional properties Growth Rate, Segments per Edge, and Segments per Radius are shown Growth Rate A number field indicate the change of mesh density in spatial. The default value is 0.3 Segments per Edge A number field indicate the element segment per edge. The default value is 1. The higher value, the more dense mesh Segments per Radius A number field indicate the element segment per radius. The default value is 2. The higher value, the more dense mesh"},{"location":"welsim/users/objects/#part","title":"Part","text":"

The Part object defines a component of the geometry that is imported from an external CAD file. An example of Part object and properties are illustrated in Figure\u00a0[fig:ch3_guide_obj_part].

"},{"location":"welsim/users/objects/#tree-dependencies_16","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_16","title":"Insertion options","text":"

Appears when you import geometry from external files. You can use any of the following methods to insert Part:

"},{"location":"welsim/users/objects/#object-properties_16","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Suppressed Include (False - default) or exclude (True) the part from the analysis Scale A number field to manipulate the size of the imported geometry. The default value is 1 Origin A vector component field to determine the location of origin. The default vector is 0 Material A drop-down field to assign the material for the selected part. The available material candidates are defined in the Material Project Structure Type A drop-down field to define the structure type. The available options are Solid, Shell, Beam, and Truss. The default is Solid Source A read-only field indicates the name of the imported geometry file"},{"location":"welsim/users/objects/#plate","title":"Plate","text":"

The Plate object defines a shape that is generated by the built-in modeler. An example of Plate object and properties are illustrated in Figure\u00a0[fig:ch3_guide_obj_part].

"},{"location":"welsim/users/objects/#tree-dependencies_17","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_17","title":"Insertion options","text":"

Appears when you create a plate shape. You can use any of the following methods to insert a Plate:

"},{"location":"welsim/users/objects/#object-properties_17","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Suppressed Include (False - default) or exclude (True) the geometry from the analysis Length A vector component field to determine the length vector of the plate. The default value is (10, 0, 0) Width A vector component field to determine the width vector from the origin. The default vector is (0, 5, 0) Material A drop-down field to assign the material for the selected part. The available material candidates are defined in the Material Project Thickness A number field to determine the thickness of the plate. The default value is 0.01 Source A read-only field indicates the shape is generated internally"},{"location":"welsim/users/objects/#results","title":"Results","text":"

The Result objects define the simulation output for displaying and analyzing the results from a solution.

"},{"location":"welsim/users/objects/#application-objects_2","title":"Application objects","text":"

Deformation, Stress, Strain, Acceleration, Velocity, Rotation, Reaction Force, Reaction Moment, Temperature, Voltage, Electric Field, Electric Displacement, Electromagnetic Energy Density, Magnetic Potential, Magnetic Flux Density, Magnetic Field, User-Defined Result.

"},{"location":"welsim/users/objects/#tree-dependencies_18","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_18","title":"Insertion options","text":"

Appears by default when you start the WELSIM application.

"},{"location":"welsim/users/objects/#object-properties_18","title":"Object properties","text":"

The properties may vary for different result types. The following lists the properties that may be shown for the most of Result objects. See the Using results section for more information.

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Suppressed Include (False - default) or exclude (True) the result object from the analysis Result By Determines the result loading type Set Number Determines the set number to retrieve the result data Maximum Value The maximum result value at the current step Minimum Value The minimum result value at the current step"},{"location":"welsim/users/objects/#solution","title":"Solution","text":"

The Solution object acts as a root object in the WELSIM application. Only one Solution can exist per simulation session, and one solution can contain multiple FEM projects.

"},{"location":"welsim/users/objects/#tree-dependencies_19","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_19","title":"Insertion options","text":"

Appears by default when you create a new FEM project.

"},{"location":"welsim/users/objects/#study","title":"Study","text":"

The Study object holds all analysis related objects such as Study Settings, Boundary Conditions, Body Conditions, and Initial Conditions. An example of Study object is shown in Figure\u00a0[fig:ch3_guide_obj_study].

"},{"location":"welsim/users/objects/#tree-dependencies_20","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_20","title":"Insertion options","text":"

Appears by default when you create a new FEM project.

"},{"location":"welsim/users/objects/#object-properties_19","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Number of Steps A number field to determine the total number of steps. The default value is 1. The input value must be positive Current Step A number field to determine the current step for the successive settings. The default value is 1. The input value must be less than or equal to the Number of Steps. Note that Current Step property of Study object is adjustable, and determines the Current Step properties in other objects such as Study Settings, and Boundary Conditions Current End Time a number field to determine the end time of the current step. The value must be larger than that of the last step"},{"location":"welsim/users/objects/#study-settings","title":"Study Settings","text":"

The Study Settings object allows you to define analysis and solving settings to customize a specific simulation model. An example of Study Settings object is shown in Figure\u00a0[fig:ch3_guide_obj_study_settings].

"},{"location":"welsim/users/objects/#tree-dependencies_21","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_21","title":"Insertion options","text":"

Appears by default when you create a new FEM project.

"},{"location":"welsim/users/objects/#object-properties_20","title":"Object properties","text":"

The properties of Study Settings vary for different Physics and Analysis types. The following lists the available properties according to Analysis Type:

"},{"location":"welsim/users/objects/#spreadsheet_1","title":"Spreadsheet","text":"

The Study Settings object can display the Spreadsheet window, which provides a friendly user interface to review properties at all steps as shown in Figure\u00a0[fig:ch3_guide_obj_study_settings]. You can double click or right click on the Study Settings object and select the Edit command to display the Spreadsheet window.

"},{"location":"welsim/users/overview/","title":"Overview","text":"

This chapter is the user guide for working with WELSIM application, which is used to perform various types of structural, thermal, and electromagnetic analyses. The entire simulation process is tied together by a unified graphical user interface.

"},{"location":"welsim/users/overview/#overview","title":"Overview","text":"

WELSIM application enables you to investigate design alternative efficiently. You can modify any aspect of analysis or vary parameters, then update the project to the see results of the change in the modeling. A typical modeling process is composed of defining the model, and boundary conditions applied to it, computing for the simulation's response to the conditions, then evaluating the solutions with a variety of tools.

The WELSIM software application has a tree structure that consists of \u201cobjects\u201d that enable you to define simulation conditions. By clicking the objects, you activate the associated properties in the property window, and you can use the corresponding command and tools to conduct the simulation study. The following sections describe in details to use the WELSIM to set up and implement simulation studies.

"},{"location":"welsim/users/results/","title":"Using results","text":"

This section describes the details of a result. The help for Results is classified by the physics and analysis types.

"},{"location":"welsim/users/results/#introduction-to-the-results","title":"Introduction to the results","text":"

You can generate results to understand the behaviors of the analyzed model. The advantages of using results in WELSIM application are:

"},{"location":"welsim/users/results/#result-application","title":"Result application","text":"

Applying results can be achieved by

"},{"location":"welsim/users/results/#result-definitions","title":"Result definitions","text":"

This section describes the fundamental features in result definitions.

"},{"location":"welsim/users/results/#result-controller","title":"Result controller","text":"

In the multi-step or transient analysis, the solution contains result data at various steps. Result By property provides a controller to select the desired step data to display. You can determine to show the result by Set Number or Time/Frequency. The default is by Set Number. Additional properties such as Set Number, Time, or Frequency shows up as you define the Result By property.

"},{"location":"welsim/users/results/#clear-generated-data","title":"Clear generated data","text":"

You can clear results data from the database using the Clear Result command from the Toolbar, Menu, or the right-click context menu on a result object.

You also can clear entire solution data from the database using the Clear Calculated Data command from the Toolbar, Menu, or the right-click context menu on an Answers object. These two commands from the context menu are shown in Figure\u00a0[fig:ch3_guide_rst_clear_data].

"},{"location":"welsim/users/results/#display-controller","title":"Display controller","text":"

You can select the Graphics tab on the result Properties View pane. As shown in Figure\u00a0[fig:ch3_guide_rst_display_prop], the following properties are available to adjust the contour display:

"},{"location":"welsim/users/results/#structural-results","title":"Structural results","text":"

The following structural results are described in this section.

"},{"location":"welsim/users/results/#deformation","title":"Deformation","text":"

Physical deformation of the modeling geometries can be calculated and plotted in the form of contour. This result is available for all structural analysis. The following gives the properties of result object:

"},{"location":"welsim/users/results/#stress","title":"Stress","text":"

The stress quantities provide mechanical insights to the given model and material of a part or an assembly under a specific structural loading environment. A general 3D stress state contains three normal and three shear stresses. The stress quantities in WELSIM application are the nodal values and available for all structural analysis. The equivalent stress (also called von-Mises stress) is related to the principal stresses by the equation:

\\[ \\sigma_{VM}=\\left[\\dfrac{(\\sigma_{11}-\\sigma_{22})^{2}+(\\sigma_{22}-\\sigma_{33})^{2}+(\\sigma_{33}-\\sigma_{11})^{2}+6(\\sigma_{12}^{2}+\\sigma_{23}^{2}+\\sigma_{31}^{2})}{2}\\right]^{1/2} \\]

The following gives the properties of result object:

"},{"location":"welsim/users/results/#strain","title":"Strain","text":"

The strain quantities provide deformation insights to the given model and material of a part or an assembly under a specific structural loading environment. This result is available for all structural analysis.

The available properties for strain result are:

"},{"location":"welsim/users/results/#acceleration","title":"Acceleration","text":"

The acceleration quantities demonstrate the acceleration of the given model and material of a part or an assembly under a specific structural loading environment. This result is available for transient structural analysis.

The available properties for acceleration result are:

Note

Acceleration result is only available for the transient structural analysis.

"},{"location":"welsim/users/results/#velocity","title":"Velocity","text":"

The velocity quantities demonstrate the velocity of the given model and material of a part or an assembly under a specific structural loading environment. This result is available for transient structural analysis.

The available properties for velocity result are:

Note

Velocity result is only available for the transient structural analysis.

"},{"location":"welsim/users/results/#rotation","title":"Rotation","text":"

The rotation quantities demonstrate the rotation of the given model and material of a part or an assembly under a specific structural loading environment. This result is available for only shell structure.

The available properties for rotation result are:

Note

Rotation result is only available for the shell structural analysis.

"},{"location":"welsim/users/results/#reaction-force-probe","title":"Reaction Force Probe","text":"

The reaction force provides an insight to abstract reaction force of the given model and material of a part or an assembly under a specific structural loading environment. This result is available for structural analysis.

The available properties for a reaction force probe are:

Note

This probe result does not show contour on the geometry. The primary output data is the Maximum Value and Minimum Value displayed in the Properties View window.

"},{"location":"welsim/users/results/#reaction-moment-probe","title":"Reaction Moment Probe","text":"

The reaction moment provides an insight to abstract quantities of the given model and material of a part or an assembly under a specific structural loading environment. This result is available for only shell structure.

The available properties for reaction moment probe are:

Note

Reaction moment probe result is only available for the shell structural analysis.

Reaction moment probe result does not show contour on the geometry. The primary output data is the Maximum Value and Minimum Value displayed in the Properties View window.

"},{"location":"welsim/users/results/#thermal-results","title":"Thermal results","text":"

The following thermal results are described in this section:

"},{"location":"welsim/users/results/#temperature","title":"Temperature","text":"

The temperature, a scalar quantity, provides an insight to the temperature distribution throughout the structure. Temperature results can be displayed as a contour plot.

The available properties for temperature are:

"},{"location":"welsim/users/results/#electric-results","title":"Electric results","text":""},{"location":"welsim/users/results/#voltage","title":"Voltage","text":"

The voltage, a scalar quantity, provides an insight to the electric potential distribution throughout the conductor bodies.

The available properties for voltage are:

"},{"location":"welsim/users/results/#electric-field","title":"Electric Field","text":"

The electric field, a vector component quantity, provides an insight to the electric field intensity distribution throughout the bodies.

The available properties for Electric Field are:

"},{"location":"welsim/users/results/#current-density","title":"Current Density","text":""},{"location":"welsim/users/results/#electric-displacement","title":"Electric Displacement","text":"

The electric displacement, a vector component quantity, provides an insight to the electric displacement intensity distribution throughout the bodies. This quantity has the constitutive relation with Electric Field as shown in equation below:

\\[ D=\\epsilon E \\]

where D is the electric displacement, E is the electric field, and \\(\\epsilon\\) is the electric permittivity. The available properties for Electric Displacement are:

"},{"location":"welsim/users/results/#energy-density","title":"Energy Density","text":"

The energy density, a scalar quantity, provides an insight to the electromagnetic energy throughout the simulation bodies.

The available properties for energy density are:

"},{"location":"welsim/users/results/#magnetic-results","title":"Magnetic results","text":"

The magnetostatic analysis provides fundamental result quantities for you to investigate the field.

"},{"location":"welsim/users/results/#electric-potential","title":"Electric Potential","text":""},{"location":"welsim/users/results/#magnetic-potential","title":"Magnetic Potential","text":"

Magnetic Potential vector components are computed throughout the simulation domain. The available properties for Magnetic Potential are:

"},{"location":"welsim/users/results/#magnetic-flux-density","title":"Magnetic Flux Density","text":"

Magnetic Flux Density vector components are computed throughout the simulation domain. The available properties for Magnetic Flux Density are:

"},{"location":"welsim/users/results/#magnetic-field","title":"Magnetic Field","text":"

Magnetic Field vector components are computed throughout the simulation domain. The available properties for Magnetic Field are:

"},{"location":"welsim/users/results/#user-defined-results","title":"User-Defined Results","text":"

This section describes the use of the User-Defined Result feature in WELSIM application. The user-defined result provides you with more flexible result evaluation methods. In addition to the system-provided result types, the User-Defined Result allows you to plot more broad kinds of results with the given expression.

Like other result types that display contours, chart, and data, the User-Defined results:

Applying a User-Defined Result can be done using one of the following methods:

An example of User Defined Result properties view is shown in Figure\u00a0[fig:ch3_guide_user_defined_rst_prop].

"},{"location":"welsim/users/results/#user-defined-result-expressions","title":"User Defined Result expressions","text":"

The property Expression accepts the capital string values, and the lower case letters are converted automatically to the capital letters. The following lists the supported Expressions used in the WELSIM application:

Expression Result description UVW Total deformation for structural analysis U Directional deformation X for structural analysis V Directional deformation Y for structural analysis W Directional deformation Z for structural analysis SIGVM von-Mises stress for the structural analysis SIG00 Normal stress X for the structural analysis SIG11 Normal stress Y for the structural analysis SIG22 Normal stress Z for the structural analysis SIG01 Shear stress XY for the structural analysis SIG12 Shear stress YZ for the structural analysis SIG02 Shear stress XZ for the structural analysis EPS00 Normal strain X for the structural analysis EPS11 Normal strain Y for the structural analysis EPS22 Normal strain Z for the structural analysis EPS01 Shear strain XY for the structural analysis EPS12 Shear strain YZ for the structural analysis EPS02 Shear strain XZ for the structural analysis RFT Total reaction force for the structural analysis RFX Directional reaction force X for the structural analysis RFY Directional reaction force Y for the structural analysis RFZ Directional reaction force Z for the structural analysis RMT Total reaction moment for the shell structural analysis RMX Directional reaction moment X for the shell structural analysis RMY Directional reaction moment Y for the shell structural analysis RMZ Directional reaction moment Z for the shell structural analysis ENEEL Total energy for the structural analysis V123 Total velocity for the transient structural analysis V1 Directional velocity X for the transient structural analysis V2 Directional velocity Y for the transient structural analysis V3 Directional velocity Z for the transient structural analysis A123 Total acceleration for the transient structural analysis A1 Directional acceleration X for the transient structural analysis A2 Directional acceleration Y for the transient structural analysis A3 Directional acceleration Z for the transient structural analysis ROTT Total rotation for shell structural analysis ROTX Directional rotation X for shell structural analysis ROTY Directional rotation Y for shell structural analysis ROTZ Directional rotation Z for shell structural analysis TEMP Temperature for thermal analysis EM_U Voltage for electromagnetic analysis EM_ET Total electric field intensity for electromagnetic analysis EM_EX Directional electric field intensity X for electromagnetic analysis EM_EY Directional electric field intensity Y for electromagnetic analysis EM_EZ Directional electric field intensity Z for electromagnetic analysis EM_DT Total electric displacement for electromagnetic analysis EM_DX Directional electric displacement X for electromagnetic analysis EM_DY Directional electric displacement Y for electromagnetic analysis EM_DZ Directional electric displacement Z for electromagnetic analysis EM_EN Energy density for electromagnetic analysis EM_HT Total magnetic field intensity for electromagnetic analysis EM_HX Directional magnetic field intensity X for electromagnetic analysis EM_HY Directional magnetic field intensity Y for electromagnetic analysis EM_HZ Directional magnetic field intensity Z for electromagnetic analysis EM_BT Total magnetic flux density for electromagnetic analysis EM_BX Directional magnetic flux density X for electromagnetic analysis EM_BY Directional magnetic flux density Y for electromagnetic analysis EM_BZ Directional magnetic flux density Z for electromagnetic analysis EM_AT Magnitude of a magnetic potential vector for electromagnetic analysis EM_A_x Magnetic potential vector component X for electromagnetic analysis EM_A_y Magnetic potential vector component Y for electromagnetic analysis EM_A_z Magnetic potential vector component Z for electromagnetic analysis"},{"location":"welsim/users/results/#result-tools","title":"Result tools","text":""},{"location":"welsim/users/results/#result-legend","title":"Result legend","text":"

The result legend feature helps you display the result range and contour colors in a specific design. The legend component is shown in the left of the Graphics window. As shown in Figure below, the legend displays the following information:

The Legend style can be adjusted by right-clicking on the Legend field. As shown in Figure\u00a0below, the Context Menu contains items:

Note

For the option of user-defined max/min settings, the input maximum value must be greater than the minimum value.

"},{"location":"welsim/users/results/#exporting-results","title":"Exporting results","text":"

The data associated with result objects can be exported in ASCII (.txt or .dat) file format by right-clicking on the desired result object and selecting the Export Result option. Once executed, you are asked to define a filename and select the directory to save the file.

Note

The desired result object must have been successfully evaluated before exporting the result data.

"},{"location":"welsim/users/steps/","title":"Steps for using the application","text":"

This section discusses the workflow in performing simulation analysis in the WELSIM application.

"},{"location":"welsim/users/steps/#creating-analysis-environment","title":"Creating analysis environment","text":"

All analyses in WELSIM are represented by one independent analysis environment. After creating a new project environment, you can choose the analysis type and define the parameters to conduct the simulation study.

"},{"location":"welsim/users/steps/#unit-system-behavior","title":"Unit system behavior","text":"

The WELSIM provides eight types of unit systems for you to chose. You can select the preferred unit system from File > Preferences > General > Units. Once the unit system is chosen, quantity units of FEM objects are fixed. However, user still can select different unit for the quantity defined in material module. The material quantity will be converted to the system units at solve.

"},{"location":"welsim/users/steps/#defining-materials","title":"Defining materials","text":"

In simulation analysis, a geometry's attribute is influenced by the material properties that are assigned to the body. When you create a new FEM project, a material project and a structural steel material object are created automatically. This material project can include multiple material objects, which contains the material properties for the successive analysis. The system-generated structural steel can be used directly.

You can add new materials by either one of the methods below:

"},{"location":"welsim/users/steps/#editing-material-properties","title":"Editing material properties","text":"

To manage material properties, you can

"},{"location":"welsim/users/steps/#defining-material-properties","title":"Defining material properties","text":"

In the material definition panel, two tabs display on the left sub-window as shown in Figure\u00a0below. The Library tab gives you a quick method to add a bundle of properties for the specific type of material. The Build allows you to add each preferred property one by one.

"},{"location":"welsim/users/steps/#defining-analysis-type","title":"Defining analysis type","text":"

There are several analysis types are supported in WELSIM. You can define the analysis type while performing an analysis. For example, if the temperature is to be calculated, you would choose a thermal analysis. In the FEM project object, you can set the Physics Type and Analysis Type from the Properties View window as shown in Figure\u00a0below. The currently available physics and analysis types are:

"},{"location":"welsim/users/steps/#generating-geometries","title":"Generating geometries","text":"

There are two ways of generating geometries in the WELSIM application. You can either create primitive shapes using built-in tools or import an existing STEP/IGES file. Since the built-in tool only can create primitive shapes such as box and cylinder, it is recommended to create your complex geometry in an external application and import the CAD file into WELSIM.

"},{"location":"welsim/users/steps/#create-primitive-shapes","title":"Create primitive shapes","text":"

The following lists the primitive shapes that WELSIM build-in tool can create:

"},{"location":"welsim/users/steps/#import-geometry-files","title":"Import geometry files","text":"

For the complex geometry or practical designs, you can create your geometry in an external CAD application, and import to WELSIM application via STEP or IGES file. The properties view of the imported geometry allows you to define the geometry attributes, as shown in Figure\u00a0below.

"},{"location":"welsim/users/steps/#defining-part-behaviors","title":"Defining part behaviors","text":"

The primitive and imported parts have slightly different behaviors, but the primary attributes are the same. This section describes the behaviors of the imported part.

"},{"location":"welsim/users/steps/#geometry-scale","title":"Geometry scale","text":"

The Scale determines the size change of the imported geometry, and the current geometry size is the original size multiplied by the scale value. The default value is 1. Increasing the scale value enlarges the geometry, reducing this value causes the geometry smaller. The scale ruler on the bottom of the Graphics Window provides a reference for users to recognize the current size of the geometry.

"},{"location":"welsim/users/steps/#spatial-parameters","title":"Spatial parameters","text":"

For the imported geometry, the Spatial Parameters allows the user to adjust the origin of geometries. The default value is the origin of global coordinates (0, 0, 0).

"},{"location":"welsim/users/steps/#material-assignment","title":"Material assignment","text":"

Once you have defined the material objects and created the geometry, you can assign the specific material to the selected geometry object. Click Material property, and the cell displays all candidate materials in the drop-down list as shown in Figure\u00a0below. Each entry includes the material object name and ID.

"},{"location":"welsim/users/steps/#structure-type","title":"Structure type","text":"

The Structure Type provides a topological reference for you to differentiate the solid, shell, and beam geometries. The default structural type is Solid.

"},{"location":"welsim/users/steps/#source-file-name","title":"Source file name","text":"

The read-only Source property shows the information of the imported geometry file name. It provides a reference for you to identify the specific imported CAD file.

"},{"location":"welsim/users/steps/#applying-mesh","title":"Applying mesh","text":"

Meshing is the process that your geometry is spatially discretized into finite elements and nodes. The quality of the mesh directly influences the final solutions. You can automatically mesh the geometry domains, and generate 3D tetrahedral elements (Tet10 and Tet4), or 3D triangle elements (Tri6 and Tri3).

If your model does not mesh, the system applies the default settings and automatically meshes the domains at solve time. However, it is recommended to mesh the domain before solving since the system provides a reference for you to examine the mesh. Mesh Settings controls are available to assist you in adjusting the mesh density and quality.

In the multi-body analysis, you can apply local Mesh Method object and scope the target bodies to achieve a finer or coarser mesh comparing to other bodies.

"},{"location":"welsim/users/steps/#defining-connections","title":"Defining connections","text":"

In some analyses, you may need to set up the connections such as contact. The available connection features are:

"},{"location":"welsim/users/steps/#defining-study-settings","title":"Defining study settings","text":"

The Study and Study Settings objects are inserted automatically when you started a new FEM project in the step of Creating Analysis Environment. These two objects define the necessary conditions for the solving, such as steps, substeps, end time, convergence tolerance, etc.

You can create multiple steps in the properties of the Study object. As shown in Figure\u00a0below, the property Number of Steps determines the total steps in the analysis. The Current Step property of determines the current step that other properties are defining on.

The spreadsheet for the Study Settings object displays the related properties for all steps.

"},{"location":"welsim/users/steps/#defining-initial-conditions","title":"Defining initial conditions","text":"

Based on the chosen analysis type, you can define the initial conditions to the analysis. The following initial conditions are supported:

"},{"location":"welsim/users/steps/#applying-boundary-conditions","title":"Applying boundary conditions","text":"

You can impose various boundary conditions based on the types of analysis. For instance, the structural analysis allows you to impose pressure, force, displacement, and other boundary conditions. The thermal analysis enable you to impose thermal flux and temperature boundary conditions.

The body conditions are imposed on the volumes instead of surfaces or edges. For example, the standard earth gravity, acceleration, and rotational velocity act on the bodies.

The boundary and body conditions act according to the steps. For the multi-step analysis, the magnitude of those conditions can vary. The Tabular Data and Chart windows show related data and curves to represent the input values along time/steps.

For the transient analysis, the Initial Status property provides options for the user to define the boundary value at the beginning of the simulation. As shown in Figure\u00a0below, you can choose the initial value to be None or Equal to Step 1.

"},{"location":"welsim/users/steps/#solving","title":"Solving","text":"

The WELSIM application contains the integrated solvers. These solvers are essentially executable applications and can be instantiated by the front-end using inter-processing scheme. During the solving process, the front-end program generates the input scripts, mesh data file and feeds these files to the solvers. After calculation, the front-end interface can consume the generated result files and displays the resulting contour on the GUI.

Depended on the analysis type, the following solvers are available in WELSIM:

"},{"location":"welsim/users/steps/#solution-progress","title":"Solution progress","text":"

The overall solution progress can be indicated by the Output window, where you can view the output information from the solvers. If an calculation is completed successfully, you can see the similar message below in the Output window: 

WelSimFemSolver2 Completed !!\n

"},{"location":"welsim/users/steps/#evaluating-results","title":"Evaluating results","text":"

The WELSIM application provides fully integrated result review module, and you can evaluate simulation results with no need of other software tools. Depends on the analysis type, various results are available for you to examine solutions. The Using Results section lists all available results that may be used in the post-processing.

The following lists the methods to add result objects:

The following steps are to evaluate results:

The following result types are available:

See the Using Results section for more details on results.

"},{"location":"welsim/users/steps/#saving-analysis-project","title":"Saving analysis project","text":"

You can save the solution with all settings into an external file, and open this file later or on a different computer that has WELSIM installed. The persisted data include two parts:

Note

The saved database file (*.wsdb) contains the information of objects and their properties. The geometry data is saved as external STEP files. The mesh and result object settings are saved. However, the mesh and result data are not included yet. You need to perform meshing and solving to obtain those data in a resumed project.

"},{"location":"welsim/users/study/","title":"Configuring study settings","text":"

This section describes the Study and Study Settings configuration.

"},{"location":"welsim/users/study/#general-settings","title":"General settings","text":"

When you start a new FEM Project, the Study and Study Settings objects are inserted in the tree automatically. With these objects selected, you can define many solving options in the Properties View window. For example, you can define the properties of Steps, Substeps, Solver, etc.

"},{"location":"welsim/users/study/#step-controls","title":"Step controls","text":"

Step Controls define the analysis steps for both static and transient analysis. These properties in the Study object has such characteristics:

"},{"location":"welsim/users/study/#nonlinear-controls","title":"Nonlinear controls","text":"

For the nonlinear analysis, the properties of the Nonlinear Settings Controls determine the convergence of the solution. Those properties are mainly related to the Newton-Raphson algorithm.

"},{"location":"welsim/users/study/#solver-controls","title":"Solver controls","text":"

Solver Controls determines the attributes of the linear algebra solvers. The following lists the related properties:

"},{"location":"welsim/users/study/#output-controls","title":"Output controls","text":"

The Output Controls determines the output rules of solving and results. The available options are:

"},{"location":"welsim/vm/electromagnetic/","title":"Electromagnetic","text":"

To be added...

"},{"location":"welsim/vm/introduction/","title":"Introduction","text":"

WELSIM Verification Manual presents a collection of test cases that demonstrate a number of the capabilities of the WELSIM analysis environment. The available tests are engineering problems that provide independent verification, usually a closed form equation. Many of them are classical engineering problems.

"},{"location":"welsim/vm/introduction/#introduction","title":"Introduction","text":""},{"location":"welsim/vm/introduction/#index-of-test-cases","title":"Index of test cases","text":"

The following lists all verification cases tested with WELSIM application. Each case entry describes the test case number, element type, analysis type, and solution options.

"},{"location":"welsim/vm/structural/","title":"Structural","text":""},{"location":"welsim/vm/structural/#statically-inteterminate-reaction-force-analysis-vm001","title":"Statically inteterminate reaction force analysis VM001","text":"

An assembly of three cylinder bars is supported at both end surfaces. Forces \\(F_{1}\\) and \\(F_{2}\\) is applied on the middle of the assembly as shown in Figure\u00a0[fig:ch5_vm_001_schematic].

The input data about material, geometry, and loads are given in Table\u00a0[tab:ch5_vm_001_parameters].

Material Properties Geometric Properties Boundary Conditions Young's Modulus E=2e11 h=10 \\(F_{1}\\)=2000 Mass Density \\(\\rho\\)=7850 a=3 \\(F_{2}\\)=1000 Poission's Ratio v=0.3 b=3

The geometries and imposed boundary conditions are shown in Figure\u00a0[fig:ch5_vm_001_bc].

The result comparison is given in Table\u00a0[tab:ch5_vm_001_result].

Results Theory WELSIM Error (%) Z Reaction Force at Top Fixed Support 1800 1810 0.556 Z Reaction Force at Bottom Fixed Support 1200 1202 0.167

This test case project file is located at [vm/VM_WELSIM_001.wsdb].

"},{"location":"welsim/vm/structural/#rectangular-plate-with-circular-hole-subjected-to-tensile-pressure-vm002","title":"Rectangular plate with circular hole subjected to tensile pressure VM002","text":"

A rectangular plate with a circular hole is fixed along one of the end faces. A tensile pressure load is imposed on another end face as shown in Figure\u00a0[fig:ch5_vm_002_schematic].

The input data about material, geometry, and loads are given in Table\u00a0[tab:ch5_vm_002_parameters].

Material Properties Geometric Properties Boundary Conditions Young's Modulus E=2e11 a=15 Pressure P=1e4 Poission's Ratio v=0.3 b=7.5 c=2.5 d=5 thickness=1

The geometries and imposed boundary conditions are shown in Figure\u00a0[fig:ch5_vm_002_bc].

The result comparison is given in Table\u00a0[tab:ch5_vm_002_result].

Results Theory WELSIM Error (%) Maximum Normal X Stress 3.125e4 3.156e4 0.992

This test case project file is located at %Installation Directory%/vm/VM_WELSIM_002.wsdb.

"},{"location":"welsim/vm/thermal/","title":"Thermal","text":""},{"location":"welsim/vm/thermal/#heat-transfer-in-a-composite-wall-vm003","title":"Heat transfer in a composite wall VM003","text":"

An assembly wall consists of fire brick and insulating brick. The temperature and surface convection coefficient are given for both end surfaces. The simulation tries to find the temperature distribution of the assembly. The schematic view of the model is shown in Figure\u00a0[fig:ch5_vm_003_schematic].

The input data about material, geometry, and loads are given in Table\u00a0[tab:ch5_vm_003_parameters].

Material Properties Geometric Properties Boundary Conditions Thermal conductivity of fire brick wall: \\(k_{F}\\) = 1.852e-5 a=14 Convection coefficient \\(h_{F}\\)=2.315e-5 Thermal conductivity of insulating wall: \\(k_{A}\\)=2.315e-6 b=9 Ambient temperature \\(T_{F}\\)=3000 cross-section=1x1 Convection coefficient \\(h_{A}\\)=3.858e-6 Ambient temperature \\(T_{A}\\)=80

The geometries and imposed boundary conditions are shown in Figure\u00a0[fig:ch5_vm_003_bc].

The result comparison is given in Table\u00a0[tab:ch5_vm_003_result].

Results Theory WELSIM Error (%) Minimum Temperature 336 336.724 0.215 Maximum Temperature 2957 2957.216 0.007

Info

This test case file is located at vm/VM_WELSIM_003.wsdb.

"}]} \ No newline at end of file +{"config":{"lang":["en"],"separator":"[\\s\\-\\.]+","pipeline":["stopWordFilter"]},"docs":[{"location":"","title":"Welcome","text":"

WELSIM was born out of a vision to create a general-purpose simulation utility that could successfully enable a wide range of engineering and science communities to conduct simulation with more confidence. Customers use our software to help ensure the integrity of their innovations. WELSIM comes with an all-in-one user interface and self-integrated features. It is a long-term-support product that aims to accurately model engineering problems using the prestigious open source solvers.

"},{"location":"#why-welsim","title":"Why WELSIM","text":""},{"location":"#where-to-start","title":"Where to start","text":"

Engineers can do a thousand things with the WELSIM simulation solutions. We recommend starting with:

If you already use WELSIM:

If you are interested in our free engineering software:

Last Updated: Oct. 14th, 2024

"},{"location":"features/","title":"Features","text":"

As a general-purpose engineering simulation software program, WELSIM contains tons of features those allow you to conduct various simulation studies.

"},{"location":"features/#specification","title":"Specification","text":"Specification Description Operaton system Microsoft Windows 10/11, 64-bit; Linux: Ubuntu 22.04 LTS and higher versions, 64-bit; 3D rendering driver: OpenGL 3.2 or higher Physical memory At least 4 GB, and 32 GB and higher is recommended Geometry modules Imported geometry formats: STEP, IGES, STL, GDS Built-in geometry generation: Box, Cylinder, Sphere, Plane, Line, Circle, Vertex Boolean operations: Union, Intersection, Cut Supported automatic mesh Tet10, Tet4, Tri6, Tri3 "},{"location":"features/#structural","title":"Structural","text":"Structural analysis Description Types Static, transient, and modal Materials Isotropic elastic, hyper-elastic, plastic, visco-elastic, and creep Deformation types Small, and finite Contact types bonded, frictionless, and frictional; small and finite sliding Boundary conditions constraints, displacement, force, pressure, velocity, acceleration Body conditions body force, acceleration, standard earth gravity, rotational velocity Results deformations, stresses, strains, velocity, acceleration Probe results reaction force (total, x, y, z) "},{"location":"features/#explicit-structural-dynamics-using-openradioss","title":"Explicit Structural Dynamics (using OpenRadioss)","text":"Structural analysis Description Materials Isotropic elasto-plastic (Johnson-Cook, Zerillii-Armstrong, Gray, Cowper-Symonds, Yoshida-Uemori, Hensel-Spittel, voce), Isotropic linear elastic (Hooke's law, Johnson-Cook), hyper-elastic (Ogden, Neo-Hookean, Mooney\u2013Rivlin), visco-elastic (Boltamann, Generalized Maxwell-Kelvin), creep, explosive (JWL), Rock (Drucker-Prager), Hill orthotropic Equation of state Compaction, Gruneisen, ideal gas, linear, LSZK, Murnaghan, NASG, Noble, Polynomial, Puff, Sesame, Tillotson Failure models Alter, Biquad, Chang, Cockcroft, EMC, Energy, Fabric, forming limit diagram, Gurson, Hashin, Johnson, Ladeveze, Mullins effect with Ogden and Roxburgh criteria, NXT, orthotropic biquad, Puck, Spalling, Wierzbicki Element type Solid, shell Contact types bonded, frictionless, and frictional; small and finite sliding Boundary conditions constraints, displacement, force, pressure, velocity, acceleration, etc. Body conditions rigid body, body force, acceleration, standard earth gravity, rotational velocity, etc. Results deformations, stresses, strains, velocity, acceleration, etc"},{"location":"features/#thermal","title":"Thermal","text":"Thermal analysis Description Types Static, and transient Materials linear and nonlinear Initial conditions Initial temperature Boundary conditions temperature, convection, radiation, heat flux, heat flow, perfectly insulated Body conditions Internal heat generation Results temperature "},{"location":"features/#computational-fluid-dynamics-through-su2","title":"Computational Fluid Dynamics (through SU2)","text":"Fluid analysis Description Types Steady-state, and transient Governing equation Euler, Navier-Stokes, RANS Boundary conditions wall, inlet, outlet, pressure, velocity, temperature, convection, heat flux Results velocity, pressure, mass density, pressure coefficient, mach number, energy "},{"location":"features/#electromangetic","title":"Electromangetic","text":"Electromagnetic analysis Description Types Electrostatic, magnetostatic, eigenmode, driven, full-wave transient Materials linear Boundary conditions ground, voltage, symmetry, zero charge, surface charge density, electric displacement, insulting, magnetic vector potential, magnetic flux density Results voltage, electric field, electric displacement, magnetic vector potential, magnetic flux density, magnetic field, energy density "},{"location":"features/#need-new-features","title":"Need new features?","text":"

Feel free to send questions, comments, requests, bug reports, and success stories. Asking for a new feature usually results in adding the request to the TODO list or, if it already is in the list, in assigning higher priority to it.

"},{"location":"glossary/","title":"Glossary","text":""},{"location":"glossary/#a","title":"A","text":""},{"location":"glossary/#b","title":"B","text":""},{"location":"glossary/#c","title":"C","text":""},{"location":"glossary/#d","title":"D","text":""},{"location":"glossary/#e","title":"E","text":""},{"location":"glossary/#f","title":"F","text":""},{"location":"glossary/#g","title":"G","text":""},{"location":"glossary/#h","title":"H","text":""},{"location":"glossary/#i","title":"I","text":""},{"location":"glossary/#j","title":"J","text":""},{"location":"glossary/#k","title":"K","text":""},{"location":"glossary/#l","title":"L","text":""},{"location":"glossary/#m","title":"M","text":""},{"location":"glossary/#n","title":"N","text":""},{"location":"glossary/#o","title":"O","text":""},{"location":"glossary/#p","title":"P","text":""},{"location":"glossary/#r","title":"R","text":""},{"location":"glossary/#s","title":"S","text":""},{"location":"glossary/#t","title":"T","text":""},{"location":"glossary/#u","title":"U","text":""},{"location":"glossary/#v","title":"V","text":""},{"location":"glossary/#w","title":"W","text":""},{"location":"glossary/#y","title":"Y","text":""},{"location":"glossary/#z","title":"Z","text":""},{"location":"license/","title":"License","text":""},{"location":"license/#welsim-license","title":"WELSIM License","text":"

WELSIM SOFTWARE LICENSE AGREEMENT Copyright (C) 2017-2024 WELSIMULATION LLC Version effective date: August 10, 2017

READ THIS SOFTWARE LICENSE AGREEMENT CAREFULLY BEFORE PROCEEDING. THIS IS A LEGALLY BINDING CONTRACT BETWEEN LICENSEE AND LICENSOR FOR LICENSEE TO USE THE PROGRAM(S), AND IT INCLUDES DISCLAIMERS OF WARRANTY AND LIMITATIONS OF LIABILITY. WELSIMULATION LLC IS WILLING TO LICENSE THE SOFTWARE ONLY UPON THE CONDITION THAT YOU ACCEPT ALL OF THE TERMS CONTAINED IN THIS SOFTWARE LICENSE AGREEMENT. PLEASE READ THE TERMS CAREFULLY. BY CLICKING ON \"I AGREE\" OR BY INSTALLING THE SOFTWARE, YOU WILL INDICATE YOUR AGREEMENT WITH THEM. IF YOU ARE ENTERING INTO THIS AGREEMENT ON BEHALF OF A COMPANY OR OTHER LEGAL ENTITY, YOUR ACCEPTANCE REPRESENTS THAT YOU HAVE THE AUTHORITY TO BIND SUCH ENTITY TO THESE TERMS, IN WHICH CASE \"YOU\" OR \"YOUR\" SHALL REFER TO YOUR ENTITY. IF YOU DO NOT AGREE WITH THESE TERMS, OR IF YOU DO NOT HAVE THE AUTHORITY TO BIND YOUR ENTITY, THEN WELSIMULATION LLC IS UNWILLING TO LICENSE THE SOFTWARE, AND YOU SHOULD NOT INSTALL THE SOFTWARE.

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THE ACCOMPANYING PROGRAM IS PROVIDED UNDER THE TERMS OF THIS COMMON PUBLIC LICENSE (\"AGREEMENT\"). ANY USE, REPRODUCTION OR DISTRIBUTION OF THE PROGRAM CONSTITUTES RECIPIENT'S ACCEPTANCE OF THIS AGREEMENT.

This software is provided 'as-is', without any express or implied warranty. In no event will the authors be held liable for any damages or consequences arising from the use of this software.

  1. Parties. The parties to this Agreement are you, the licensee (\"You\") and WELSIMULATION LLC. If You are not acting on behalf of Yourself as an individual, then \"You\" means Your company or organization. A company or organization shall in either case mean a single business entity, and shall not include its affiliates or wholly owned subsidiaries.

  2. The Software. The accompanying materials including, but not limited to, source code, binary executables, documentation, images, and scripts, which are distributed by WELSIMULATION LLC, and derivatives of that collection and/or those files are referred to herein as the \"Software\".

  3. Restrictions. WELSIMULATION LLC encourages You to promote use of the Software. However this Agreement does not grant permission to use the trade names, trademarks, service marks, or product names of WELSIMULATION LLC, except as required for reasonable and customary use in describing the origin of the Software. In particular, You cannot use any of these marks in any way that might state or imply that WELSIMULATION LLC endorses Your work, or might state or imply that You created the Software covered by this Agreement. Except as expressly provided herein, you may not:

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  5. Infringement Indemnification. You shall defend or settle, at Your expense, any action brought against WELSIMULATION LLC based upon the claim that any modifications to the Software or combination of the Software with products infringes or violates any third party right; provided, however, that: (i) WELSIMULATION LLC shall notify Licensee promptly in writing of any such claim; (ii) WELSIMULATION LLC shall not enter into any settlement or compromise any such claim without Your prior written consent; (iii) You shall have sole control of any such action and settlement negotiations; and (iv) WELSIMULATION LLC shall provide You with commercially reasonable information and assistance, at Your request and expense, necessary to settle or defend such claim. You agree to pay all damages and costs finally awarded against WELSIMULATION LLC attributable to such claim.

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  7. Licensee Outside The U.S. If You are located outside the U.S.,then the following provisions shall apply: (i) The parties confirm that this Agreement and all related documentation is and will be in the English language; and (ii) You are responsible for complying with any local laws in your jurisdiction which might impact your right to import, export or use the Software, and You represent that You have complied with any regulations or registration procedures required by applicable law to make this license enforceable.

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"},{"location":"misc/","title":"MISC","text":""},{"location":"misc/#comparison-explicit-and-implicit-time-integrations","title":"Comparison explicit and implicit time integrations","text":"\u663e\u5f0f\u7b97\u6cd5 \u9690\u5f0f\u7b97\u6cd5 \u9002\u7528\u95ee\u9898 \u52a8\u529b\u5b66\uff08\u52a8\u6001\uff09 \u9759\u529b\u5b66\uff08\u9759\u6001\uff09\u548c\u52a8\u529b\u5b66\uff08\u52a8\u6001\uff09 \u963b\u5c3c \u4eba\u5de5\u963b\u5c3c \u6570\u503c\u963b\u5c3c \u65f6\u95f4\u6b65\u6c42\u89e3\u65b9\u6cd5 \u77e9\u9635\u4e58\u6cd5 \u7ebf\u6027\u65b9\u7a0b\u7ec4 \u7ec4\u88c5\u521a\u5ea6\u77e9\u9635 \u5426 \u662f \u6570\u636e\u5b58\u50a8\u9700\u6c42 \u5c0f \u5927 \u6bcf\u6b65\u8ba1\u7b97\u901f\u5ea6 \u5feb \u4e2d \u8fed\u4ee3\u6536\u655b\u6027 \u65e0 \u6709 \u786e\u5b9a\u6027 \u6709\u786e\u5b9a\u89e3 \u53ef\u80fd\u662f\u75c5\u6001\u65e0\u786e\u5b9a\u89e3 \u65f6\u95f4\u7a33\u5b9a\u6027 \u6709\u6761\u4ef6 \u65e0\u6761\u4ef6 \u65f6\u95f4\u6b65 \u5c0f \u5927 \u8ba1\u7b97\u7cbe\u5ea6 \u4f4e \u9ad8 Explicit method Implicit method Target problems Dynamic(transient) Static and dynamic(transient) Damping Artificial damping Numerical damping Time stepping method Matrix multiplication Linear algebra equations Assemble stiffness matrix No Yes Data storage requirement Small Large Solving speed each step Quick Mediate Iteration convergence No Yes Solution Certain solution Could be uncertain solution Stability Conditionally stable Unconditionally stable Time step Small Large Accuracy Low High \u5e94\u529b-\u5e94\u53d8\u66f2\u7ebf\u542b\u6709 \u9002\u7528\u7684Mooney-Rivlin\u51fd\u6570 \u53c2\u6570\u6b63\u5b9a\u6027\u8981\u6c42 \u6ca1\u6709\u62d0\u70b9(\u5355\u66f2\u7387) 2-\u62163-\u53c2\u6570 C10 + C01 > 0 1\u4e2a\u62d0\u70b9(\u53cc\u66f2\u7387) 5-\u53c2\u6570

C10 + C01 > 0C20 > 0C02 < 0C20 + C11 + C02 > 0

2\u4e2a\u62d0\u70b9 9-\u53c2\u6570

C10 + C01 > 0C30>0C03 < 0C30 + C21 + C12 + C03 > 0

Strain-stress curve Suitable Mooney-Rivlin model Parameter requirement for positive definiteness No inflection point (single curvature) 2- or 3-parameter C10 + C01 > 0 One inflection point (double curvature) 5-parameter

C10 + C01 > 0C20 > 0C02 < 0C20 + C11 + C02 > 0

Two inflection points 9-parameter

C10 + C01 > 0C30>0C03 < 0C30 + C21 + C12 + C03 > 0

"},{"location":"support/","title":"Support","text":"

Thanks so much for choosing WELSIM! At WELSIM, we want all engineers and scientists to excel. We believe that given the right tools and guidance, all engineers can be highly productive. We strive to provide tools that give their users super powers and we\u2019re happy to provide any guidance we can to help you use them most effectively. If you have any questions or need any help of any kind, don\u2019t hesitate to contact us in whatever way is most convenient for you.

We exist to help you be as productive you can be. Let us know how we can help you. Happy simulation!

"},{"location":"beamsection/beamsection_getstart/","title":"Getting Started","text":"

Using BeamSection is straightforward, this section shows you how to calculate the beam properties step by step.

"},{"location":"beamsection/beamsection_getstart/#graphical-interface","title":"Graphical Interface","text":"

An overview of the Graphical User Interface (GUI) with notation is shown in the figure below.

"},{"location":"beamsection/beamsection_getstart/#menu","title":"Menu","text":"

This section provides you basic actions in using CurveFitter. The actions include:

"},{"location":"beamsection/beamsection_getstart/#toolbox","title":"Toolbox","text":"

This section lists all available curves for you to choose from. The default curve is the straight line (first-order polynomial). The curves are grouped by the characteristics as follows.

"},{"location":"beamsection/beamsection_getstart/#basic-curves","title":"Basic Curves","text":"

Straight line, Natural logarithm, Exponential, Power, Gaussian

"},{"location":"beamsection/beamsection_getstart/#polynomial-curves","title":"Polynomial Curves","text":"

2nd Order Polynomial, 3rd Order Polynomial, 4th Order Polynomial, 5th Order Polynomial

"},{"location":"beamsection/beamsection_getstart/#nonlinear-curves","title":"Nonlinear Curves","text":"

Symmetrical Sigmoidal, Asymmetrical Sigmoidal, Rectangular Hyperbola, Basic Exponential, Half-Life Exponential, Proportional Rate Growth or Decrease

"},{"location":"beamsection/beamsection_getstart/#hyperelastic-material-model-curves","title":"Hyperelastic Material Model Curves","text":"

Arruda-Boyce, Gent, Mooney-Rivlin 2, 3, 5, and 9 Parameters, Neo-Hookean, Ogden 1st-3rd Orders, Polynomial 1st-3rd Orders, Yeoh 1st-3rd Orders

"},{"location":"beamsection/beamsection_getstart/#electromagnetic-model-curves","title":"Electromagnetic Model Curves","text":"

Electrical Steel, Power Ferrite

"},{"location":"beamsection/beamsection_getstart/#curve-description","title":"Curve Description","text":"

This section contains details about the selected curve, such as the function or energy functional, parameters to fit, variable descriptions.

For the hyperelastic model curves, additional Hyperelastic Test Data checkboxes shows in this seciton. It allows users to set/edit the test data at different deformations.

"},{"location":"beamsection/beamsection_getstart/#fitted-parameters","title":"Fitted Parameters","text":"

This section outputs the fitted parameters for users. You also can edit the constants in the line edit widget and review the curves in the Chart window.

"},{"location":"beamsection/beamsection_getstart/#actions","title":"Actions","text":"

There are three actions provided for users to analyze or fit the test data.

"},{"location":"beamsection/beamsection_getstart/#chart-windows","title":"Chart Windows","text":"

This section displays the test data dots and fitted curves in the same window, these dots and curves can be differentiated by legends and colors. Zoom in and out showing area are supported. You also can set the logarithmic axis for the curve display.

"},{"location":"beamsection/beamsection_getstart/#workflow","title":"Workflow","text":"

This section demonstrates the procedures in applying curve fitting. The steps are followed:

  1. Select the designated curve type from the toolbox.

  2. Edit table data or import data from an external file.

  3. Review the test data in the Chart.

  4. Check the input data (Optional). A pop-up message box indicates the status of the input data.

  5. Solve the curves with the input tabular data. If it succeeded, the Constants line edits are filled with fitted parameters, and the Chart window displays the fitted curves along with the test data. These fitted parameters are the answers that we want.

  6. Adjust parameters to evaluate the similar curves (Optional). You can change the parameters and hit the Update Chart button to see the new curves with modified parameters.

Note

Your test data is critical for your fitted constants, please ensure that the test data cover the entire range of your curve expreience.

"},{"location":"beamsection/beamsection_overview/","title":"Beam Cross-Section Overview","text":"

BeamSection is a free beam cross-section software program for engineers. This tool provides you comprehensive beam property calculations those are often used in engineering simulation and practice.

"},{"location":"beamsection/beamsection_overview/#questions-or-comments","title":"Questions or Comments?","text":"

Feel free to send questions, comments, requests, bug reports, and success stories. Asking for a new feature usually results in adding the request to the TODO list or, if it already is in the list, in assigning higher priority to it.

"},{"location":"curvefitter/curvefit_getstart/","title":"Getting Started","text":"

Using CurveFitter is straightforward, this section shows you how to conduct the curve fitting step by step.

"},{"location":"curvefitter/curvefit_getstart/#graphical-interface","title":"Graphical Interface","text":"

An overview of the Graphical User Interface (GUI) with notation is shown in the figure below.

"},{"location":"curvefitter/curvefit_getstart/#menu","title":"Menu","text":"

This section provides you basic actions in using CurveFitter. The actions include:

"},{"location":"curvefitter/curvefit_getstart/#toolbox","title":"Toolbox","text":"

This section lists all available curves for you to choose from. The default curve is the straight line (first-order polynomial). The curves are grouped by the characteristics as follows.

"},{"location":"curvefitter/curvefit_getstart/#basic-curves","title":"Basic Curves","text":"

Straight line, Natural logarithm, Exponential, Power, Gaussian

"},{"location":"curvefitter/curvefit_getstart/#polynomial-curves","title":"Polynomial Curves","text":"

2nd Order Polynomial, 3rd Order Polynomial, 4th Order Polynomial, 5th Order Polynomial

"},{"location":"curvefitter/curvefit_getstart/#nonlinear-curves","title":"Nonlinear Curves","text":"

Symmetrical Sigmoidal, Asymmetrical Sigmoidal, Rectangular Hyperbola, Basic Exponential, Half-Life Exponential, Proportional Rate Growth or Decrease

"},{"location":"curvefitter/curvefit_getstart/#hyperelastic-material-model-curves","title":"Hyperelastic Material Model Curves","text":"

Arruda-Boyce, Gent, Mooney-Rivlin 2, 3, 5, and 9 Parameters, Neo-Hookean, Ogden 1st-3rd Orders, Polynomial 1st-3rd Orders, Yeoh 1st-3rd Orders

"},{"location":"curvefitter/curvefit_getstart/#electromagnetic-model-curves","title":"Electromagnetic Model Curves","text":"

Electrical Steel, Power Ferrite

"},{"location":"curvefitter/curvefit_getstart/#curve-description","title":"Curve Description","text":"

This section contains details about the selected curve, such as the function or energy functional, parameters to fit, variable descriptions.

For the hyperelastic model curves, additional Hyperelastic Test Data checkboxes shows in this seciton. It allows users to set/edit the test data at different deformations.

"},{"location":"curvefitter/curvefit_getstart/#fitted-parameters","title":"Fitted Parameters","text":"

This section outputs the fitted parameters for users. You also can edit the constants in the line edit widget and review the curves in the Chart window.

"},{"location":"curvefitter/curvefit_getstart/#actions","title":"Actions","text":"

There are three actions provided for users to analyze or fit the test data.

"},{"location":"curvefitter/curvefit_getstart/#tabular-data-windows","title":"Tabular Data Windows","text":"

This section enables you to edit and review the table data. For most of curves, the tables have two columns. The frequency-dependent curves have a sub-table for each frequency row. You can input tabular values cell by cell, or import a plain text or Excel file to input massive data. The external file formats are depicted here.

You also can export the tabular data to an external file in plain text or Excel format.

"},{"location":"curvefitter/curvefit_getstart/#chart-windows","title":"Chart Windows","text":"

This section displays the test data dots and fitted curves in the same window, these dots and curves can be differentiated by legends and colors. Zoom in and out showing area are supported. You also can set the logarithmic axis for the curve display.

"},{"location":"curvefitter/curvefit_getstart/#workflow","title":"Workflow","text":"

This section demonstrates the procedures in applying curve fitting. The steps are followed:

  1. Select the designated curve type from the toolbox.

  2. Edit table data or import data from an external file.

  3. Review the test data in the Chart.

  4. Check the input data (Optional). A pop-up message box indicates the status of the input data.

  5. Solve the curves with the input tabular data. If it succeeded, the Constants line edits are filled with fitted parameters, and the Chart window displays the fitted curves along with the test data. These fitted parameters are the answers that we want.

  6. Adjust parameters to evaluate the similar curves (Optional). You can change the parameters and hit the Update Chart button to see the new curves with modified parameters.

Note

Your test data is critical for your fitted constants, please ensure that the test data cover the entire range of your curve expreience.

"},{"location":"curvefitter/curvefit_io/","title":"I/O File Format","text":"

The I/O file format is consistent to the Import/Export format in MatEditor module. For more details please refer to the Import/Export Tabular Data

"},{"location":"curvefitter/curvefit_overview/","title":"Curve Fitter Overview","text":"

CurveFitter is a free software program for nonlinear curve fitting of analytical functions to experimental data. It provides tools for linear, polynomial, exponential, power, Schulz-Flory, nonlinear, hyperelastic materials, magnetic core loss curve fitting along with validation, and goodness-of-fit tests. The easy-to-use graphical user interface enables you to start fitting projects with no learning curves. You can summarize and present your results with customized fitting reports. There are many time-saving options such as an import-export feature which allows you to quickly input/output massive tabular data from/to external files.

Curve fitting is one of the most widely used analysis methods in science and technology. Curve fitting examines the relationship between one or more predictors (independent variables) and a response variable (dependent variable), with the goal of defining a \"best fit\" model of the relationship. It is reportedly used in crystallography, chromatography, photoluminescence and photoelectron spectroscopy, infrared, Raman spectroscopy, and finite element analysis.

"},{"location":"curvefitter/curvefit_overview/#specification","title":"Specification","text":"

The system requirements for running CurveFitter are given in the table below.

Specification Description Operation system Microsoft Windows 10 to 11; 64-bit Physical memory At least 4 GB Import/Export file format Plain text, Excel

The supported functions/curves are listed in the table below.

Category Materials Basic Straight line, Natural logarithm, Exponential, Power, Gaussian Polynomial 2nd-5th Order Polynomial Schulz-Flory 1nd-6th Order Schulz-Flory Nonlinear Symmetrical Sigmoidal, Asymmetrical Sigmoidal, Rectangular Hyperbola, Basic Exponential, Half-Life Exponential, Proportional Rate Growth or Decrease Hyperelastic material model Arruda-Boyce, Gent, Mooney-Rivlin 2 3 5 and 9 Parameters, Neo-Hookean, 1st-3rd Order Ogden, 1st-3rd Order Polynomial, 1st-3rd Order Yeoh Electromagnetic Core loss Model Electrical Steel, Power Ferrite (Steinmetz)"},{"location":"curvefitter/curvefit_overview/#linear-polynomial-regression","title":"Linear, Polynomial Regression","text":"

Linear and Polynomial regressions in CurveFitter make use of the least-square method to fit a linear model function or a polynomial model function to data, respectively.

"},{"location":"curvefitter/curvefit_overview/#nonlinear-curve-fitting","title":"Nonlinear Curve Fitting","text":"

CurveFitter's nonlinear fit tool is powerful, flexible, and easy to use. This tool includes more than 10 built-in fitting functions, selected from a wide range of categories and disciplines.

"},{"location":"curvefitter/curvefit_overview/#hyperelastic-material-model-fitting","title":"Hyperelastic Material Model Fitting","text":"

CurveFitter's hyperelastic model fitting tool allows you to obtain material constants from the uniaxial, biaxial, or shear test data. You can choose the available test data type by toggling the corresponding checkbox. The supported hyperelastic models are: Arruda-Boyce, Gent, Mooney-Rivlin, Neo-Hookean, Ogden, Polynomial, and Yeoh. The input test data is engineering strain and engineering stress.

"},{"location":"curvefitter/curvefit_overview/#magnetic-core-loss-model-fitting","title":"Magnetic Core Loss Model Fitting","text":"

Core Loss Model fitting tool enables you to fit the parameters in estimating energy loss analysis. The tabular data window contains both regular tables and sub-tables for you to input multiple frequency-based data. The chart supports the logarithmic axis to better review the frequency-based curves.

"},{"location":"curvefitter/curvefit_overview/#questions-or-comments","title":"Questions or Comments?","text":"

Feel free to send questions, comments, requests, bug reports, and success stories. Asking for a new feature usually results in adding the request to the TODO list or, if it already is in the list, in assigning higher priority to it.

"},{"location":"curvefitter/curvefit_theory/","title":"Curve Fitting Theory","text":"

The section shows you the theoretical details of each curve or function.

"},{"location":"curvefitter/curvefit_theory/#basic-curves","title":"Basic Curves","text":"

The group of Basic contains all commonly used curves.

"},{"location":"curvefitter/curvefit_theory/#straight-line","title":"Straight line","text":"

The function of this curve is given by

\\[ y(x)=a+bx \\]

where \\(a\\) and \\(b\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair. This function is also called 1st order polynomial.

"},{"location":"curvefitter/curvefit_theory/#natural-logarithm","title":"Natural logarithm","text":"

The function of this curve is given by

\\[ y(x)=a+b \\cdot ln(x) \\]

where \\(a\\) and \\(b\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

Note

Independent variable \\(x\\) must be larger than zero.

"},{"location":"curvefitter/curvefit_theory/#exponential","title":"Exponential","text":"

The function of this curve is given by

\\[ y(x)=ae^{bx} \\]

where \\(a\\) and \\(b\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

Note

Dependent variable \\(y\\) must be larger than zero.

"},{"location":"curvefitter/curvefit_theory/#power","title":"Power","text":"

The function of this curve is given by

\\[ y(x)=ax^{b} \\]

where \\(a\\) and \\(b\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

Note

Variables \\(x\\) and \\(y\\) must be larger than zero.

"},{"location":"curvefitter/curvefit_theory/#gaussian","title":"Gaussian","text":"

The function of this curve is given by

\\[ y(x)=a \\exp{(-\\dfrac{(x-b)^2}{2c^2})} \\]

where \\(a\\), \\(b\\), and \\(c\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

Note

Dependent variables \\(y\\) must be larger than zero.

"},{"location":"curvefitter/curvefit_theory/#polynomial-curves","title":"Polynomial Curves","text":"

The group of Polynomial contains polynomial curves. The first-order polynomial is located in the Basic group as Straight Line.

"},{"location":"curvefitter/curvefit_theory/#2nd-order-polynomial","title":"2nd Order Polynomial","text":"

The function of this curve is given by

\\[ y(x)=a+bx+cx^2 \\]

where \\(a\\), \\(b\\), and \\(c\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

"},{"location":"curvefitter/curvefit_theory/#3rd-order-polynomial","title":"3rd Order Polynomial","text":"

The function of this curve is given by

\\[ y(x)=a+bx+cx^2+dx^3 \\]

where \\(a\\), \\(b\\), \\(c\\), and \\(d\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

"},{"location":"curvefitter/curvefit_theory/#4th-order-polynomial","title":"4th Order Polynomial","text":"

The function of this curve is given by

\\[ y(x)=a+bx+cx^2+dx^3+ex^4 \\]

where \\(a\\), \\(b\\), \\(c\\), \\(d\\), and \\(e\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

"},{"location":"curvefitter/curvefit_theory/#5th-order-polynomial","title":"5th Order Polynomial","text":"

The function of this curve is given by

\\[ y(x)=a+bx+cx^2+dx^3+ex^4+ex^5 \\]

where \\(a\\), \\(b\\), \\(c\\), \\(d\\), \\(e\\), and \\(f\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

"},{"location":"curvefitter/curvefit_theory/#schulz-flory-functions","title":"Schulz-Flory functions","text":"

Schulz Flory distribution function to describe relative ratios of polymers after a polymerization process. The function of this curve is given by

\\[ y(x) = \\sum_{i=1}^{n} ln(10) \\dfrac{a_i}{b_i^2} \\exp{(4.6x-\\dfrac{\\exp{(2.3x)}}{b_i})} \\]

where \\(a_i\\) and \\(b_i\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair. The parameter must satisfy the condition: \\(0<a_i<1\\).

"},{"location":"curvefitter/curvefit_theory/#nonlinear-curves","title":"Nonlinear Curves","text":"

The group of Nonlinear curves contains nonlinear curves that do not belong to the polynomial.

"},{"location":"curvefitter/curvefit_theory/#symmetrical-sigmoidal","title":"Symmetrical Sigmoidal","text":"

The function of this curve is given by

\\[ y(x)=d + \\dfrac{a-d}{1+(\\dfrac{x}{c})^b} \\]

where \\(a\\), \\(b\\), \\(c\\), and \\(d\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

"},{"location":"curvefitter/curvefit_theory/#asymmetrical-sigmoidal","title":"Asymmetrical Sigmoidal","text":"

The function of this curve is given by

\\[ y(x)=d + \\dfrac{a-d}{ (1+(\\dfrac{x}{c})^b)^m } \\]

where \\(a\\), \\(b\\), \\(c\\), \\(d\\), and \\(m\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

"},{"location":"curvefitter/curvefit_theory/#rectangular-hyperbola","title":"Rectangular Hyperbola","text":"

The function of this curve is given by

\\[ y(x)=\\dfrac{V_{max}x}{ K_m + x} \\]

where \\(V_{max}\\) and \\(K_m\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

"},{"location":"curvefitter/curvefit_theory/#basic-exponential","title":"Basic Exponential","text":"

The function of this curve is given by

\\[ y(x)=a + be^{-cx} \\]

where \\(a\\), \\(b\\), and \\(c\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

"},{"location":"curvefitter/curvefit_theory/#half-life-exponential","title":"Half-Life Exponential","text":"

The function of this curve is given by

\\[ y(x)=a + \\dfrac{b}{2^{(\\dfrac{x}{c})}} \\]

where \\(a\\), \\(b\\), and \\(c\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

"},{"location":"curvefitter/curvefit_theory/#proportional-rate-growth-or-decrease","title":"Proportional Rate Growth or Decrease","text":"

The function of this curve is given by

\\[ y(x)=Y_0 + \\dfrac{V_0}{K}(1-e^{-Kx}) \\]

where \\(Y_0\\), \\(V_0\\), and \\(K\\) are constants to fit, \\(x\\) and \\(y\\) are the test data pair.

"},{"location":"curvefitter/curvefit_theory/#log-normal-particle-size-distribution","title":"Log-Normal Particle Size Distribution","text":"

The function of this curve is given by

\\[ \\dfrac{dy(x)}{d\\ln{x}}=\\dfrac{C_t}{\\sigma_g\\sqrt{2}\\pi} \\exp{(-\\dfrac{(\\ln{x}-\\ln{D_m})^2}{2\\ln{\\sigma_g}^2})} \\]

where \\(D_m\\), \\(\\sigma_g\\), and \\(C_t\\) are constants to fit, x and y are test data pair. In the computation, the Left-Hand-Side term (\\(dy(x)/d\\ln{x}\\)) is calculated using finite difference scheme.

Note

Independent variables \\(x\\) must be larger than zero. The number of input x-y pairs must be large than 3.

"},{"location":"curvefitter/curvefit_theory/#hyperelastic-material-model-curves","title":"Hyperelastic Material Model Curves","text":"

The group of hyperelastic material models contains the commonly used hyperelastic models in the finite element analysis. The test data pair is engineering strain and stress.

"},{"location":"curvefitter/curvefit_theory/#arruda-boyce","title":"Arruda-Boyce","text":"

The form of the strain-energy potential for Arruda-Boyce model is

\\[ \\begin{array}{ccl} W & = & \\mu[\\dfrac{1}{2}(\\bar{I}_{1}-3)+\\dfrac{1}{20\\lambda_{m}^{2}}(\\bar{I_{1}^{2}}-9)+\\dfrac{11}{1050\\lambda_{m}^{4}}(\\bar{I_{1}^{3}}-27)\\\\ & + & \\dfrac{19}{7000\\lambda_{m}^{6}}(\\bar{I_{1}^{4}}-81) + \\dfrac{519}{673750\\lambda_{m}^{8}}(\\bar{I_{1}^{5}}-243)] \\end{array} \\]

where \\(\\mu\\) is the initial shear modulus of the material, \\(\\lambda_{m}\\) is limiting network stretch.

"},{"location":"curvefitter/curvefit_theory/#gent","title":"Gent","text":"

The form of the strain-energy potential for the Gent model is:

\\[ W=-\\frac{\\mu J_{m}}{2}\\mathrm{ln}\\left(1-\\frac{\\bar{I}_{1}-3}{J_{m}}\\right) \\]

where \\(\\mu\\) is the initial shear modulus of the material, \\(J_m\\) is limiting value of \\(\\bar{I}_1-3\\).

"},{"location":"curvefitter/curvefit_theory/#mooney-rivlin-2-3-5-and-9-parameters","title":"Mooney-Rivlin 2 3 5 and 9 Parameters","text":"

This model includes two-, three-, five-, and nine-terma Mooney-Rivlin models. The form of the strain-energy potential for a two-parameter Mooney-Rivlin model is

\\[ W=C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right) \\]

where \\(C_{10}\\), \\(C_{01}\\), and \\(D_{1}\\) are the material constants.

The form of strain-energy potential for a three-parameter Mooney-Rivlin model is

\\[ W=C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right)+C_{11}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right) \\]

where \\(C_{10}\\), \\(C_{01}\\), and \\(C_{11}\\) are material constants.

The form of strain-energy potential for a five-parameter Mooney-Rivlin model is

\\[ \\begin{array}{ccl} W & = & C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right)+C_{20}\\left(\\bar{I}_{1}-3\\right)^{2}\\\\ & + & C_{11}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right)+C_{02}\\left(\\bar{I}_{2}-3\\right)^{2} \\end{array} \\]

where \\(C_{10}\\), \\(C_{01}\\), \\(C_{20}\\), \\(C_{11}\\), and \\(C_{02}\\) are material constants.

The form of strain-energy potential for a nine-parameter Mooney-Rivlin model is

\\[ \\begin{array}{ccl} W & = & C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right)+C_{20}\\left(\\bar{I}_{1}-3\\right)^{2}\\\\ & + & C_{11}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right)+C_{02}\\left(\\bar{I}_{2}-3\\right)^{2}+C_{30}\\left(\\bar{I}_{1}-3\\right)^{3}\\\\ & + & C_{21}\\left(\\bar{I}_{1}-3\\right)^{2}\\left(\\bar{I}_{2}-3\\right)+C_{12}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right)^{2}+C_{03}\\left(\\bar{I}_{2}-3\\right)^{3} \\end{array} \\]

where \\(C_{10}\\), \\(C_{01}\\), \\(C_{20}\\), \\(C_{11}\\), \\(C_{02}\\), \\(C_{30}\\), \\(C_{21}\\), \\(C_{12}\\), and \\(C_{03}\\) are material constants.

"},{"location":"curvefitter/curvefit_theory/#neo-hookean","title":"Neo-Hookean","text":"

The Neo-Hookean model is a well-known hyperelastic model with an expanded linear rule (Hooke rule) having isotropy so that it can respond to finite deformation problems. The elastic potential is as follows.

\\[ W=\\frac{\\mu}{2}(\\bar{I}_{1}-3) \\]

where \\(\\mu\\) is initial shear modulus of materials.

"},{"location":"curvefitter/curvefit_theory/#ogden","title":"Ogden","text":"

The strain-energy potential of the Ogden compressible foam model is based on the principal stretches of left Cauchy strain tensor, which has the form:

\\[ W=\\sum_{i=1}^{N}\\frac{\\mu_{i}}{\\alpha_{i}}\\left(\\bar{\\lambda}_{1}^{\\alpha_{i}}+\\bar{\\lambda}_{2}^{\\alpha_{i}}+\\bar{\\lambda}_{3}^{\\alpha_{i}}-3\\right)+\\sum_{k=1}^{N}\\frac{1}{D_{k}}\\left(J-1\\right)^{2k} \\]

where N determines the order of the polynomial, \\(\\mu_i\\), \\(\\alpha_i\\) are material constants. The reduced principal strench is defined by:

\\[ \\bar{\\lambda}_{p}=J^{-\\frac{1}{3}}\\lambda_p,\\; J=(\\lambda_{1}\\lambda_{2}\\lambda_{3})^{\\frac{1}{2}} \\]

When parameters N=1, \\(\\alpha_1\\)=2, the Ogden model is converted to the neo-Hookean model. When parameters N=2, \\(\\alpha_1\\)=2 and \\(\\alpha_2\\)=-2, the Ogden model is converted to the 2-parameter Mooney-Rivlin model.

"},{"location":"curvefitter/curvefit_theory/#polynomial","title":"Polynomial","text":"

The polynomial form of strain-energy potential is:

\\[ W=\\sum_{i+j=1}^{N}c_{ij}\\left(\\bar{I}_{1}-3\\right)^{i}\\left(\\bar{I_{2}}-3\\right)^{j} \\]

where \\(N\\) determines the order of the polynomial, \\(c_{ij}\\) are material constants.

The Polynomial model is converted to following models with specific parameters:

Parameters of Polynomial model Equivalent model N=1, \\(C_{01}\\)=0 neo-Hookean N=1 2-parameter Mooney-Rivlin N=2 5-parameter Mooney-Rivlin N=3 9-parameter Mooney-Rivlin"},{"location":"curvefitter/curvefit_theory/#yeoh","title":"Yeoh","text":"

The Yeoh model is also called the reduced polynomial form. The strain-energy potential is

\\[ W=\\sum_{i=1}^{N}c_{i0}\\left(\\bar{I}_{1}-3\\right)^{i} \\]

where N denotes the order of the polynomial, \\(C_{i0}\\) are material constants. When N=1, Yeoh becomes neo-Hookean model.

"},{"location":"curvefitter/curvefit_theory/#electromagnetic-model-curves","title":"Electromagnetic Model Curves","text":"

This group includes the commonly used fitting curves in the electromagnetic analysis.

"},{"location":"curvefitter/curvefit_theory/#electrical-steel","title":"Electrical Steel","text":"

The iron-core loss without DC flux bias is expressed as the following:

\\[ p_v=P_h+P_c+P_e=K_{f} f (B_m)^2 + K_c (fB_m)^2 + K_e(fB_m)^{1.5} \\]

where

"},{"location":"curvefitter/curvefit_theory/#power-ferrite","title":"Power Ferrite","text":"

The iron-core loss is expressed as the Steinmetz approximation

\\[ p_v=C_m f^x B_m^y \\]

where \\(p_v\\) is the average power density, \\(f\\) is the excitation frequency, and \\(B_m\\) is the peak flux density, is commonly used to characterize core loss data for sinusoidal excitation, but can also be applied to square-wave data.

To linearize the equation for curve fitting, we used base-10 logarithms. The equation above can be rewritten to

\\[ log(p_v)=c + x\\cdot log(f) + y \\cdot(B_m) \\]

where \\(c=log(C_m)\\).

"},{"location":"install/licensing/","title":"WELSIM licensing guide","text":""},{"location":"install/licensing/#preface","title":"Preface","text":"

This document contains information for running the WELSIM License Manager with all WelSimulation LLC products.

"},{"location":"install/licensing/#supported-hardware-platforms","title":"Supported hardware platforms","text":"

This document details information about licensing WelSimulation LLC products on the hardware platforms listed below.

For specific operating system requirements, contact the customer support for the product and platform you are running.

"},{"location":"install/licensing/#conventions-used-in-this-document","title":"Conventions used in this document","text":"

Computer prompts and responses and user input are printed using this font:

/welsim_com/shared_files/licensing/welslic_admin\n

Wild card arguments and variables are italicized. Commands appear in bold face.

"},{"location":"install/licensing/#introduction","title":"Introduction","text":"

WelSimulation LLC uses the internal license manager for all of its licensed products. The communication between the WELSIM applications and license manager occurs through an internal process. The communication is nearly transparent; you should not see any noticeable difference in your day-to-day operation of WELSIM products.

You do not need to run the license manager installation. The license manager is installed together with the WELSIM application package.

"},{"location":"install/licensing/#the-licensing-process","title":"The licensing process","text":"

The licensing process for WELSIM is as follows:

  1. Install the software.
  2. Start the software and generate your unique Computer ID, send the Computer ID to info@welsim.com.
  3. After you receive your license file, run the License Manager Wizard from Toolbar of WELSIM application.
  4. Set up the licensing environment and input license. See Activating the WELSIM.
"},{"location":"install/licensing/#explanation-of-licensing-terms","title":"Explanation of licensing terms","text":"

The main components of the licensing are:

These components are explained in more detail in the following sections.

"},{"location":"install/licensing/#the-license-file","title":"The license file","text":"

Licensing data is stored in a text file called the license file. The license file is created by WelSimulation LLC and is installed by the end user. It contains information about the version, signature, and date.

The default and recommended location for the WELSIM license file (wsimkey.dat) is in the %APPDATA%/WELSIM directory. The application can automatically place the license file at this location after activation. End users can manually copy the license file to that directory, although are not suggested.

"},{"location":"install/licensing/#license-file-format","title":"License file format","text":"

License files usually contain eight lines. You cannot modify any these data items in the license files.

Note

Everything in the license key should be entered exactly as supplied. All data in the license file is case sensitive, unless otherwise indicated.

"},{"location":"install/licensing/#application-line","title":"Application line","text":"

The application line specifies the application name. Normally a license file for WELSIM application uses the \u201c[WELSIM]\u201d. The example of the application line is: 

[WELSIM]\n

"},{"location":"install/licensing/#license-version-line","title":"License version line","text":"

The license version line specifies the version of current license file. The example of the this line is shown below: 

license_verion = 100\n

"},{"location":"install/licensing/#license-signature-line","title":"License signature line","text":"

A license signature line describes the password key to use a product. The example of the signature line is: 

license_signature = Tvp919deAq5od+nCUjRF15mgeBIKCLgscLgvR8eFYAlBrqqcjETIyuY0Lu/brYbOKYrIPOXqFzWn8asLqieImA== \n

"},{"location":"install/licensing/#computer-id-line","title":"Computer ID line","text":"

The computer ID line is the string generated from client's computer. The example of the Computer ID line is: 

client_signature = KXfe-uAAA-KXfe-uQAA\n

"},{"location":"install/licensing/#application-version-lines","title":"Application version lines","text":"

The application version lines include two parts, one is the start version number and another is the end version. The example of the application version lines are: 

from_sw_version = 100\nto_sw_version = 100\n

"},{"location":"install/licensing/#effective-date-lines","title":"Effective date lines","text":"

The effective date lines include both start and end date. The example of the effective date lines are: 

from_date = 2017-07-02\nto_date = 2018-08-02\n

"},{"location":"install/licensing/#sample-license-files","title":"Sample license files","text":"

A sample license file is shown here. This file is for WELSIM v1.8 and later tasks. 

[WELSIM]\nlicense_version = 100\nlicense_signature = Tvp919deAq5od+nCUjRF15mgeBIKCLgscLgvR8eFYAlBrqqcjETIyuY0Lu/brYbOKYrIPOXqFzWn8asLqieImA==\nclient_signature = KXfe-uAAA-KXfe-uQAA\nfrom_sw_version = 100\nto_sw_version = 100\nfrom_date = 2023-07-02\nto_date = 2024-07-02\n

"},{"location":"install/licensing/#recognizing-a-welsim-license-file","title":"Recognizing a WELSIM license file","text":"

If you receive a license file and are not sure if it is a WELSIM license file, you can determine if it is by looking at the contents of the license file. If it is a WELSIM license file, then

"},{"location":"install/licensing/#installing-the-welsim-license-manager","title":"Installing the WELSIM license manager","text":"

The WelSim License Manager is included in the WELSIM application installation. As the user installs the application, the license manager is already installed.

"},{"location":"install/licensing/#troubleshooting","title":"Troubleshooting","text":"

This section lists problems and error messages that you may encounter while setting up licensing. The possible error messages are:

An example of the license message error message is shown in Figure\u00a0[fig:ch10_license_not_found].

"},{"location":"install/linux/","title":"Linux installation guide","text":""},{"location":"install/linux/#installation-prerequisites-for-linux","title":"Installation prerequisites for Linux","text":"

This document describes the steps necessary to correctly install and configure WELSIM application on Linux platforms. These products include:

"},{"location":"install/linux/#system-prerequisites","title":"System prerequisites","text":"

WELSIM application is supported on the Linux platforms and operating system levels listed in Table\u00a0below.

Platform Operating system Availability Linux x64 Ubuntu 22.04 LTS or higher Download

Note

  1. If you run WELSIM on Ubuntu, we recommand Ubuntu 22.04 LTS or higher with the latest libstdc++ and libfortran libraries.
"},{"location":"install/linux/#disk-space-and-memory-requirements","title":"Disk space and memory requirements","text":"

You will need the disk space shown in Table\u00a0below for installation and proper functioning.

Product Disk space Memory WELSIM application at least 1 GB at least 4 GB"},{"location":"install/linux/#platform-details","title":"Platform details","text":"

For all 64-bit Linux platforms, the libraries listed below should be installed.

"},{"location":"install/linux/#installing-the-welsim-for-a-linux-system","title":"Installing the WELSIM for a Linux system","text":"

This section explains how to download and install WELSIM.

You can install WELSIM as root, or non-root; however, if you are root user, you can install the application in the system directory. The application can be used by different users.

"},{"location":"install/linux/#product-download-instructions","title":"Product download instructions","text":"

To download the installation files from our website, you will need to agree the US Export Restrictions. You only need to download one installer file.

  1. From the website1, select the Linux version of WELSIM and click the download button on the webpage.
  2. The downloaded installer file has the name like: WelSim%version%SetupUbuntu.run. For example, the installer of 2024R1 is WelSim28SetupUbuntu.run.
  3. Begin the product installation as described in the next section.
"},{"location":"install/linux/#production-installation","title":"Production installation","text":"

1.Navigate to the directory where you placed the installer file. Run the commands below in a terminal window. Note that we take the version of 2024R1 as an example, if you are installing a different version, replace the installer name in the command line below. 

$ chmod +x WelSim28SetupUbuntu.run\n$ ./WelSim28SetupUbuntu.run\n

Note

Running the installer requires the libxcb-xinerama0 library installed in your system.

2.The WELSIM installation Launcher appears as shown below.

3.Click the Next button to start the installation on your computer.

4.The installation folder setting appears as shown below. You can input your designated directory or keep the default one. After specifying the directory, Click Next.

5.The component selection interface appears as shown below. You can select the components that you want to install. The user can keep the default selection, and know the occupied disk space for this installation. Click Next.

6.The license agreement appears as shown below. Read the agreement, and if you agree to the terms and conditions, select I Agree. Click Next.

7.The installation needs your conformation to start as shown below. Click Install.

8.The installation completed as shown below. Click Next.

"},{"location":"install/linux/#starting-the-software-on-linux","title":"Starting the software on Linux","text":"

After installation, starting the WELSIM software application is straightforward. Here are steps:

1.Install the dependencies to your Ubuntu OS 

sudo apt update\nsudo apt upgrade\nsudo apt install openmpi-bin libomp-dev\n

2.Allocate the installed WELSIM application folder, double click the executable file runWelSim.

Note

If the WELSIM does not start, the executable file may have no exectuable attribute on your machine. You could open a terminal window and type commends below. 

$ chmod +x runWelSim.sh\n$ ./runWelSim.sh \n

3.WELSIM application starts, the GUI shows the system information in Figure\u00a0below.

"},{"location":"install/linux/#uninstalling-the-software","title":"Uninstalling the software","text":"

To uninstall WELSIM, you can browse file explorer into the installation folder, and double click on the Uninstaller. Following the instructions on the Uninstaller, you can remove the application from your computer.

You also can simply delete the installation folder to uninstall the WELSIM.

  1. https://welsim.com/download \u21a9

"},{"location":"install/windows/","title":"Windows installation guide","text":""},{"location":"install/windows/#installation-prerequisites-for-windows","title":"Installation prerequisites for Windows","text":"

This document describes the steps essential to correctly install and configure WELSIM on Windows platform.

"},{"location":"install/windows/#system-prerequisites","title":"System prerequisites","text":"

WELSIM is supported on the following Windows platforms and operating system levels.

Platform Operating System Platform Architecture Availability x64 Windows 11 winx64 Download"},{"location":"install/windows/#disk-space-and-memory-requirements","title":"Disk space and memory requirements","text":"

You will need the disk space shown in Table\u00a0[tab:ch11_win_disk_space] for installation and proper functioning. The numbers listed here are the maximum amount of disk space you will need.

Product Disk Space Memory WELSIM 1 GB at least 4GB"},{"location":"install/windows/#software-prerequisites","title":"Software prerequisites","text":"

You need to have the following software installed on your system. These software prerequisites will be installed automatically when you launch the product installation. If you have finished an installation successfully, the prerequisites executable are located under the %Installed Folder%\\Prerequisites directory.

"},{"location":"install/windows/#digital-signatures","title":"Digital signatures","text":"

WELSIM installer and executable files are signed with digital certificates. The signer name is: WelSimulation LLC.

"},{"location":"install/windows/#platform-details","title":"Platform details","text":""},{"location":"install/windows/#compiler-requirements-for-windows-systems","title":"Compiler requirements for Windows systems","text":"

The compiler requirements for Windows systems are listed in Table\u00a0[tab:ch12_win_compiler_req].

No. WELSIM Compilers 1 Visual Studio 2022 (including the Microsoft C++ compiler) 2 Intel Visual Fortran 2022 compiler

Note

Those compilers are not required if you only use WELSIM application.

"},{"location":"install/windows/#installing-the-welsim-for-a-windows-system","title":"Installing the WELSIM for a Windows system","text":"

This section includes the steps required for installing WELSIM and licensing configuration on one Windows machine.

"},{"location":"install/windows/#downloading-the-installation-file","title":"Downloading the installation file","text":"

To download the installation files from our website, you will need to agree the US Export Restrictions.

You only need to download one installer file.

  1. From the website, select the Windows version of WELSIM and click the download button on the webpage.
  2. The downloaded installer file has the name: WelSim28Setup.exe
  3. Begin the product installation as described in the next section.
"},{"location":"install/windows/#installing-welsim","title":"Installing WELSIM","text":"
  1. Navigate to the directory where you placed the installer file. Run the installer by double click.
  2. The WELSIM installation Launcher appears as shown in Figure\u00a0below.
  3. Click the Next button to start the installation on your computer.
  4. The license agreement appears as shown in Figure\u00a0below. Read the agreement, and if you agree to the terms and conditions, select I Agree. Click Next.
  5. The installation folder setting appears as shown in the figure below. You can input your designated directory or keep the default one. After specifying the directory, Click Next.
  6. The prerequesites libraries installation appears as shown in the figure below. Your system requires these libraries to run the WELSIM application. Click Yes.
  7. The installation completed as shown in the figure\u00a0below. Click Finish.

Note

WELSIM relies on the latest version of Microsoft MPI. If the Microsoft MPI redistributable installation conflicts with your pre-existing MS MPI libraries, please uninstall the pre-existing MPI from the Control Panel and reinstall the WELSIM.

"},{"location":"install/windows/#activating-the-welsim","title":"Activating the WELSIM","text":"

In this section, assuming you already received the license file wsimkey.dat. To activate WELSIM on your computer with client licensing, you can follow the steps below:

  1. Start WELSIM application on your computer.
  2. Click the License Manager from the menu: HELP -> License Manager
  3. WELSIM License Manager user interface appears. There are five buttons on the interface:
    1. Generate Computer ID: generate user's unique ID for license key generation.
    2. Evaluate: click to continue using the trial version.
    3. Exit: quit the License Manager with no software activation.
    4. Buy Now: open your default internet browser and direct your visit to the pricing page.
    5. Enter Code: If you have received the license key file, click this button to import the license file.
  4. If the user are running software at the first time, generate the Computer ID by clicking the button of \u201cGenerate Computer ID\u201d, and send this string (format of xxxx-xxxx-xxxx-xxxx) to info@welsim.com. The user will receive the license key within 24 hours.
  5. After receiving the license file (wsimkey.dat), click \u201cEnter Code\u201d button to import the license. In the License Code interface, the user can paste the license content from clipboard, or directly import the license from file.
  6. Click OK button to activate the WELSIM. A successfully activated software is shown in figure\u00a0below.

"},{"location":"install/windows/#starting-the-software","title":"Starting the software","text":"

After installation, starting the WELSIM software is straightforward. Here are three methods:

  1. Double click the shortcut of WELSIM, if you toggle the option \u201cCreate Desktop Shortcut\u201d during the last step of installation.
  2. Click the shortcut of WELSIM from the Start menu. From Start -> WELSIM ->WELSIM v1.8.
  3. Browse the directory of installation, double click the runWelSim.exe file.

As shown in the figure\u00a0below, WESLIM application is started successfully on the Windows operation system.

"},{"location":"install/windows/#uninstalling-the-software","title":"Uninstalling the software","text":"

Uninstalling the software is straightforward. The user can run the unint.exe from one of methods below:

  1. Click the shortcut of WELSIM uninstaller from the Start menu. From Start -> WELSIM ->Uninstall.
  2. Browse the directory of installation, double click the uninst.exe file.
  3. Unstall the WELSIM application from the system Control Panel.
"},{"location":"legal/","title":"Legal notice","text":""},{"location":"legal/#copyright-and-trademark-information","title":"Copyright and trademark information","text":"

\u00a92023 WelSimulation LLC. All rights reserved. Unauthorized use, distribution or duplication is prohibited.

WELSIM and any and all WelSimulation LLC brand, product, service and feature names, logos and slogans are registered trademarks or trademarks of WelSimulation LLC. or its subsidiaries in the United States or other countries. All other brand, product, service and feature names or trademarks are the property of their respective owners.

"},{"location":"legal/#disclaimer-notice","title":"Disclaimer notice","text":"

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"},{"location":"legal/contact/","title":"WelSimulation LLC contact information","text":"

WelSimulation LLC

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USA

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"},{"location":"legal/trademarks/","title":"WELSIM Trademarks List","text":""},{"location":"mateditor/mat_core_loss/","title":"Core loss model","text":"

The core loss combines eddy current losses and hysteresis losses for a transient solution type. It is a post-processing calculation, based on already calculated transient magnetic field quantities. It is applicable for the evaluation of core losses in steel laminations (frequently used in applications such as electric machines, transformers) or in power ferrites.

Hysteresis loss is associated with loss density fields in 2D and 3D eddy current solutions only. Hysteresis loss is short for magnetic hysteresis loss and represents power loss in some magnetic materials (electric steels or ferrites) in alternating (sinusoidal) magnetic fields. This loss is due to a phenomenon called \"magnetic viscosity\" which causes the B and H fields to have a phase shift between them. In the B-H plane, for linear materials, the relationship between these two fields describes an ellipse. The hysteresis loss is proportional to the area of the ellipse.

"},{"location":"mateditor/mat_core_loss/#core-loss-models-for-an-electromagnetic-material","title":"Core loss models for an electromagnetic material","text":"

MatEditor provides two core loss models: electrical steel and power ferrite. The coefficients are given in the table below.

Type Associated properties Electrical Steel Hystersis coefficient \\(K_h\\), Classcial eddy coefficient \\(K_c\\), Excess coefficient \\(K_e\\). Power Ferrite Steinmetz coefficients \\(C_m\\), \\(X\\), and \\(Y\\).

Note

In Transient Solver, X must be less than Y.

"},{"location":"mateditor/mat_core_loss/#calculating-properties-for-core-loss-b-p-curve","title":"Calculating properties for core loss (B-P curve)","text":"

To be able to extract parameters from the loss characteristics (B-P Curve), you first set the Core Loss Model of the material to Electrical Steel or Power Ferrite as a material property in the Property View.

Additional parameters appear in the following table Core Loss Model (\\(K_h\\), \\(K_c\\), and \\(K_e\\) for electrical steel, and \\(C_{m}\\), \\(X\\), and \\(Y\\) for power ferrite). If the P-B test data is already presented in the current material, you can add curve fitting property from the RMB context menu. This allows the electrical steel coefficients \\(K_h\\), \\(K_c\\), and \\(K_e\\), or the power ferrite coefficients \\(C_m\\), \\(X\\), and \\(Y\\) to be derived from a manufacturer-provided core loss curve.

Node

The accuracy in inputting the data for B-P Curve for the electrical steel material has a significant effect on the correctness of the analyses to the electromagnetic devices. You should input the data for B-P Curve according to accurate data provided by material manufacturers. Typically core material suppliers provide the average loss over a cycle for a peak B, of sinusoidal nature. Therefore for BP curve input in WelSim, B (Tesla) should be peak and P should be average.

As the input data (value or unit) changes, the following parameters are not automatically updated unless you resolve the curve fitting:

"},{"location":"mateditor/mat_core_loss/#calculate-core-loss-coefficients-from-loss-curves","title":"Calculate core loss coefficients from loss curves","text":"

This section introduces how to calculate core loss coefficients for electrical steel and power ferrite materials according to the given P-B test data.

  1. Add P-B Test Data material property, and edit the frequency-based data. You also can import the data from a plain text or Excel file. Check the data curves by clicking the row of frequency. Click the header of the frequency column displays all curves in the chart.

  2. Add Core Loss Model material property, and set the Core Loss Model Type of the property to Electrical Steel or Power Ferrite.

  3. Add Curve Fitting sub-property from the RMB context menu.

  4. Solve the curve fit from the RMB context menu.

  5. If the solve succeeds. The calculated parameters will be shown in the table.

  6. Copy the solved values to the properties from RMB context menu. You also can review the calculated curves in the chart.

  7. Display curves in the logarithmic axis (optional).

"},{"location":"mateditor/mat_core_loss/#computation-of-electrical-steel-core-loss-from-loss-curves","title":"Computation of electrical steel core loss from loss curves","text":"

The iron-core loss without DC flux bias is expressed as the following:

\\[ p_v=P_h+P_c+P_e=K_{f} f (B_m)^2 + K_c (fB_m)^2 + K_e(fB_m)^{1.5} = K_1B_m^2+K_2B_m^{1.5} \\]

where

Minimize the quadratic form to obtain \\(K_h\\) , \\(K_c\\), and \\(K_e\\) directly.

\\[ err(K_h,K_c,K_e)=\\sum_{i=1}^m \\sum_{j=1}^{n_i} \\left[p_{ij}-\\left(K_{h}f_{i}B_{mij}^2 +K_{c}\\left(fB_{mij}\\right)^{2}+ K_{e}\\left(f_iB_{mij}\\right)^{1.5} \\right) \\right]^2=min \\]

where \\(m\\) is the number of loss curves, \\(n_i\\) is the number of points of the \\(i\\)-th loss curve, and \\(p_{ij} = f(f_i , B_{mij})\\) is two dimensional lookup table for loss curves.

Note

Since the manufacturer-provided loss curve is obtained under sinusoidal flux conditions at a given frequency, these coefficients can be derived in the frequency domain.

"},{"location":"mateditor/mat_core_loss/#computation-of-power-ferrite-core-loss-from-loss-curves","title":"Computation of power ferrite core loss from loss curves","text":"

The principles of the computation algorithm are summarized as follows. The iron-core loss is expressed as the Steinmetz approximation

\\[ p_v=C_m f^x B_m^y \\]

where \\(p_v\\) is the average power density, \\(f\\) is the excitation frequency, and \\(B_m\\) is the peak flux density, is commonly used to characterize core loss data for sinusoidal excitation, but can also be applied to square-wave data.

To linearize the equation for curve fitting, we used base-10 logarithms. The equation above can be rewritten to

\\[ log(p_v)=c + x\\cdot log(f) + y \\cdot(B_m) \\]

where \\(c=log(C_m)\\).

Minimize the quadratic form to obtain \\(C\\), \\(x\\) and \\(y\\).

\\[ err(C_m,x,y)=\\sum_{i=1}^{m}\\sum_{j=1}^{n_i}\\left[log(p_{vij})-\\left(c+xlog(f_i)+ylog(B_{mij}) \\right) \\right]^2=min \\]

where \\(m\\) is the number of loss curves, \\(n_i\\) is the number of points of the \\(i\\)-th loss curve, and \\(P_{vij} = f(f_i , B_{mij})\\) is two dimensional lookup table for multi-frequency loss curves. Then \\(C_m\\) is calculated from the equation \\(c=log(C_m)\\).

"},{"location":"mateditor/mat_file_format/","title":"Material library file format","text":"

Material library data follows the MatML 3.1 Schema for saving material data to external libraries on disk. More information about MatML can be found at http://matml.org. For an example of the format see the Export individual data item in the Perform Basic Tasks in Material section and then open the file with a text/xml editor.

"},{"location":"mateditor/mat_gui/","title":"Graphical user interface","text":"

The MatEditor workspace is an independent interface and display relavant items as you configured.

"},{"location":"mateditor/mat_gui/#layout-reference","title":"Layout reference","text":"

Presented below are two layout configurations for the MatEditor view. The first configuration is displayed by clicking on \"Library\" tab in toolbox. The second configure is shown by clicking on \"Build\" tab in toolbox. You can switch this two layout mode by clicking the tabs.

Legend Name Description A Menu Bar Operations for MatEditor. B Toolbar Selected operations that often used for MatEditor. C Material Outline Pane Material items that are created in MatEditor. D Library Outline Pane Displays the available prebuild material sources. E Property Outline Pane Displays the available material property sources that can be included into a material. F Properties Pane Displays the properties of the current material. G Table Pane Shows the tabular data for the selected item in the Properties pane. H Chart Pane Shows the chart of the item selected in the Properties pane."},{"location":"mateditor/mat_gui/#menu-bar","title":"Menu bar","text":"

The following items in the menu bar are provided by MatEditor:

"},{"location":"mateditor/mat_gui/#file","title":"File","text":""},{"location":"mateditor/mat_gui/#edit","title":"Edit","text":""},{"location":"mateditor/mat_gui/#units","title":"Units","text":"

This menu provides all avilable unit systems and units. Once one unit (system) is chosen, the default unit is determined. The units for the newly created material data will be automatically set to the chosen unit(system).

"},{"location":"mateditor/mat_gui/#help","title":"Help","text":""},{"location":"mateditor/mat_gui/#toolbar","title":"Toolbar","text":"

The following item in the toolbar is provided by MatEditor:

Icon Name Description New Create a new material object in the tree window. Open Retrieve material data from an external XML file. This command remove all existing material data in the system. Save Save current material data into an external XML file. Help Direct the user to the online user manual. About Display the software and hardware information dialog."},{"location":"mateditor/mat_gui/#toolbox","title":"Toolbox","text":"

MatEditor Toolbox contains two tabs: Library and Build. These two tabs function as:

"},{"location":"mateditor/mat_gui/#material-outline-pane","title":"Material outline pane","text":"

The Outline pane shows an outline of the contents of the created material data source. You can perform the following actions in this pane:

"},{"location":"mateditor/mat_gui/#items-status","title":"Items status","text":"

The itmes column shows the name of the items contained in the data source. When the name of material object is in bold, the material is activated for editing.

"},{"location":"mateditor/mat_gui/#library-outline-pane","title":"Library outline pane","text":"

The Library Outline pane shows an outline of availble predefined materials. These materials are grouped into several categories.

"},{"location":"mateditor/mat_gui/#property-outline-pane","title":"Property outline pane","text":"

The Property Outline pane shows an outline of availble material properties. These material properties are grouped into several categories.

"},{"location":"mateditor/mat_gui/#properties-pane","title":"Properties pane","text":"

The Properties pane shows the properties for the item selected in the Property Outline pane. You can perform the following actions in this pane:

"},{"location":"mateditor/mat_gui/#property-column","title":"Property column","text":"

The property column lists the properties for the item selected in the Property Outline pane. Clicking a property will change the contents of the Table pane and Chart pane.

"},{"location":"mateditor/mat_gui/#material-property","title":"Material property","text":"

The status of the material property is indicated as follows:

"},{"location":"mateditor/mat_gui/#value-column","title":"Value column","text":"

The value column is used to change data for a property or indicates that the data for the property is tabular ().

"},{"location":"mateditor/mat_gui/#unit-column","title":"Unit column","text":"

The unit column displays the unit of the data shown in the value column . If the column is editable (see Units Menu), changing the unit will convert the value into the selected unit (there is no net change in the data, so the solution is still valid).

"},{"location":"mateditor/mat_gui/#suppression-column","title":"Suppression column","text":"

The suppression column shows the suppression status of the item and may also be used to switch the status (see Suppression).

"},{"location":"mateditor/mat_gui/#table-pane","title":"Table pane","text":"

The Table pane shows the tabular data for the item selected in the Properties pane. If there are independent variables (for instance, Temperature) for the selected item and the item is constant, you may change it to a table by entering a value into the independent variables data cell. If a row is shown with an index of *, you may add additional rows of data.

Note

You also can change the unit by clicking the header of table

"},{"location":"mateditor/mat_gui/#chart-pane","title":"Chart pane","text":"

The Chart pane shows the chart of the selected item in the Properties pane. The chart data is idenital to the table data.

"},{"location":"mateditor/mat_hyperelasticity_curvefit/","title":"Curve Fitting","text":""},{"location":"mateditor/mat_hyperelasticity_curvefit/#calculate-material-constants-from-test-data","title":"Calculate material constants from test data","text":"

This section introduces how to calculate material coefficients for the selected hyperelastic models according to the given uniaxial, biaxial, shear, and volumetric test data. Enginering strain and stress pair is used for input data.

  1. Add Uniaxial Test Data, Biaxial Test Data, or Shear Test Data material property, and edit the strain-stress data. You also can import the data from a plain text or Excel file. Set the temperature value if it is available. Check the data points by clicking the row of temperature.

  2. Add one of hyperelastic material properties from the toolbox, the supported hyperelastic models include Neo-Hookean, Mooney-Rivlin, Arruda-Boyce, Blatz-Ko, Gent, Ogden, Polynomial, and Yeoh. An example of Mooney-Rivlin 9 is given here.

  3. Add Curve Fitting sub-property from the RMB context menu.

  4. Solve the curve fit from the RMB context menu.

  5. If the solve succeeds. The calculated parameters will be shown in the table.

  6. Copy the solved values to the properties from RMB context menu. You also can review the calculated curves in the chart.

Note

  1. The test data should cover the entire strain range in the following simulation.
  2. It is recommended to input all uniaxial, biaxial, and shear test data if those data are available from the experiments.
"},{"location":"mateditor/mat_io/","title":"Mutually exclusive properties 1","text":"

Some properties are mutually exclusive of each other and require that only one property in the mutually exclusive set be unsuppressed. The addition or removing of the suppression for one of these properties automatically suppresses the other mutually exclusive properties.

For example, defining Isotropic Elasticity and Orthotropic Elasticity for the same material represents redundant elasticity behavior. Only one behavior can be active for the material. When such a conflict occurs, the property defined last is used and the previously defined, conflicting property is automatically suppressed.

The properties that are mutually exclusive are grouped in the following table.

Group Material Property Elastic properties Isotropic Elasticity, Orthotropic Elasticity, Anisotropic Elasticity, Mooney-Rivlin, Neo-Hookean, Polynomial, Yeoh, Ogden, Arruda-Boyce, Gent, Blatz-Ko, Ogden Foam, Extended Tube, Mullins Effect Plastic properties Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening Thermal conductivity properties Thermal Conductivity Isotropic, Thermal Conductivity Orthotropic Resistivity properties Isotropic Resistivity, Orthotropic Resistivity Electric permittivity properties Isotropic Relative Permittivity, Orthotropic Relative Permittivity Dielectric loss properties Isotropic Dielectric Loss Tangent, Orthotropic Dielectric Loss Tangent Magnetic permeability properties Isotropic Relative Permeability, Orthotropic Relative Permeability Magnetic loss properties Isotropic Relative Imaginary Permeability, Isotropic Magnetic Loss Tangent, Orthotropic Magnetic Loss Tangent"},{"location":"mateditor/mat_io_openradioss/","title":"OpenRadioss format","text":"

The format of exported material scripts is based on the OpenRadioss version 2022, more details please refer to the OpenRadioss user reference manual.

The import of OpenRadioss scripts is not supported yet in MatEditor/WELSIM.

"},{"location":"mateditor/mat_io_openradioss/#supported-openradioss-units","title":"Supported OpenRadioss units","text":"

At present, MatEditor supports eight types of unit systems commonly used in engineering simulation, which are as follows.

"},{"location":"mateditor/mat_io_openradioss/#supported-openradioss-materials","title":"Supported OpenRadioss materials","text":""},{"location":"mateditor/mat_io_openradioss/#basic","title":"Basic","text":""},{"location":"mateditor/mat_io_openradioss/#hyperelasticity-and-viscoelasticity","title":"Hyperelasticity and Viscoelasticity","text":""},{"location":"mateditor/mat_io_openradioss/#plasticity","title":"Plasticity","text":""},{"location":"mateditor/mat_io_openradioss/#failure-models","title":"Failure Models","text":""},{"location":"mateditor/mat_io_openradioss/#equation-of-state-eos","title":"Equation of State (EOS)","text":""},{"location":"mateditor/mat_io_openradioss/#fluids","title":"Fluids","text":"

More materials will be added upon user request.

"},{"location":"mateditor/mat_mutually_exclusive/","title":"Mutually exclusive properties","text":"

Some properties are mutually exclusive of each other and require that only one property in the mutually exclusive set be unsuppressed. The addition or removing of the suppression for one of these properties automatically suppresses the other mutually exclusive properties.

For example, defining Isotropic Elasticity and Orthotropic Elasticity for the same material represents redundant elasticity behavior. Only one behavior can be active for the material. When such a conflict occurs, the property defined last is used and the previously defined, conflicting property is automatically suppressed.

The properties that are mutually exclusive are grouped in the following table.

Group Material Property Elastic properties Isotropic Elasticity, Orthotropic Elasticity, Anisotropic Elasticity, Mooney-Rivlin, Neo-Hookean, Polynomial, Yeoh, Ogden, Arruda-Boyce, Gent, Blatz-Ko, Ogden Foam, Extended Tube, Mullins Effect Plastic properties Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening Thermal conductivity properties Thermal Conductivity Isotropic, Thermal Conductivity Orthotropic Resistivity properties Isotropic Resistivity, Orthotropic Resistivity Electric permittivity properties Isotropic Relative Permittivity, Orthotropic Relative Permittivity Dielectric loss properties Isotropic Dielectric Loss Tangent, Orthotropic Dielectric Loss Tangent Magnetic permeability properties Isotropic Relative Permeability, Orthotropic Relative Permeability Magnetic loss properties Isotropic Relative Imaginary Permeability, Isotropic Magnetic Loss Tangent, Orthotropic Magnetic Loss Tangent"},{"location":"mateditor/mat_overview/","title":"Overview","text":"

Material Module serves as a database for material properties used in analysis projects. The module not only provides a material library but allow you to create a material using the given properties. The properties view of a Material object is the primary user interface designed to let you create, save, and retrieve material models. The well-defined material object can be saved and used in the subsequent projects.

Note

The WELSIM Material module and MatEditor share the same features. For the completed and latest content, you can refer to the manual of MatEditor.

"},{"location":"mateditor/mat_overview/#graphical-user-interface","title":"Graphical user interface","text":"

The ease-of-use Material Module contains the following graphical user interface components:

"},{"location":"mateditor/mat_overview/#predefined-materials","title":"Predefined materials","text":"

WELSIM also provide predefined materials, which covers most of commonly used materials. Users can choose these materials and apply to the successive finite element analysis.

Category Materials General Materials Structural Steel, Stainless Steel, Aluminum Alloy, Concrete, Copper Alloy, Gray Cast Iron, Titanium Alloy Nonlinear Materials Aluminum Alloy NL, Concrete NL, Copper Alloy NL, Stainless Steel NL, Structural Steel NL, Titanium Alloy NL Hyperelastic Materials Elastomer Mooney-Rivlin, Elastomer Neo-Hookean, Elastomer Ogden, Elastomer Yeoh, Neoprene Rubber Thermal Materials Brass, Bronze, Copper, Diamond, Ferrite, Nodular Cast Iron, Solder, Teflon, Tungsten, Wood Electromagnetic Materials SS416, Supermendure Other Materials Water Liquid, Argon, Ash"},{"location":"mateditor/mat_overview/#material-properties","title":"Material properties","text":"

The supported material properties are listed in the table below.

Category Materials Basic Density, Isotropic Thermal Expansion, Isotropic Instantaneous Thermal Expansion, Orthotropic Thermal Expansion, Orthotropic Instantaneous Thermal Expansion, Constant Damping Coefficient Linear Elastic Isotropic Elasticity, Orthotropic Elasticity, Viscoelastic Hyperelastic Test Data Uniaxial Test Data, Biaxial Test Data, Shear Test Data, Volumetric Test Data, SimpleShear Test Data, Uniaxial Tension Test Data, Uniaxial Compression Test Data Hyperelastic Arruda-Boyce, Blatz-Ko, Gent, Mooney-Rivlin 2, Mooney-Rivlin 3, Mooney-Rivlin 5, Mooney-Rivlin 9, Neo-Hookean, Ogden 1st Order, Ogden 2nd Order, Ogden 3rd Order, Polynomial 1st Order, Polynomial 2nd Order, Polynomial 3rd Order, Yeoh 1st Order, Yeoh 2nd Order, Yeoh 3rd Order Plasticity Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening, Anand Viscoplasticity Creep Strain Hardening, Time Hardening, Generalized Exponential, Generalized Graham, Generalized Blackburn, Modified Time Hardening, Modified Strain Hardening, Generalized Garofalo, Exponential Form, Norton, Combined Time Hardening, Rational Polynomial, Generalized Time Hardening Visco-elastic Prony Shear Relaxation, Prony Volumetric Relaxation Other Mechanical Strain Life Parameters, Compressive Ultimate Strength, Compressive Yield Strength, LaRc0304 Constants, Orthotropic Strain Limits, Orthotropic Stress Limits, Puck Constants, Tensile Ultimate Strength, Tensile Yield Strength, Tsai-Wu Constants, Shape Memory Effect, Drucker-Prager Strength Piecewise, Drucker-Prager Strength Linear, Ideal Gas EOS, Crushable Foam, Nonlinear Elastic Model Damage, Plakin Special Hardening, Tensile Pressure Failure, Crack Softening Failure Thermal Enthalpy, Isotropic Thermal Conductivity, Orthotropic Thermal Conductivity, Specific Heat Electromagnetics B-H Curve, Isotropic Relative Permeability, Orthotropic Relative Permeability, Isotropic Resistivity, Orthotropic Resistivity"},{"location":"mateditor/mat_overview/#working-with-material-data","title":"Working with material data","text":""},{"location":"mateditor/mat_overview/#exporting","title":"Exporting","text":"

You can export the complete material data to an external XML file. The following format is supported for export:

"},{"location":"mateditor/mat_properties/","title":"Libraries and properties","text":""},{"location":"mateditor/mat_properties/#definitions","title":"Definitions","text":"

We make use of the following terminology for materials:

Term Definition Material An identifier that contains a property or multiple properties Property An identifier the singular information (for example, Density) Property data An identifier for tabular data (for example, Thermal Conductivity)"},{"location":"mateditor/mat_properties/#sample-libraries","title":"Sample libraries","text":"

MatEditor provides sample material data categorized into several libraries. However, you still need to validate that the data is consistent with the material you are using in your analysis.

The following materials are included:

"},{"location":"mateditor/mat_properties/#supported-properties","title":"Supported properties","text":"

The supported material properties are listed by category here.

"},{"location":"mateditor/mat_properties/#basics","title":"Basics","text":""},{"location":"mateditor/mat_properties/#linear-elastic","title":"Linear Elastic","text":""},{"location":"mateditor/mat_properties/#hyperelastic-test-data","title":"Hyperelastic Test Data","text":""},{"location":"mateditor/mat_properties/#hyperelastic","title":"Hyperelastic","text":""},{"location":"mateditor/mat_properties/#plasticity","title":"Plasticity","text":""},{"location":"mateditor/mat_properties/#creep","title":"Creep","text":""},{"location":"mateditor/mat_properties/#visco-elastic","title":"Visco-elastic","text":""},{"location":"mateditor/mat_properties/#thermal","title":"Thermal","text":""},{"location":"mateditor/mat_properties/#electromagnetics","title":"Electromagnetics","text":""},{"location":"mateditor/mat_table_data/","title":"Import/Export Tabular Data","text":"

Import and export tabular data is supported in MatEditor, CurveFitter and WELSIM, this feature facilitates you to input and output massive tabular data with no need to manually input and output data, specifically test data for the hyperelastic and magnetic core loss materials.

The import and export buttons are allocated on the top of the Tabular Data Window, as shown in the figure below:

"},{"location":"mateditor/mat_table_data/#default-file-format","title":"Default file format","text":"

The default file format used in MatEditor/CurveFitter/WELSIM contains a header block that gives the quantity name, unit, and dependency. This header data allows you to define the units from the external file. The latest version supports both plain text and Excel formats. Both formats share a similar schema. The details of each format are discussed below.

Note

The number of columns of import data must match the pre-defined headers.

The plain text data file looks like below:

An example of Excel file is shown below:

"},{"location":"mateditor/mat_table_data/#format-with-no-header-data","title":"Format with no header data","text":"

MatEditor/CurveFitter/WELSIM also supports the external data that contains no header information (pure value data). You need to ensure unit consistency when importing such data files. Both plain text and Excel file formats are supported.

The plain text file with no header dat looks like below:

Note

Due to the lack of the header information, the units of the imported data is determined by the current units of the Table. In addition, the pivoting column may not be set if the file does not contain such data. The number of columns must be identicial to that of the pre-defined table quantities.

"},{"location":"mateditor/mat_table_data/#examples","title":"Examples","text":"

The examples of the import/export tabular data are available at our GitHub page.

"},{"location":"mateditor/mat_theory/","title":"Material Theory","text":"

Some properties are mutually exclusive of each other and require that only one property in the mutually exclusive set be unsuppressed. The addition or removing of the suppression for one of these properties automatically suppresses the other mutually exclusive properties.

For example, defining Isotropic Elasticity and Orthotropic Elasticity for the same material represents redundant elasticity behavior. Only one behavior can be active for the material. When such a conflict occurs, the property defined last is used and the previously defined, conflicting property is automatically suppressed.

The properties that are mutually exclusive are grouped in the following table.

Group Material Property Elastic properties Isotropic Elasticity, Orthotropic Elasticity, Anisotropic Elasticity, Mooney-Rivlin, Neo-Hookean, Polynomial, Yeoh, Ogden, Arruda-Boyce, Gent, Blatz-Ko, Ogden Foam, Extended Tube, Mullins Effect Plastic properties Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening Thermal conductivity properties Thermal Conductivity Isotropic, Thermal Conductivity Orthotropic Resistivity properties Isotropic Resistivity, Orthotropic Resistivity Electric permittivity properties Isotropic Relative Permittivity, Orthotropic Relative Permittivity Dielectric loss properties Isotropic Dielectric Loss Tangent, Orthotropic Dielectric Loss Tangent Magnetic permeability properties Isotropic Relative Permeability, Orthotropic Relative Permeability Magnetic loss properties Isotropic Relative Imaginary Permeability, Isotropic Magnetic Loss Tangent, Orthotropic Magnetic Loss Tangent"},{"location":"mateditor/mat_theory_eos/","title":"Equations of State (EOS)","text":"

MatEditor allows you to define the EOS material properties. The supported properties are listed below.

"},{"location":"mateditor/mat_theory_eos/#compaction-eos","title":"Compaction EOS","text":"

Plastic compaction is along path defined by equation:

\\[ p=C_0 + C_1 \\mu +C_2 \\mu^2 + C_3 \\mu^3 \\]

where \\(P\\) is the hydrodynamic pressure in material. \\(\\mu\\) is the volumetric strain that can be obtained by \\(\\mu=\\dfrac{\\rho}{\\rho_0}-1\\).

Unloading bulk modulus \\(B\\) is the bulk modules for the unloading process.

Pressure Shift \\(P_{sh}\\) is used to model the relative pressure formulation.

"},{"location":"mateditor/mat_theory_eos/#gruneisen-eos","title":"Gruneisen EOS","text":"

In the Gruneisen EOS model, the hydrodynamic pressure is described by the following equations:

For the compressed material, \\(\\mu\\)>0

\\[ p = \\dfrac{\\rho_0C^2\\mu[1+(1-\\dfrac{\\gamma_0}{2})\\mu-\\dfrac{\\alpha}{2}\\mu^2]}{[1-(S_1-1)\\mu-S_2\\dfrac{\\mu^2}{\\mu+1}-S_3\\dfrac{\\mu^3}{(\\mu+1)^2}]^2} + (\\gamma_0+\\alpha\\mu)E \\]

For the expanding material, \\(\\mu\\)<0 $$ p = \\rho_0C^2\\mu + (\\gamma_0+\\alpha\\mu)E $$

where the \\(\\mu=\\dfrac{\\rho}{\\rho_0}-1\\).

"},{"location":"mateditor/mat_theory_eos/#ideal-gas-eos","title":"Ideal Gas EOS","text":"

The pressure in the Ideal Gas model can be represented by the function:

\\[ p = (\\gamma-1)(1+\\mu)E \\]

where unitless parameter \\(\\gamma\\) is determined by the heat capacity \\(C_v\\) and \\(C_p\\), \\(\\gamma=\\dfrac{C_p}{C_v}\\). The initial heat capacity \\(C_v\\) is calculated from the initial conditions:

\\[ C_v=\\dfrac{E_0}{\\rho_0T_0} \\]"},{"location":"mateditor/mat_theory_eos/#linear-eos","title":"Linear EOS","text":"

The pressure in linear EOS is given by

\\[ p = p_0 + B\\mu \\]

where \\(p_0\\) i initial pressure and \\(B\\) is the initial bulk modulus. Linear EOS is a simplified form of polynomial EOS:

\\[ p=C_0+C_1\\mu + C_2\\mu + C_3\\mu + (C_4+C_5)E_0 \\]

where, \\(C_0=p_0\\), \\(C_1=B\\), \\(C_2=C_3 = C_4 = C_5 = 0\\).

Bulk modulus is usually treated as \\(B=\\rho_0c_0^2\\), where \\(c_0\\) is the initial sound speed.

"},{"location":"mateditor/mat_theory_eos/#lszk-landau-stanyukovich-zeldovich-kompaneets-eos","title":"LSZK (Landau-Stanyukovich-Zeldovich-Kompaneets) EOS","text":"

This EOS model is the short for the Landau-Stanyukovich-Zeldovich-Kompaneets EOS, used for the detonation modeling. The pressure is given by

\\[ p = (\\gamma-1)\\rho e + a \\rho^b \\]

where \\(\\rho\\) is the mass density, \\(e\\) is the internal energy density by mass, \\(b\\) is the material parameter.

"},{"location":"mateditor/mat_theory_eos/#murnaghan-eos","title":"Murnaghan EOS","text":"

This EOS is also known as Tait EOS. The pressure is defined by

\\[ p = \\dfrac{K_0}{K_1}[(\\dfrac{V}{V_0})^{-K_1}-1] \\]

where \\(K_0\\), \\(K_1\\) are material parameters, \\(V\\) is the volume.

This model is also expressed in terms of the compressibility \\(\\mu\\):

\\[ p = p_0 + \\dfrac{K_0}{K_1}[(1+\\mu)^{K_1}-1] \\]

Note

Murnaghan EOS is independent to the energy.

"},{"location":"mateditor/mat_theory_eos/#nasg-noble-abel-stiffened-gas-eos","title":"NASG (Noble-Abel Stiffened Gas) EOS","text":"

The pressure can be computing by

\\[ p = \\dfrac{(\\gamma-1)(1+\\mu)(E-\\rho_0q)}{1-b\\rho_0(1+\\mu)} - \\gamma p_{\\infty} \\]

where \\(p_{\\infty}\\) is the stiffness parameter.

"},{"location":"mateditor/mat_theory_eos/#noble-abel-eos","title":"Noble-Abel EOS","text":"

This EOS can apply to dense gases at high pressure, as the volume occupied by the moledules is no longer negligible.

\\[ p = \\dfrac{(\\gamma-1)(1+\\mu)E}{1-b\\rho_0(1+\\mu)} \\]

where \\(\\gamma=\\dfrac{C_p}{C_v}\\)

Note

Covolume parameter b is usually in the range between [0.9e-3, 1.1e-3] \\(m^3/kg\\).

"},{"location":"mateditor/mat_theory_eos/#osborne-eos","title":"Osborne EOS","text":"

This EOS is also called quadratic EOS.

$$ p = \\dfrac{A_1\\mu+A_2\\mu |\\mu| + (B_0+B_1\\mu+B_2\\mu^2)E + (C_0 + C_1\\mu)E^2 }{E+D_0} $$ where \\(E\\) is the internal energy by initial volume.

"},{"location":"mateditor/mat_theory_eos/#polynomial-eos","title":"Polynomial EOS","text":"

The pressure for the linear polynomial EOS can be calculated by

\\[ p=C_0+C_1\\mu + C_2\\mu + C_3\\mu + (C_4+C_5)E \\]

where \\(E\\) is the internal energy density by volume.

Note

For the expanding status (\\(\\mu\\)<0), the term \\(C_2\\mu^2\\)=0.

"},{"location":"mateditor/mat_theory_eos/#puff-eos","title":"Puff EOS","text":"

This EOS model describes pressure accroding to the compressibility \\(\\mu\\) and sublimation energy density by volume \\(E_s\\).

When \\(\\mu\\geq\\) 0:

\\[ p = (C_1\\mu+C_2\\mu^2+C_3\\mu^3)(1-\\dfrac{\\gamma\\mu}{2})+\\gamma(1+\\mu)E \\]

when \\(\\mu\\)<0 and \\(E\\geq E_s\\):

\\[ p = (T_1\\mu+T_2\\mu^2)(1-\\dfrac{\\gamma\\mu}{2})+\\gamma(1+\\mu)E \\]

when \\(\\mu\\)<0 and \\(E<E_s\\):

\\[ p = \\eta[H+(\\gamma_0-H)\\sqrt{\\eta}][E-E_s(1-exp(\\dfrac{N(\\eta-1)}{\\eta^2}))] \\]

with \\(N=\\dfrac{C_1\\eta}{\\gamma_0E_s}\\).

"},{"location":"mateditor/mat_theory_eos/#stiffened-gas-eos","title":"Stiffened Gas EOS","text":"

This EOS was originally designed to simulate water for underwater explosions.

The pressure can be calculated by $$ p = (\\gamma-1)(1+\\mu)E - \\gamma p_{\\star} $$

where \\(E=\\dfrac{E_{int}}{V_0}\\), \\(\\mu=\\dfrac{\\rho}{\\rho_0}-1\\). The additional pressure term \\(p^{\\star}\\) is introduced here.

This EOS can be derived from the Polynomial EOS: $$ p=C_0+C_1\\mu + C_2\\mu + C_3\\mu + (C_4+C_5)E $$ when \\(C_0 = -\\gamma p^{\\star}\\), \\(C_1=C_2=C3=0\\), \\(C_4=C_5=\\gamma-1\\), \\(E_0=\\dfrac{P_0-C_0}{C_4}\\).

"},{"location":"mateditor/mat_theory_eos/#tillotson-eos","title":"Tillotson EOS","text":"

The pressure is defined by

$$ p = C_1\\mu + C_2\\mu^2 +(a+\\dfrac{b}{\\omega})\\eta E $$ with \\(\\omega=1+\\dfrac{E}{E_r}\\eta^2\\) for the region \\(\\mu \\geq\\) 0.

$$ p = C_1\\mu+(a+\\dfrac{b}{\\omega})\\eta E $$ for the region \\(\\mu<0\\), \\(\\dfrac{V}{V_0}<V_s\\), and \\(E<E_s\\).

and $$ p = C_1 e^{\\beta x} e^{-\\alpha x^2}\\mu + (a + \\dfrac{be^{-\\alpha x^2}}{\\omega}) \\eta E $$

"},{"location":"mateditor/mat_theory_failure/","title":"Failure Models","text":"

MatEditor allows you to define the failure material properties. The supported properties are listed below.

"},{"location":"mateditor/mat_theory_failure/#bi-quadratic","title":"Bi-Quadratic","text":"

The failure strain is described by two parabolic functions that user input.

"},{"location":"mateditor/mat_theory_failure/#cockcroft","title":"Cockcroft","text":"

A nonlinear stress-strain based failure criterion with linear damage accumulation.

\\[ C_0 = \\int _0 ^{\\bar{\\epsilon}_f} max(\\sigma_1, 0) \\cdot d\\bar{\\epsilon} \\]

where \\(\\epsilon_1\\) is the first principal tension stress, \\(\\bar{\\epsilon}\\) is the equivalent strain.

"},{"location":"mateditor/mat_theory_failure/#extended-mohr-coulomb","title":"Extended Mohr-Coulomb","text":"

The failure criteria is calculated as:

\\[ D = \\sum \\dfrac{\\Delta \\bar{\\epsilon}_p}{\\bar{\\epsilon}_{p,fail}} \\]

where effective failure strain is

\\[ \\bar{\\epsilon}_{p,fail} = b \\cdot (1+c)^{\\frac{1}{n}} \\cdot \\{[\\dfrac{1}{2}((f_1-f_2)^a + (f_2-f_3)^a + (f_1 - f_3)^a )]^{\\frac{1}{a}} + c(2\\eta+f_1+f_3) \\}^{-\\frac{1}{n}} \\]

the coefficient b is computed as

\\[ b = b_0[1+\\gamma ln(\\dfrac{\\dot{\\bar{\\epsilon}}_p}{\\dot{\\bar{\\epsilon}}_0})] \\quad if\\, \\dot{\\bar{\\epsilon}}_p > \\dot{\\bar{\\epsilon}}_0 \\]

or

\\[ b = b_0 \\quad if\\, \\dot{\\bar{\\epsilon}}_p \\le \\dot{\\bar{\\epsilon}}_0 \\]"},{"location":"mateditor/mat_theory_failure/#energy","title":"Energy","text":"

The damage is defined as

\\[ D = \\dfrac{E-E_1}{E_2 - E_1} \\]

where the energy density is the current internal energy of the element divided by the current element volume.

"},{"location":"mateditor/mat_theory_failure/#fabric","title":"Fabric","text":"

The failure and damage is defined independently in each direction (\\(i\\)=1,2)

\\[ D_i = \\dfrac{\\epsilon_i - \\epsilon_{fi}}{\\epsilon_{ri} - \\epsilon_{fi}} \\]

where \\(\\epsilon_i \\ge \\epsilon_{fi}\\).

"},{"location":"mateditor/mat_theory_failure/#hashin","title":"Hashin","text":"

This model can be used for the composite materials.

The damage factor is calculated as

\\[ D = Max(F_1,F_2,F_3, F_4, F_5) \\quad for\\quad uni-directional\\, lamina\\, model \\] \\[ D = Max(F_1,F_2,F_3, F_4, F_5, F_6, F_7) \\quad for\\quad fabric\\, lamina\\, model \\]"},{"location":"mateditor/mat_theory_failure/#for-the-uni-directional-lamina-model","title":"For the uni-directional lamina model:","text":"

Tensile/shear fiber mode:

\\[ F_1 = (\\dfrac{\\langle\\sigma_{11}\\rangle}{\\sigma_1^t})^2 + (\\dfrac{\\sigma_{12}^2 + \\sigma_{13}^2}{{\\sigma_{12}^f}^2}) \\]

Compression fiber mode:

\\[ F_2 = (\\dfrac{\\langle \\sigma_a \\rangle}{ \\sigma_1^c})^2 \\]

with \\(\\sigma_{\\alpha} = -\\sigma_{11}+\\langle -\\dfrac{\\sigma_{22}+\\sigma_{33}}{2} \\rangle\\).

Crush mode:

\\[ F_3 = (\\dfrac{\\langle p \\rangle}{\\sigma_c})^2 \\]

with \\(p=-\\dfrac{\\sigma_{11}+\\sigma_{22}+\\sigma_{33}}{3}\\).

Failure matrix mode:

\\[ F_4 = (\\dfrac{\\langle \\sigma_{22} \\rangle}{\\sigma_2^t})^2 + (\\dfrac{\\sigma_{23}}{S_{23}})^2 + (\\dfrac{\\sigma_{12}}{S_{12}})^2 \\]

Delamination mode:

\\[ F_5 = S^2_{del}[(\\dfrac{\\langle \\sigma_{33} \\rangle}{\\sigma^t_2})^2 + (\\dfrac{\\sigma_{23}}{\\tilde{S}_{23}})^2 + (\\dfrac{\\sigma_{12}}{S_{12}})^2 ] \\]"},{"location":"mateditor/mat_theory_failure/#for-the-fabirc-lamina-model","title":"For the fabirc lamina model:","text":"

Tensile/shear fiber mode

\\[ F_1 = (\\dfrac{\\langle\\sigma_{11}\\rangle}{\\sigma_1^t})^2 + (\\dfrac{\\sigma_{12}^2 + \\sigma_{13}^2}{{\\sigma_{a}^f}^2}) \\] \\[ F_2 = (\\dfrac{\\langle\\sigma_{22}\\rangle}{\\sigma_2^t})^2 + (\\dfrac{\\sigma_{12}^2 + \\sigma_{23}^2}{{\\sigma_{b}^f}^2}) \\]

Compression fiber mode:

\\[ F_3 = (\\dfrac{\\langle \\sigma_a \\rangle}{ \\sigma_1^c})^2 \\] \\[ F_4 = (\\dfrac{\\langle \\sigma_b \\rangle}{ \\sigma_2^c})^2 \\]

Crush mode:

\\[ F_5 = (\\dfrac{\\langle p \\rangle}{\\sigma_c})^2 \\]

Shear failure matrix mode:

\\[ F_6 = (\\dfrac{\\sigma_12}{\\sigma_12^m})^2 \\]

Matrix failure mode:

\\[ F_7 = S^2_{del}[(\\dfrac{\\langle \\sigma_{33} \\rangle}{\\sigma^t_3})^2 + (\\dfrac{\\sigma_{23}}{\\tilde{S}_{23}})^2 + (\\dfrac{\\sigma_{12}}{S_{12}})^2 ] \\]"},{"location":"mateditor/mat_theory_failure/#hosford-coulomb","title":"Hosford-Coulomb","text":"

The failure strain is described y the Hosford-Coulomb function.

The damage is defined as

\\[ D = \\sum \\dfrac{\\Delta \\bar{\\epsilon}_p} {\\bar{\\epsilon}^{pr}_{HC}(\\eta) } \\]

where the strain is calcualted as

\\[ \\bar{\\epsilon}^{pr}_{HC}(\\eta, \\theta) = b(1+c)^{\\frac{1}{n_f}} \\{[\\dfrac{1}{2}((f_1-f_2)^a + (f_2-f_3)^a + (f_1-f_3)^a)]^{\\frac{1}{a}} + c(a\\eta + f_1 +f_2) \\}^{\\frac{1}{n_f}} \\]"},{"location":"mateditor/mat_theory_failure/#johnson-cook","title":"Johnson-Cook","text":"

The failure strain is calculated by the constutitive relation:

\\[ \\epsilon_f = [D_1+D_2exp(D_3\\sigma^*)] [1+D_4 ln(\\dot{\\epsilon}^*)] (1 + D_5 T^*) \\]

The damage factor is defined as

\\[ D = \\sum \\dfrac{\\Delta \\epsilon_p}{\\epsilon_f} \\]"},{"location":"mateditor/mat_theory_failure/#ladeveze-delamination","title":"Ladeveze Delamination","text":"

This is the Ladeveze failure model for delamination (interlaminar fracture). The damage parameters are defined as

\\[ Y_{d_3} = \\dfrac{\\partial E_D}{\\partial d_3} \\vert _{\\sigma=cst}=\\dfrac{1}{2} \\dfrac{\\langle\\sigma_{33}\\rangle^2}{K_3(1-d_3)^2} \\quad Mode\\,I \\] \\[ Y_{d_2} = \\dfrac{\\partial E_D}{\\partial d_2} \\vert _{\\sigma=cst}=\\dfrac{1}{2} \\dfrac{\\langle\\sigma_{32}\\rangle^2}{K_2(1-d_2)^2} \\quad Mode\\,II \\] \\[ Y_{d_1} = \\dfrac{\\partial E_D}{\\partial d_1} \\vert _{\\sigma=cst}=\\dfrac{1}{2} \\dfrac{\\langle\\sigma_{31}\\rangle^2}{K_1(1-d_1)^2} \\quad Mode\\,III \\]

The damage value can be

\\[ D = \\dfrac{k}{a}[1- exp(-a\\langle w(Y)-d\\rangle)] \\]"},{"location":"mateditor/mat_theory_failure/#mullins-effect","title":"Mullins Effect","text":"

This failure model is used with the hyperelastic materials. The stress during the first loading process is equal to the undamaged stress. Upon unloading and reloading the strss is multiplied by a positive softening factor as

\\[ \\sigma = \\eta dev(\\sigma) - pI \\]

where dev(\\(\\sigma\\)) is the deviatoric part of the stress, \\(p\\) is the hydrostatic pressure. The damage factor \\(\\eta\\) is given as

\\[ \\eta = 1 - \\dfrac{1}{R} erf(\\dfrac{W_{max}-W}{m+\\beta W_{max}}) \\]

where \\(erf\\) is the Gauss error function.

"},{"location":"mateditor/mat_theory_failure/#nxt","title":"NXT","text":"

This model describes the forming limit baed on stresses. This failure is used for shell elements only.

An instability factor is defined as:

\\[ \\lambda_f=\\dfrac{\\sigma/h - (\\sigma/h)_{SR}}{(\\sigma/h)_{3D}-(\\sigma/h)_{SR}} + 1 \\]

The material is defined as free if \\(0<\\lambda_f<1\\), warning if \\(1<\\lambda_f<2\\), failure if \\(\\lambda_f \\ge 2\\).

"},{"location":"mateditor/mat_theory_failure/#orthotropic-bi-quadratic","title":"Orthotropic Bi-Quadratic","text":"

The failure strain is described by two parabolicfunctions calculated using curve fitting from user input failure strains.

"},{"location":"mateditor/mat_theory_failure/#orthotropic-strain","title":"Orthotropic Strain","text":"

A damage factor is the maximum over time and is calculated for each direction and stress state via:

\\[ d_ijl = \\dfrac{\\epsilon_{ijf\\_l}}{\\epsilon_{ijl}} \\cdot \\dfrac{\\epsilon_{ijl}-\\alpha\\cdot\\epsilon_{ijd\\_l}}{\\epsilon_{ijf\\_l}-\\epsilon_{ijd\\_l}} \\]

where the direction is indicated by using the common \\(ij\\) notation and loading state is either compression (\\(l=c\\)) or tension (\\(l=t\\)). The parameter \\(\\alpha=factor_{el}\\cdot factor_{rate}\\).

The element size correction factor is :

\\[ factor_{el} = Fscale_{el} \\cdot f_{el} \\dfrac{Size_{el}}{El_ref} \\]

where \\(f_{el}\\) is the element size correction factor function, \\(Size_{el}\\) is the characteristic element size.

The strain rate factor is

\\[ factor_{rate} = f_{ijl}(\\dfrac{\\dot{\\epsilon}_{ijl}}{\\dot{\\epsilon}_0}) \\]

where \\(f_ijl\\) is strain rate factor function, \\(\\dot{\\epsilon}_{ijl}\\) is the current strain rate in direction ij and load case l, and \\(\\dot\\epsilon_0\\) is the reference strate rate.

Generally, the damange for this model is

\\[ D = Max(d_{ijl}) = Max(\\dfrac{\\epsilon_{ijf\\_l}}{\\epsilon_{ijl}} \\cdot \\dfrac{\\epsilon_{ijl}-\\alpha\\cdot\\epsilon_{ijd\\_l}}{\\epsilon_{ijf\\_l}-\\epsilon_{ijd\\_l}}) \\]"},{"location":"mateditor/mat_theory_failure/#puck","title":"Puck","text":"

This failure model can be applied for both solid and shell elements.

For the fiber fraction failure, the damage parameter \\(e_f\\) is defined by

\\[ e_f=\\dfrac{\\sigma_{11}}{\\sigma_{1}^t} \\quad for\\, tensile \\]

or

\\[ e_f=\\dfrac{|\\sigma_{11}|}{\\sigma_{1}^c} \\quad for\\, compression \\]

For the inter fiber failure: the damage parameter \\(e_f\\) is

\\[ e_f=\\dfrac{1}{\\bar{\\sigma}_{12}} [ \\sqrt{(\\dfrac{\\bar{\\sigma}_{12}}{\\sigma_2^t} -p^+_{12})^2\\sigma_{22}^2 + \\sigma_{12}^2}+p^+_{12}\\sigma_{22}] \\quad for\\, Mode\\, A \\]

or

\\[ e_f=[(\\dfrac{\\sigma_{12}}{2(1+p^-_{22})\\bar{\\sigma}_{12}})^2 + (\\dfrac{\\sigma_{22}}{\\sigma_2^c})^2](\\dfrac{\\sigma^c_2}{-\\sigma_{22}}) \\quad for\\, Mode\\, C \\]

or

\\[ e_f=\\dfrac{1}{\\bar{\\sigma}_{12}} ( \\sqrt{\\sigma_{12}^2+(p^-_{12}\\sigma_{22})^2}+p^-_{12}\\sigma_{22}) \\quad for\\, Mode\\, B \\]

when the damage parameter \\(e_f \\ge 1.0\\), the stresses are decreased by using an exponential function to avoid numerical instabilities.

The damage is defined by

\\[ D = Max(e_f(tensile),e_f(compression), e_f(ModaA), e_f(ModeB), e_f(ModeC) ) \\]"},{"location":"mateditor/mat_theory_failure/#tuler-butcher","title":"Tuler-Butcher","text":"

An element fails once the damage is greater than specified critical damage value K. For ductile materials, the cumulative damage parameter is:

\\[ D=\\int_0^t{max(0, \\sigma-\\sigma_r)^{\\lambda})dt}>K \\]

where \\(\\sigma_r\\) is initial fracture stress, \\(\\sigma\\) maximum principal stress, \\(\\lambda\\) is material constant, \\(t\\) is the time when the element cracks, \\(D\\) is the damage integral, \\(K\\) is the critical value of the damage integral.

For brittle materials (shells only), the damage parameter is: $$ \\dot{D} = \\dfrac{1}{K}(\\sigma - \\sigma_r)^a $$ $$ \\sigma_r=\\sigma_0(1-D)^b $$ $$ D=D+\\dot{D}\\Delta t $$

"},{"location":"mateditor/mat_theory_failure/#tensile-strain","title":"Tensile Strain","text":"

This is a strain-based failure model that is compatible with both solid and shell elements. The damage is calculated by:

\\[ D = \\dfrac{\\epsilon - \\epsilon_{t1}}{\\epsilon_{t2} - \\epsilon_{t1}} \\]

where \\(\\epsilon\\) is either the quivlent strain or maximum principal tensile strain.

"},{"location":"mateditor/mat_theory_failure/#wierzbicki-model","title":"Wierzbicki model","text":"

This model describes the Bao-Xue-Wierzbicki failure model. The damage is defined by

\\[ D=\\sum{\\dfrac{\\Delta\\epsilon_{p}}{\\bar{\\epsilon}_f}} \\]

where the effective failure strain is

\\[ \\bar{\\epsilon}_f =\\{ \\bar{\\epsilon}_{max}n-[\\bar{\\epsilon}_{max}n - \\bar{\\epsilon}_{min}n](1-\\bar{\\xi}^m)^{\\dfrac{1}{m}} \\}^{\\dfrac{1}{n}} \\]

where \\(\\bar{\\epsilon}_{max} = C_1 e^{-1C_{2}\\eta}\\), and \\(\\bar{\\epsilon}_{min} = C_{3} e^{-1C_{4}\\eta}\\).

For solid element, the parameters \\(\\bar{\\xi}\\) and \\(\\bar{\\eta}\\) are defined by the two options.

The option 1 (default) is : $$ \\bar{\\xi}=\\dfrac{\\sigma_m}{\\sigma_{VM}} \\quad \\bar{\\eta}=\\dfrac{27J_3}{2\\sigma^3_{VM}} $$

The option 2 is: $$ \\bar{\\xi}=\\dfrac{\\int_0^{\\epsilon_p}\\dfrac{\\sigma_m}{\\sigma_{VM}}d\\epsilon_p}{\\epsilon_p} \\quad \\bar{\\eta}=\\dfrac{\\int_0^{\\epsilon_p} \\dfrac{27J_3}{2\\sigma^3_{VM}} d\\epsilon_p}{\\epsilon_p} $$

For shell element, the parameters \\(\\bar{\\xi}\\) and \\(\\bar{\\eta}\\) are $$ \\bar{\\xi}=\\dfrac{\\sigma_m}{\\sigma_{VM}} \\quad \\bar{\\eta}=-\\dfrac{27}{2}\\bar{\\eta}(\\bar{\\eta}^2-\\dfrac{1}{3}) $$

where \\(\\sigma_m\\) is Hydrostatic stress, \\(\\sigma_{VM}\\) is von Mises stress, and \\(J_3\\) is the third invariant deviatoric stress.

"},{"location":"mateditor/mat_theory_failure/#wilkins-model","title":"Wilkins model","text":"

The cumulative damage is given by:

\\[ D_c = \\int W_1 W_2 d \\bar{\\epsilon_p} \\]

where \\(W_1=(\\dfrac{1}{1-\\dfrac{P}{P_{lim}}})^{\\alpha}\\), \\(W_2=(2-A)^{\\beta}\\), and hydro-pressure \\(P=-\\dfrac{1}{3}\\sum_{j=1}^{3}\\sigma_{jj}\\), \\(A=max(\\dfrac{s_2}{s_1}, \\dfrac{s_2}{s_3})\\). \\(s_1\\), \\(s_2\\), \\(s_3\\) are the deviatoric stresses, and \\(s_1 \\ge s_2 \\ge s_3\\).

"},{"location":"mateditor/mat_theory_hyper-elasticity/","title":"Hyperelasticity and Curve Fitting","text":""},{"location":"mateditor/mat_theory_hyper-elasticity/#isotropic-hyperelasticity","title":"Isotropic hyperelasticity","text":"

The elastic potential energy in hyperelastic material can be obtained from the initial state with no stress activation. Therefore, we have the main invariable terms of the right Cauchy-Green deformation tensor C(\\(I_{1}\\), \\(I_{2}\\), \\(I_{3}\\)), or the main invariable of the deformation tensor excluding the volume changes (\\(\\bar{I}_{1}\\), \\(\\bar{I}_{2}\\), \\(\\bar{I}_{3}\\)). The potential can be expressed as \\(\\mathbf{W}=\\mathbf{W}(I_{1},I_{2},I_{3})\\), or \\(\\mathbf{W}=\\mathbf{W}(\\bar{I}_{1},\\bar{I}_{2},\\bar{I}_{3})\\).

The nonlinear constitutive relation of a hyperelastic material is defined by the relation between the second-order Piola-Kirchhoff stress and the Green-Lagrange strain, the total Lagrange method is more efficient in solving such models.

When the elastic potential energy \\(W\\) of the hyperelasticity is known, the second Piola-Kirchhoff stress and strain-stress relationship can be calculated as follows

\\[ S=2\\dfrac{\\partial W}{\\partial C} \\] \\[ C=4\\dfrac{\\partial^{2}W}{\\partial C\\partial C} \\]

The following are several forms of strain-energy potential (W) provided for the modeling of incompressible or nearly incompressible hyperelastic materials.

"},{"location":"mateditor/mat_theory_hyper-elasticity/#arruda-boyce-model","title":"Arruda-Boyce model","text":"

The form of the strain-energy potential for Arruda-Boyce model is

\\[ \\begin{array}{ccl} W & = & \\mu[\\dfrac{1}{2}(\\bar{I}_{1}-3)+\\dfrac{1}{20\\lambda_{m}^{2}}(\\bar{I_{1}^{2}}-9)+\\dfrac{11}{1050\\lambda_{m}^{4}}(\\bar{I_{1}^{3}}-27)\\\\ & + & \\dfrac{19}{7000\\lambda_{m}^{6}}(\\bar{I_{1}^{4}}-81) + \\dfrac{519}{673750\\lambda_{m}^{8}}(\\bar{I_{1}^{5}}-243)]\\\\ & + & \\dfrac{1}{D_1}(\\dfrac{J^{2}-1}{2}-\\mathrm{ln}J) \\end{array} \\]

where \\(\\mu\\) is the initial shear modulus of the material, \\(\\lambda_{m}\\) is limiting network stretch, and \\(D_1\\) is the material incompressibility parameter.

The initial shear modulus is

\\[ \\mu=\\dfrac{\\mu_{0}}{1+\\dfrac{3}{5\\lambda_{m}^{2}}+\\dfrac{99}{175\\lambda_{m}^{4}}+\\dfrac{513}{875\\lambda_{m}^{6}}+\\dfrac{42039}{67375\\lambda_{m}^{8}}} \\]

The initial bulk modulus is

\\[ K=\\dfrac{2}{D_1} \\]

As the parameter \\(\\lambda_L\\) goes to infinity, the model is equivalent to neo-Hookean form.

"},{"location":"mateditor/mat_theory_hyper-elasticity/#blatz-ko-foam-model","title":"Blatz-Ko foam model","text":"

The form of strain-energy potential for the Blatz-Ko model is:

\\[ W=\\frac{\\mu}{2}\\left(\\frac{I_{2}}{I_{3}}+2\\sqrt{I_{3}}-5\\right) \\]

where \\(\\mu\\) is the initial shear modulus of material. The initial bulk modulus is defined as :

\\[ K = \\frac{5}{3}\\mu \\]"},{"location":"mateditor/mat_theory_hyper-elasticity/#gent-model","title":"Gent model","text":"

The form of the strain-energy potential for the Gent model is:

\\[ W=-\\frac{\\mu J_{m}}{2}\\mathrm{ln}\\left(1-\\frac{\\bar{I}_{1}-3}{J_{m}}\\right)+\\frac{1}{D_1}\\left(\\frac{J^{2}-1}{2}-\\mathrm{ln}J\\right) \\]

where \\(\\mu\\) is the initial shear modulus of material, \\(J_m\\) is limiting value of \\(\\bar{I}_1-3\\), \\(D_1\\) is material incompressibility parameter.

The initial bulk modulus is

\\[ K=\\dfrac{2}{D_1} \\]

When the parameter \\(J_m\\) goes to infinity, the Gent model is equivalent to neo-Hookean form.

"},{"location":"mateditor/mat_theory_hyper-elasticity/#mooney-rivlin-model","title":"Mooney-Rivlin model","text":"

This model includes two-, three-, five-, and nine-terma Mooney-Rivlin models. The form of the strain-energy potential for a two-parameter Mooney-Rivlin model is

\\[ W=C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right)+\\frac{1}{D_1}\\left(J-1\\right)^{2} \\]

where \\(C_{10}\\), \\(C_{01}\\), and \\(D_{1}\\) are the material constants.

The form of strain-energy potential for a three-parameter Mooney-Rivlin model is

\\[ W=C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right)+C_{11}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right)+\\frac{1}{D_1}\\left(J-1\\right)^{2} \\]

where \\(C_{10}\\), \\(C_{01}\\), \\(C_{11}\\), and \\(D_1\\) are material constants.

The form of strain-energy potential for a five-parameter Mooney-Rivlin model is

\\[ \\begin{array}{ccl} W & = & C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right)+C_{20}\\left(\\bar{I}_{1}-3\\right)^{2}\\\\ & + & C_{11}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right)+C_{02}\\left(\\bar{I}_{2}-3\\right)^{2}+\\frac{1}{D_1}\\left(J-1\\right)^{2} \\end{array} \\]

where \\(C_{10}\\), \\(C_{01}\\), \\(C_{20}\\), \\(C_{11}\\), \\(C_{02}\\), and \\(D_1\\) are material constants.

The form of strain-energy potential for a nine-parameter Mooney-Rivlin model is

\\[ \\begin{array}{ccl} W & = & C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right)+C_{20}\\left(\\bar{I}_{1}-3\\right)^{2}\\\\ & + & C_{11}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right)+C_{02}\\left(\\bar{I}_{2}-3\\right)^{2}+C_{30}\\left(\\bar{I}_{1}-3\\right)^{3}\\\\ & + & C_{21}\\left(\\bar{I}_{1}-3\\right)^{2}\\left(\\bar{I}_{2}-3\\right)+C_{12}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right)^{2}+C_{03}\\left(\\bar{I}_{2}-3\\right)^{3}\\\\ & + & \\frac{1}{D_1}\\left(J-1\\right)^{2} \\end{array} \\]

where \\(C_{10}\\), \\(C_{01}\\), \\(C_{20}\\), \\(C_{11}\\), \\(C_{02}\\), \\(C_{30}\\), \\(C_{21}\\), \\(C_{12}\\), \\(C_{03}\\), and \\(D_1\\) are material constants.

The initial shear modulus is given by:

\\[ \\mu=2(C_{10}+C_{01}) \\]

The initial bulk modulus is

\\[ K=\\dfrac{2}{D_1} \\]"},{"location":"mateditor/mat_theory_hyper-elasticity/#neo-hookean-model","title":"Neo-Hookean model","text":"

The Neo-Hookean model is a well-known hyperelastic model with an expanded linear rule (Hooke rule) having isotropy so that it can respond to finite deformation problems. The elastic potential is as follows.

\\[ W=\\frac{\\mu}{2}(\\bar{I}_{1}-3)+\\dfrac{1}{D_{1}}(J-1)^{2} \\]

where \\(\\mu\\) is initial shear modulus of materials, \\(D_{1}\\) is the material constant.

The initial bulk modulus is given by:

\\[ K=\\dfrac{2}{D_1} \\]"},{"location":"mateditor/mat_theory_hyper-elasticity/#ogden-compressible-foam-model","title":"Ogden compressible foam model","text":"

The strain-energy potential of the Ogden compressible foam model is based on the principal stretches of left Cauchy strain tensor, which has the form:

\\[ W=\\sum_{i=1}^{N}\\frac{\\mu_{i}}{\\alpha_{i}}\\left(J^{\\alpha_{i}/3}\\left(\\bar{\\lambda}_{1}^{\\alpha_{i}}+\\bar{\\lambda}_{2}^{\\alpha_{i}}+\\bar{\\lambda}_{3}^{\\alpha_{i}}\\right)-3\\right)+\\sum_{i=1}^{N}\\frac{\\mu_{i}}{\\alpha_{i}\\beta_{i}}\\left(J^{-\\alpha_{i}\\beta_{i}}-1\\right) \\]

where N determines the order of the polynomial, \\(\\mu_i\\), \\(\\alpha_i\\) are material constants, \\(D_k\\) is incompressiblity parameter. The reduced principal strench is defined by:

\\[ \\bar{\\lambda}_{p}=J^{-\\frac{1}{3}}\\lambda_p,\\; J=(\\lambda_{1}\\lambda_{2}\\lambda_{3})^{\\frac{1}{2}} \\]

The initial shear modulus is given by:

\\[ \\mu=\\dfrac{\\sum_{i=1}^{N}\\mu_{i}\\alpha_{i}}{2} \\]

The initial bulk modulus K is defined by

\\[ K = \\sum_{i=1}^{N}\\mu_{i}\\alpha_{i}\\left(\\dfrac{1}{3}+\\beta_{i}\\right) \\]

When parameters N=1, \\(\\alpha_1\\)=-2, \\(\\mu_1\\)=-\\(\\mu\\), and \\(\\beta\\)=0.5, the Ogden compressible model is converted to the Blatz-Ko model.

"},{"location":"mateditor/mat_theory_hyper-elasticity/#ogden-model","title":"Ogden model","text":"

The strain-energy potential of the Ogden compressible foam model is based on the principal stretches of left Cauchy strain tensor, which has the form:

\\[ W=\\sum_{i=1}^{N}\\frac{\\mu_{i}}{\\alpha_{i}}\\left(\\bar{\\lambda}_{1}^{\\alpha_{i}}+\\bar{\\lambda}_{2}^{\\alpha_{i}}+\\bar{\\lambda}_{3}^{\\alpha_{i}}-3\\right)+\\sum_{k=1}^{N}\\frac{1}{D_{k}}\\left(J-1\\right)^{2k} \\]

where N determines the order of the polynomial, \\(\\mu_i\\), \\(\\alpha_i\\) are material constants, \\(D_k\\) is incompressiblity parameter. The reduced principal strench is defined by:

\\[ \\bar{\\lambda}_{p}=J^{-\\frac{1}{3}}\\lambda_p,\\; J=(\\lambda_{1}\\lambda_{2}\\lambda_{3})^{\\frac{1}{2}} \\]

The initial shear modulus is given by:

\\[ \\mu=\\dfrac{\\sum_{i=1}^{N}\\mu_{i}\\alpha_{i}}{2} \\]

The initial bulk modulus K is defined by

\\[ K = \\dfrac{2}{D_1} \\]

When parameters N=1, \\(\\alpha_1\\)=2, the Ogden model is converted to the neo-Hookean model. When parameters N=2, \\(\\alpha_1\\)=2 and \\(\\alpha_2\\)=-2, the Ogden model is converted to the 2-parameter Mooney-Rivlin model.

"},{"location":"mateditor/mat_theory_hyper-elasticity/#polynomial-form","title":"Polynomial form","text":"

The polynomial form of strain-energy potential is:

\\[ W=\\sum_{i+j=1}^{N}c_{ij}\\left(\\bar{I}_{1}-3\\right)^{i}\\left(\\bar{I_{2}}-3\\right)^{j}+\\sum_{k=1}^{N}\\frac{1}{D_{k}}\\left(J-1\\right)^{2k} \\]

where \\(N\\) determines the order of polynomial, \\(c_{ij}\\), \\(D_k\\) are material constants.

The initial shear modulus is given by:

\\[ \\mu=2\\left(C_{10}+C_{01}\\right) \\]

The initial bulk modulus K is defined by

\\[ K = \\dfrac{2}{D_1} \\]

The Polynomial model is converted to following models with specific parameters:

Parameters of Polynomial model Equivalent model N=1, \\(C_{01}\\)=0 neo-Hookean N=1 2-parameter Mooney-Rivlin N=2 5-parameter Mooney-Rivlin N=3 9-parameter Mooney-Rivlin"},{"location":"mateditor/mat_theory_hyper-elasticity/#yeoh-model","title":"Yeoh model","text":"

The Yeoh model is also called the reduced polynomial form. The strain-energy potential is

\\[ W=\\sum_{i=1}^{N}c_{i0}\\left(\\bar{I}_{1}-3\\right)^{i}+\\sum_{k=1}^{N}\\frac{1}{D_{k}}\\left(J-1\\right)^{2k} \\]

where N denotes the order of the polynomial, \\(C_{i0}\\) and \\(D_k\\) are material constants. When N=1, Yeoh becomes neo-Hookean model.

The initial shear modulus is defined:

\\[ \\mu=2c_{10} \\]

The initial bulk modulus is:

\\[ K=\\frac{2}{D_1} \\]"},{"location":"mateditor/mat_theory_hyper-elasticity/#hyperelasticity-material-curve-fitting","title":"Hyperelasticity Material Curve Fitting","text":"

The mechanical response of hyperelastic materials is determined by the hyperelastic constants in the strain energy density function of a model. To get correct results during a hyperelastic analysis, it is required to precisely assess the material constants of the materials being tested. These constants are usually derived for a material based on the experimental strain-stress data. The test data are generally taken from several modes of deformation over a wide range of strain values. The material constants could be fit using test data in at least as many deformation states as will be experienced in the finite element analysis.

For hyperelastic materials, simple deformation tests can be used to characterize the material constants. The six different deformation modes are graphically illustrated in the figure below. Combinations of data from multiple tests will enhance the characterization of the hyperelastic behavior of a material.

Although these six different deformation states are accepted, we find that upon the addition of hydrostatic stresses, the following modes of deformation are the same:

  1. Uniaxial Tension and Equibiaxial Compression.
  2. Uniaxial Compression and Equibiaxial Tension.
  3. Planar Tension and Planar Compression.

With these equivalent modes of testing, we now have only three independent deformation modes for which one can get experimental data.

In the analysis, when the coordinate system is chosen to consistent with the principal directions of deformation, the right Cauchy-Green strain tensor can be written in matrix form by:

\\[ [C] = \\begin{bmatrix} \\lambda_1^2 & 0 & 0\\\\ 0 & \\lambda_2^2 & 0\\\\ 0 & 0 & \\lambda_3^2 \\end{bmatrix} \\]

where \\(\\lambda_i\\)=1+\\(\\epsilon_i\\) is principal stretch ratio in the i-th direction, \\(epsilon_i\\) is principal value of the engineering strain tensor in the i-th direction. The principal invariants of right Cauchy-Green strain tensor \\(C_{ij}\\) are:

\\[ I_1 = \\lambda_1^2+\\lambda_2^2+\\lambda_3^2 \\] \\[ I_2 = \\lambda_1^2\\lambda_2^2 + \\lambda_1^2\\lambda_3^2 + \\lambda_2^2\\lambda_3^2 \\] \\[ I_3 = \\lambda_1^2\\lambda_2^2\\lambda_3^2 \\]

For the fully incompressible material, the principal invariant \\(I_3\\) is one:

\\[ \\lambda_1^2\\lambda_2^2\\lambda_3^2=1 \\]"},{"location":"mateditor/mat_theory_hyper-elasticity/#uniaxial-tension-equibiaxial-compression","title":"Uniaxial tension (Equibiaxial compression)","text":"

For the uniaxial tension deformation, the principal stretch ratios in the directions orthogonal to the 'pulling' axis is identical. Thus, the principal stretches during uniaxial tension \\(\\lambda_i\\) are given by:

Due to incompressibility:

\\[ \\lambda_2\\lambda_3=\\lambda^{-1} \\]

and with

\\[ \\lambda_2=\\lambda_3=\\lambda_1^{-1/2} \\]

For uniaxial tension, the first and second strain invariants then become:

\\[ I_1= \\lambda_1^2+2\\lambda_1^{-1}\\\\ I_2=2\\lambda_1+\\lambda_1^{-2} \\]

The corresponding engineering stress can be expressed using principal stretch ratio:

\\[ T_1=2(\\lambda_1-\\lambda_1^{-2})[\\dfrac{\\partial W}{\\partial I_1}+\\lambda_1^{-1}\\dfrac{\\partial W}{\\partial I_2}] \\]"},{"location":"mateditor/mat_theory_hyper-elasticity/#equibiaxial-tension-uniaxial-compression","title":"Equibiaxial tension (Uniaxial compression)","text":"

During an equibiaxial tension test, the principal stretch ratios in the directions being loaded are identical. Therefore, for quibiaxial tension, the principal stretches, \\(\\lambda_i\\) are given by:

According to incompressibility, we have

\\[ \\lambda_3=\\lambda_1^{-2} \\]

For equibiaxial tension, the first and second strain invariants then become:

\\[ I_1=2\\lambda_1^2+\\lambda_1^{-4} \\\\ I_2=\\lambda_1^4+2\\lambda_1^{-2} \\]

The corresponding engineering stress can be expressed using principal stretch ratio:

\\[ T_1=2(\\lambda_1-\\lambda_1^{-5})[\\dfrac{\\partial W}{\\partial I_1} + \\lambda_1^2\\dfrac{\\partial W}{\\partial I_2}] \\]"},{"location":"mateditor/mat_theory_hyper-elasticity/#pure-shear-uniaxial-tension-and-uniaxial-compression-in-orthogonal-directions","title":"Pure Shear (Uniaxial tension and uniaxial compression in orthogonal directions)","text":"

For pure shear deformation mode, plane strain is generally assumed so that there is no deformation in the 'wide' direction of the specimen. Including the incompressibility, we have

\\[ \\lambda_2=1 \\\\ \\lambda_3 = \\lambda_1^{-1} \\]

For pure shear, the first and second strain invariants are:

\\[ I_1=I_2=\\lambda_1^2+\\lambda_1^{-2}+1 \\]

The corresponding engineering stress can be expressed using principal stretch ratio:

\\[ T_1=2(\\lambda_1 - \\lambda_1^{-3})[\\dfrac{\\partial W}{\\partial I_1} + \\dfrac{\\partial W}{\\partial I_2}] \\]"},{"location":"mateditor/mat_theory_hyper-elasticity/#volumetric-deformation","title":"Volumetric Deformation","text":"

The volumetric deformation is given as:

\\[ \\lambda_1=\\lambda_2=\\lambda_3=\\lambda\\\\ J=\\lambda^3 \\]

As nearly incompressible is assumed, we have:

\\[ \\lambda \\approx 1 \\]

The pressure P is directly related to the volume ratio J:

\\[ P=\\dfrac{\\partial W}{\\partial J} \\]"},{"location":"mateditor/mat_theory_hyper-elasticity/#deformations-for-principal-stretches-based-models","title":"Deformations for principal stretches based models","text":"

For the models based on the principal stretches, such Ogden model, the strain-stress relation can be obtained by deriving the strain energy with respect to the stretch.

\\[ \\sigma(\\lambda)=\\dfrac{\\partial W(\\lambda)}{\\partial \\lambda} \\]

The corresponding engineering stress is:

\\[ T_1 = \\dfrac{\\partial W(\\lambda_1)}{\\partial \\lambda_1} \\lambda_1^{-1} \\]"},{"location":"mateditor/mat_theory_hyper-elasticity/#material-stability-check","title":"Material stability check","text":"

Stability checks are critical for the following analysis. A nonlinear material is stable if the secondary work required for an arbitrary change in the deformation is always positive. We usually use the Drucker stability criterion to determine the stability of the hyperelastic materials. Mathematically, this is:

\\[ d\\sigma_{ij}d\\epsilon_{ij}>0 \\]

where \\(d\\sigma\\) is the change in the Cauchy stress tensor corresponding to a change in the logarithmic strain.

The material stability checks can be done at the end of preprocessing but before an analysis actually begins. Checking for the stability of a material can be more conveniently accomplished by checking for the positive definiteness of the material stiffness. The program checks for the loss of stability of six typical stress paths including uniaxial tension and compression, equibiaxial tension and compression, and planar tension and compression. the range of the stretch ratio over which the stability is checked is chosen from 0.1 to 10.

"},{"location":"mateditor/mat_theory_io/","title":"Theory IO","text":"

Some properties are mutually exclusive of each other and require that only one property in the mutually exclusive set be unsuppressed. The addition or removing of the suppression for one of these properties automatically suppresses the other mutually exclusive properties.

For example, defining Isotropic Elasticity and Orthotropic Elasticity for the same material represents redundant elasticity behavior. Only one behavior can be active for the material. When such a conflict occurs, the property defined last is used and the previously defined, conflicting property is automatically suppressed.

The properties that are mutually exclusive are grouped in the following table.

Group Material Property Elastic properties Isotropic Elasticity, Orthotropic Elasticity, Anisotropic Elasticity, Mooney-Rivlin, Neo-Hookean, Polynomial, Yeoh, Ogden, Arruda-Boyce, Gent, Blatz-Ko, Ogden Foam, Extended Tube, Mullins Effect Plastic properties Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening Thermal conductivity properties Thermal Conductivity Isotropic, Thermal Conductivity Orthotropic Resistivity properties Isotropic Resistivity, Orthotropic Resistivity Electric permittivity properties Isotropic Relative Permittivity, Orthotropic Relative Permittivity Dielectric loss properties Isotropic Dielectric Loss Tangent, Orthotropic Dielectric Loss Tangent Magnetic permeability properties Isotropic Relative Permeability, Orthotropic Relative Permeability Magnetic loss properties Isotropic Relative Imaginary Permeability, Isotropic Magnetic Loss Tangent, Orthotropic Magnetic Loss Tangent"},{"location":"mateditor/mat_theory_plasticity/","title":"Plasticity","text":"

This section describes the plastic laws in details.

"},{"location":"mateditor/mat_theory_plasticity/#johnson-cook-model","title":"Johnson-Cook Model","text":"

In this model the material behaves as a linear-elastic material when the quivalent stress is lower than the plastic yield stress. For higher stress values, the material behavior is plastic, and the true stress is calculated as:

\\[ \\sigma = (a+b\\epsilon_p^n)(1+c\\cdot ln\\dfrac{\\dot{\\epsilon}}{\\dot{\\epsilon}_0})(1-(\\dfrac{T-T_r}{T_{melt}-T_r})^m) \\]

where \\(\\epsilon_p\\) is the plastic strain, \\(\\dot{\\epsilon}\\) is strain rate, \\(T\\) is the temperature, \\(T_r\\) is the ambient temperature, \\(T_{melt}\\) is the melting temperature. The plastic yield stress \\(a\\) should always be greater than zero. The plastic hardening exponent \\(n\\) must be less than or equal to 1.

"},{"location":"mateditor/mat_theory_plasticity/#zerilli-armstrong-model","title":"Zerilli-Armstrong Model","text":"

The stress during plastic deformation is defined by

\\[ \\sigma = C_0 + C_1 exp(-C_3 T + C_4 T ln \\dfrac{\\dot{\\epsilon}}{\\dot{\\epsilon}_0} ) + C_5 \\epsilon_p ^n \\]

where the yield stress \\(C_0\\) should be positive, plastic hardening exponent \\(n\\) must be less than 1.

"},{"location":"mateditor/mat_theory_plasticity/#hill-model","title":"Hill Model","text":"

The Hill model describes the orthotropic plastic material. The yield stress can be input by parameters or tabular data. The yield stress is defined as:

\\[ \\sigma_y = a(\\epsilon_0+\\epsilon_p)^n \\mathrm{max}(\\dot{\\epsilon}, \\dot{\\epsilon}_0)^m \\]

The maximum elastic stress is given by

\\[ \\sigma_0 = a(\\epsilon_0)^n (\\dot{\\epsilon}_0)^m \\]

The yield stress is compresed to the equivalent stress: $$ \\sigma_{eq} = \\sqrt{A_1 \\sigma_1^2 + A_2 \\sigma_2^2 -A_3 \\sigma_1 \\sigma_2 +A_{12} \\sigma_{12}^2} $$

where parameters \\(A_1\\), \\(A_2\\), \\(A_3\\), and \\(A_{12}\\) are defined by the Lankford constants.

"},{"location":"mateditor/mat_theory_plasticity/#orthotropic-hill-model","title":"Orthotropic Hill Model","text":"

This model describes the orthotropic elastic behavior material with Hill plasticity. The yield stress is compared to an equivalent stress for the orthotropic materials. The equivalent stress for solid elements is defined as:

\\[ \\sigma_{eq} = \\sqrt{F(\\sigma_{22}^2 - \\sigma_{33}^2) + G(\\sigma_{33}^2 - \\sigma_{11}^2) + H(\\sigma_{11} - \\sigma_{22}^2) + 2L\\sigma_{23}^2 + 2M\\sigma_{31}^2 + 2N\\sigma_{12}^2} \\]

For the shell element, the equivalent yield stress is :

\\[ \\sigma_{eq} = \\sqrt{(G+H)\\sigma_{11}^2 +(F+H) \\sigma_{22}^2 - 2H \\sigma_{11} \\sigma_{22} + 2N\\sigma_{12}^2} \\]"},{"location":"mateditor/mat_theory_plasticity/#rate-dependent-multilinear-hardening","title":"Rate-Dependent MultiLinear Hardening","text":"

This model describes an isotropic elasto-plastic material using user-input funcitons for the strain-stress curves at the different strain rates. No yield stress equations are needed because constitutive relations are given by the tabular data.

"},{"location":"mateditor/mat_theory_plasticity/#cowper-symonds-model","title":"Cowper-Symonds Model","text":"

Similar to the Johnson-Cook model, Cowper-Symonds law models isotropic elasto-plastic materials. The yield stress is defined by the stress constants, tabular data, or a combination of both. The pure constant formulation is given here:

\\[ \\sigma = (a+b\\epsilon_p^n)(1+(\\dfrac{\\dot{\\epsilon}}{c})^{\\frac{1}{p}}) \\]

where the yield stress \\(a\\) should be positive, plastic hardening exponent \\(n\\) must be less than 1.

"},{"location":"mateditor/mat_theory_plasticity/#zhao-model","title":"Zhao Model","text":"

Zhao model describes the isotropic plastic strain rate-dependent materials. The strain-stress relation is based on the formula below:

\\[ \\sigma = (A + B \\epsilon_p^n) + (C-D\\epsilon_p^m)\\cdot \\mathrm{ln}\\dfrac{\\dot{\\epsilon}}{\\dot{\\epsilon}_0}+E_1 \\dot{\\epsilon}^k \\]

where the yield stress \\(A\\) should be positive, plastic hardening exponent \\(n\\) must be less than 1. If \\(\\dot{\\epsilon} \\le \\dot{\\epsilon}_0\\), the term \\((C-D\\epsilon_p^m)\\cdot \\mathrm{ln}\\dfrac{\\dot{\\epsilon}}{\\dot{\\epsilon}_0}=0\\), the stress becomes:

\\[ \\sigma = (A + B \\epsilon_p^n) + E_1 \\dot{\\epsilon}^k \\]"},{"location":"mateditor/mat_theory_plasticity/#steinberg-guinan-model","title":"Steinberg-Guinan Model","text":"

This model defines an isotropic elasto-plastic mateial with thermal softening. When the material approaches melting temperature, the yield strength and shear modulus decrease to zeero. The melting energy is given as

\\[ E_m = E_c + \\rho_0 C_p T_m \\]

where \\(E_c\\) is the cold compression energy.

When the internal energy \\(E\\) is less than \\(Em\\), the shear modulus and the yield stress are :

\\[ G = G_0 [1 + b_1 p V^{\\frac{1}{3}} - h(T-T_0)] e^{-\\frac{fE}{E-E_m}} \\] \\[ \\sigma_y = \\sigma_0(1+\\beta \\epsilon_p^{\\mathrm{(max)}})^n [1 + b_2 p V^{\\frac{1}{3}} -h(T-T_0)]e^{-\\frac{fE}{E-E_m}} \\]

where initial shear modulus \\(G_0 = \\dfrac{E_0}{2(1+\\nu)}\\).

"},{"location":"mateditor/mat_theory_plasticity/#gurson-model","title":"Gurson Model","text":"

The Gurson law can be used to model visco-elasto-plastic strain rate-depdent porous materials. The yield stress can be obtained from the tabular data or the Cowper-Symond's law, the latter formulation is defined as:

\\[ \\sigma_M = (A + B \\epsilon_M^n) (1 + (\\dfrac{\\dot{\\epsilon}}{c})^{\\frac{1}{p}}) \\]

The von Mises critera for the viscoplastic flow are given as

\\[ \\Omega_{vm} = \\sigma_{qt} - \\sigma_{M}\\sqrt{1 + q_3 f^{*2} - 2q_1 f^{*2} \\mathrm{cosh}(\\dfrac{3q_2\\sigma_m}{2\\sigma_M})} \\]

or

\\[ \\Omega_{vm} =\\dfrac{\\sigma^2_{qe}}{\\sigma^2_M} + 2q_1 f^* \\mathrm{cosh}(\\dfrac{3}{2}q_2 \\dfrac{\\sigma_m}{\\sigma_M}) - (1 + q_3 f^{*2}) \\]

where \\(\\sigma_M\\) is the admissible stress, \\(\\sigma_m\\) is the trace, \\(\\sigma_eq\\) is the von Mises stress, \\(q_1\\), \\(q_2\\), and \\(q_3\\) are the Gurson material constants. The specific coalescence function \\(f*\\) is defined as

\\[ f^* = f_c + \\dfrac{f_u - f_c}{f_F - f_c}(f - f_c) \\quad \\mathrm{if}\\, f \\gt f_c \\]"},{"location":"mateditor/mat_theory_plasticity/#barlat3-model","title":"Barlat3 Model","text":"

This is an orthotropic elastoplastic law for modeling anisotropic materials in metal forming process. Thus it is widely applied in the shell elements. The plastic hardening is described by the input parameters or user-defined tabular data. The anisotropic yield criteria F for plane stress is given by:

\\[ F = a |K_1 + K_2|^m + a |K_1 - K_2|^m + c |2K_2|^m - 2\\sigma_y^m = 0 \\]

where coefficient \\(K_1 = \\frac{\\sigma_{xx} + h \\sigma_{yy}}{2}\\) and \\(K_2 = \\sqrt{(\\frac{\\sigma_{xx} - h \\sigma_{yy}}{2})^2 + p^2 \\sigma_{xy}^2}\\). The constants \\(a\\), \\(c\\), and \\(h\\) can be obtained from the Lankford constants.

When the Young's modulus is based on the input parameters. The expression is

\\[ E(t) = E - (E_0-E_{inf})[1-\\mathrm{exp}(-C_E \\bar{\\epsilon}_p)] \\]

where \\(E_0\\) is the initial Youngs' modulus, \\(E_{inf}\\) is the asymptotic Young's modulus, and \\(\\bar{\\epsilon}_p\\) is the accumulated equivalent plastic strain.

"},{"location":"mateditor/mat_theory_plasticity/#yoshida-uemori-model","title":"Yoshida-Uemori Model","text":"

This model can describe the large strain cyclic plasticity of metals. The law is based on the yielding and bounding surfaces.

For solid elements, von Mises yield criterion is used as:

\\[ f = \\dfrac{3}{2} (\\mathbf{s} - \\mathbf{\\alpha}) \\colon (\\mathbf{s} - \\mathbf{\\alpha}) - Y^2 \\]

For shell elements, Hill or Barlat3 yield criterion is used. The Hill law is expressed as:

\\[ f_{Hill} = \\varphi(\\mathbf{\\sigma} - \\mathbf{\\alpha})- Y^2 \\]

where \\(Y\\) is yield stress, and \\(\\mathbf{\\alpha}\\) is total back stress. Let \\(\\mathbf{A}=\\mathbf{\\sigma}-\\mathbf{\\alpha}\\), the function \\(\\varphi\\) becomes

\\[ \\varphi(A) = A_{xx}^2 - \\dfrac{2r_0}{1+r_0}A_{xx}A_{yy} + \\dfrac{r_0(1+r_{90})}{r_{90}(1+r_0)}A_{yy}^2 + \\frac{r_0 + r_{90}}{r_{90}(1+r_0)}(2r_{45}+1)A_{xy}^2 \\]

The Barlat law is defined as:

\\[ f_{Barlat} = \\phi(\\sigma - \\alpha) - 2Y^M \\]

where \\(M\\) is the exponent in Barlat's yield criterion.

"},{"location":"mateditor/mat_theory_plasticity/#hohnson-holmquist-model","title":"Hohnson-Holmquist Model","text":"

This law describes the behaivor of brittle materials, such as glass and ceramics.

\\[ \\sigma^* = (1-D)\\sigma^*_i + D \\sigma_f^* \\]

where the equivalent stress of the intact materials \\(\\sigma_i^*\\) can be expressed as

\\[ \\sigma_i^* = a (P^* + T^*)^n (1 + c\\mathrm{ln}\\dfrac{\\dot{\\epsilon}}{\\dot{\\epsilon}_0}) \\]

and the equivalent stress of the failed materials \\(\\sigma_f^*\\) is

\\[ \\sigma_f^* = b(P^*)^m (1+c\\mathrm{ln}\\dfrac{\\dot{\\epsilon}}{\\dot{\\epsilon}_0}) \\]"},{"location":"mateditor/mat_theory_plasticity/#swift-voce-model","title":"Swift-Voce Model","text":"

Swift-Voce elastoplastic model can combine the Johnson-Cook strain rate hardening and temperature softening. This model can be applied for the orthotropic materials and allows a quadratic non-assoicated flow rule. The yield stress can be calculated using a combination of Swift and Voce models as shown below.

\\(\\sigma_y = \\{ \\alpha [A(\\bar{\\epsilon}_p + \\epsilon_0)^n] + (1+\\alpha)[K_0 + Q(1-\\mathrm{exp}(-B\\bar{\\epsilon }_p))]\\} (1+C \\mathrm{ln}\\dfrac{\\dot{\\bar{\\epsilon}}_p}{\\dot{\\epsilon}_0}) [1 - (\\dfrac{T-T_{ref}}{T_{melt} - T_{ref}})^m]\\)

The plastic non-associated flow rule is computed as:

\\[ \\Delta \\epsilon_p = \\Delta \\bar{\\epsilon}_p \\dfrac{\\partial g(\\sigma)}{\\partial \\sigma} \\]

where \\(g(\\sigma) = \\sqrt{\\sigma^TG\\sigma}\\).

"},{"location":"mateditor/mat_theory_plasticity/#hensel-spittel-model","title":"Hensel-Spittel Model","text":"

The hensel-Spittel yield stress is a function of strain, strain rate, and temperature. This model is often used in hot forging simulations. The yield stress is defined as :

\\[ \\sigma_y = A_0 e^{m_1 T} \\epsilon^{m_2} \\dot{\\epsilon}^{m_3} e^{\\frac{m_4}{\\epsilon}} (1+\\epsilon)^{m_5T} e^{m_7\\epsilon} \\]

where true strain \\(\\epsilon = \\epsilon_0 + \\bar{\\epsilon}_p\\), \\(\\dot{\\epsilon}\\) is the true strain rate.

"},{"location":"mateditor/mat_theory_plasticity/#vegter-model","title":"Vegter Model","text":"

The yield function is defined as

\\[ \\phi = \\bar{\\sigma} - \\sigma_Y \\]

where \\(\\bar{\\sigma}\\) is the interpolated Vegter equivalent stress.

"},{"location":"mateditor/mat_workflow/","title":"Material workflow","text":"

This section discusses about the material data, and precedures for working with MatEditor.

"},{"location":"mateditor/mat_workflow/#material-data","title":"Material data","text":"

Material data is the source of the material information that is used for the analysis of the system it is contained in. The information in a material data component system is used if shared to an analysis system. MatEditor allows you to view, edit, and add data for use in your analysis system.

"},{"location":"mateditor/mat_workflow/#importing","title":"Importing","text":"

You can import data into an system as a new material. The following types of files are supported for import:

Note

When you import material data, the materials contained in that source will be added to the material outline.

"},{"location":"mateditor/mat_workflow/#editing","title":"Editing","text":"

Property and Table panes provide constant and tabular data input. You can edit both constant and tabular data.

"},{"location":"mateditor/mat_workflow/#constant-data","title":"Constant data","text":"

You edit constant data by changing the value and/or unit of that data in the Properties pane. The value is modified by clicking the cell in the Value column and typing in the new value. If available, changing the unit will convert the value to correspond to the new unit. If the value entered is invalid or not acceptable it will be indicated in yellow or red to gain users' attention.

"},{"location":"mateditor/mat_workflow/#tabular-data","title":"Tabular data","text":"

If Value cell shows a tabular format indication. This data is edited in the Table pane and each datum is a value and unit as one integral piece. If the value entered is invalid or not acceptable it will be indicated in yellow or red to gain users' attention. The unit is shown in the header, and you can change unit if necessary. The units between table header and Property pane column are connnected. Modifying either one of them changes units on both areas.

"},{"location":"mateditor/mat_workflow/#suppression","title":"Suppression","text":"

A material property may be defined but suppressed to prevent it from being sent to analysis process in the system. A data item may be suppressed by selecting the dropdown in the suppression column. Suppressed items and its children are shown by a strike through the name (for example, ) and the dropdown being set to True in the suppression column.

"},{"location":"mateditor/mat_workflow/#perform-material-tasks-in-mateditor","title":"Perform material tasks in MatEditor","text":"

All material related tasks require that you perform the following basic tasks:

Task Procedure Create new material. In the Menu or Toolbar, click New Material to add a new material. Add material properties.
  1. Activate the material in the Material Outline pane that is to receive the additional property.
  2. Toggle the property in the Property Outline pane that you want to add.
Delete material properties.
  1. Activate the material in the Material Outline pane whose property is to be deleted.
  2. Select the material property in the Properties pane.
  3. Right-click and choose Delete or on the menu bar, choose Delete.
Modify material properties.
  1. Activate the material in the Material Outline pane that contains the property you want to modify.
  2. In the Properties pane change the value or unit for constant data.
  3. Perform one of the following:
Suppress material properties.
  1. Activate the material in the Material Outline pane that contains the property you want to suppress.
  2. Select the dropdown in the suppression column for the property you want to suppress.
"},{"location":"mateditor/mateditor_overview/","title":"Overview","text":"

MatEditor is a free material editor software program for engineers. This tool provides you comprehensive material properties those are often used in engineering simulation and finite element analysis.

"},{"location":"mateditor/mateditor_overview/#specification","title":"Specification","text":"Specification Description Operation system Microsoft Windows 7 to 10; 64-bit Physical memory At least 4 GB

Supported unit systems :

"},{"location":"mateditor/mateditor_overview/#material-properties","title":"Material properties","text":"

The supported material properties are listed in the table below.

Category Materials Basic Density, Isotropic Thermal Expansion, Isotropic Instantaneous Thermal Expansion, Orthotropic Thermal Expansion, Orthotropic Instantaneous Thermal Expansion, Constant Damping Coefficient Linear Elastic Isotropic Elasticity, Orthotropic Elasticity, Viscoelastic Hyperelastic Test Data Uniaxial Test Data, Biaxial Test Data, Shear Test Data, Volumetric Test Data, SimpleShear Test Data, Uniaxial Tension Test Data, Uniaxial Compression Test Data Hyperelastic Arruda-Boyce, Blatz-Ko, Gent, Mooney-Rivlin 2, Mooney-Rivlin 3, Mooney-Rivlin 5, Mooney-Rivlin 9, Neo-Hookean, Ogden 1st Order, Ogden 2nd Order, Ogden 3rd Order, Polynomial 1st Order, Polynomial 2nd Order, Polynomial 3rd Order, Yeoh 1st Order, Yeoh 2nd Order, Yeoh 3rd Order Plasticity Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening, Anand Viscoplasticity, Johnson-Cook, Zerilli-Armstrong Creep Strain Hardening, Time Hardening, Generalized Exponential, Generalized Graham, Generalized Blackburn, Modified Time Hardening, Modified Strain Hardening, Generalized Garofalo, Exponential Form, Norton, Combined Time Hardening, Rational Polynomial, Generalized Time Hardening Visco-elastic Prony Shear Relaxation, Prony Volumetric Relaxation Equations of State (EOS) Compaction, Gruneisen, Ideal Gas, Linear, LSZK, Murnaghan, NASG, Noble-Abel, Osborne, Polynomial, Puff, Stiff Gas, Tillotson Failure Johnson Other Mechanical Strain Life Parameters, Compressive Ultimate Strength, Compressive Yield Strength, LaRc0304 Constants, Orthotropic Strain Limits, Orthotropic Stress Limits, Puck Constants, Tensile Ultimate Strength, Tensile Yield Strength, Tsai-Wu Constants, Shape Memory Effect, Drucker-Prager Strength Piecewise, Drucker-Prager Strength Linear, Ideal Gas EOS, Crushable Foam, Nonlinear Elastic Model Damage, Plakin Special Hardening, Tensile Pressure Failure, Crack Softening Failure Thermal Enthalpy, Isotropic Thermal Conductivity, Orthotropic Thermal Conductivity, Specific Heat Electromagnetics B-H Curve, Isotropic Relative Permeability, Orthotropic Relative Permeability, Isotropic Resistivity, Orthotropic Resistivity, Isotropic Relative Permittivity, Orthotropic Relative Permittivity, Isotropic Dielectric Loss Tangent, Isotropic Magnetic Loss Tangent, Isotropic Relative Imaginary Permeability, Orthotropic Dielectric Loss Tangent, Orthotropic Magnetic Loss Tangent Fluid Dynamic Viscosity, Kinematic Viscosity, Lemalar Prandtl Number, Turbulent Prandtl Number, ALE"},{"location":"mateditor/mateditor_overview/#predefined-materials","title":"Predefined materials","text":"

WELSIM also provide predefined materials, which covers most of commonly used materials. Users can choose these materials and apply to the successive finite element analysis.

Category Materials General Materials Structural Steel, Stainless Steel, Aluminum Alloy, Concrete, Copper Alloy, Gray Cast Iron, Titanium Alloy Nonlinear Materials Aluminum Alloy NL, Concrete NL, Copper Alloy NL, Stainless Steel NL, Structural Steel NL, Titanium Alloy NL Hyperelastic Materials Elastomer Mooney-Rivlin, Elastomer Neo-Hookean, Elastomer Ogden, Elastomer Yeoh, Neoprene Rubber Thermal Materials Brass, Bronze, Copper, Diamond, Ferrite, Nodular Cast Iron, Solder, Teflon, Tungsten, Wood Electromagnetic Materials SS416, Supermendure, TDK-K1, TDK-M33, TDK-N30, TDK-N41, TDK-N45, TDK-N48, TDK-N49, TDK-N87, TDK-N97, TDK-T38, TDK-T66 Other Materials Water Liquid, Argon, Ash"},{"location":"mateditor/mateditor_overview/#download","title":"Download","text":"

MatEditor software is available at our official website.

"},{"location":"mateditor/material_data/","title":"Defining materials","text":"

This section describes how to create material objects and define material properties in the WELSIM application.

"},{"location":"mateditor/material_data/#overview","title":"Overview","text":"

Material Module serves as a database for material properties used in a modeling project. The module not only provides a material library but also allow you to create a material using the given properties. The spreadsheet of a Material object is the primary user interface designed to let you create, save, and retrieve material models. The well-defined material object can be saved and used in the subsequent projects.

Material Module is shown as a Material Project and Material Objects in the Project Explorer (tree) window. The solution system contains only one Material Project, which acts as a material repository in the modeling system. The Material Project may include multiple Material Objects, where the properties can be added or edited by users.

To access Material Object properties, you can choose one of the following methods: * Double click on the Material Object. * Right click on a Material Object, and select Edit item from the context menu.

"},{"location":"mateditor/material_data/#modes-of-operation","title":"Modes of operation","text":"

The data included in the Material Module is automatically saved as you save the project.

"},{"location":"mateditor/material_data/#user-interface","title":"User interface","text":"

The Material Editor spreadsheet is an essential portion of the WELSIM user interface, and it displays material-related components that allow users to edit material data easily.

"},{"location":"mateditor/material_data/#editing-mode","title":"Editing mode","text":"

Presented in this section are two configurations for the material property editing. The first configuration method is based on the library as shown in Figure\u00a0[fig:ch3_guide_mat_ui_lib], and the second configuration is designed to manually combine the properties for the material object as shown in Figure\u00a0[fig:ch3_guide_mat_ui_build]. You can click on the Library or Build tab to switch these two editing modes.

Note

  1. You can click on category tabs to browse different materials.
  2. Loading a material dataset from the library removes all pre-existing properties.
"},{"location":"mateditor/material_data/#build-outline-tab","title":"Build outline tab","text":"

The Build Outline Tab shows an outline of the contents of the togglable material properties. You can add a property data entry to the material by toggling on the property entry or remove property by toggling off the property entry.

"},{"location":"mateditor/material_data/#properties-pane","title":"Properties pane","text":"

The Properties pane displays all properties that are going to be added to the Material Object. You can tune the property values at this pane. The columns in this spreadsheet pane are:

You can delete a property by right-clicking on a row and select Remove Rows from the pop-up context menu.

The Material Properties pane provides the following command buttons to the bottom of the window:

"},{"location":"mateditor/material_data/#working-with-material-data","title":"Working with material data","text":""},{"location":"mateditor/material_data/#exporting","title":"Exporting","text":"

You can export the complete material data to an external file. The following format is supported for export:

To implement the exporting, you can use one of the following methods:

"},{"location":"mateditor/material_data/#mateditor-applicaiton","title":"MatEditor applicaiton","text":"

MatEditor is a free application allow you to create and edit material data for the computer aided engineering. It is a smaller and concise application but has most of features that material module of WELSIM has. More details about MatEditor, please visit MatEditor page.

"},{"location":"unitconverter/unitconverter/","title":"UnitConverter","text":"

UnitConverter is a free unit conversion software program for engineers. This tool allows you to convert a large number of engineering units quickly and accurately.

"},{"location":"unitconverter/unitconverter/#specification","title":"Specification","text":"Specification Description Operation system Microsoft Windows 7 to 10; 64-bit Physical memory At least 4 GB

Supported unit systems :

"},{"location":"unitconverter/unitconverter/#supported-units","title":"Supported units","text":"

The supported units are listed in the table below.

Category Materials Base Angle, Current, Length, Mass, Temperature, Time Common Area, Density, Energy, Frequency, Volume Mechanical Acceleration, Angular Acceleration, Angular Velocity, Force, Moment of Inertia, Power, Pressure, Torque, Velocity Thermal Heat Flux Density, Heat Transfer Coefficient, Specific Heat Capacity, Thermal Conductivity, Thermal Expansivity Electrical Capacitance, Electric Charge, Electrical Conductance, Electrical Conductivity, Inductance, Surface Charge Density, Surface Current Density, Voltage, Volume Charge Density Magnetic Magnetic field strength, Magnetic flux density"},{"location":"unitconverter/unitconverter/#download","title":"Download","text":"

UnitConverter software is available at our official website.

"},{"location":"welsim/release_notes/","title":"WELSIM release notes","text":"

This release notes are specific to WELSIM 2024R1 and arranged by the version and features.

"},{"location":"welsim/release_notes/#upgrading","title":"Upgrading","text":"

To upgrade WELSIM to the latest version, download the installer from our official website . \u200b

Since version 2.1, WelSim provides a version checker in the application, users can click Help -> Check for Updates on the menu and know if a new version is available.

To inspect the currently installed version, open the About dialog in WELSIM application.

"},{"location":"welsim/release_notes/#changelog","title":"Changelog","text":""},{"location":"welsim/release_notes/#2024r1-28-jan-at-2024","title":"2024R1 (2.8) Jan. at 2024","text":""},{"location":"welsim/release_notes/#2023r3-27-sept-at-2023","title":"2023R3 (2.7) Sept. at 2023","text":""},{"location":"welsim/release_notes/#2023r2-26-april-at-2023","title":"2023R2 (2.6) April at 2023","text":""},{"location":"welsim/release_notes/#2023r1-25-jan-at-2023","title":"2023R1 (2.5) Jan. at 2023","text":""},{"location":"welsim/release_notes/#24-dec-at-2022","title":"2.4 Dec. at 2022","text":""},{"location":"welsim/release_notes/#23-july-at-2022","title":"2.3 July at 2022","text":""},{"location":"welsim/release_notes/#22-may-at-2022","title":"2.2 May at 2022","text":""},{"location":"welsim/release_notes/#21-dec-at-2021","title":"2.1 Dec. at 2021","text":""},{"location":"welsim/release_notes/#20-january-at-2021","title":"2.0 January at 2021","text":""},{"location":"welsim/release_notes/#191-july-at-2020","title":"1.9.1 July at 2020","text":""},{"location":"welsim/release_notes/#19-november-2019","title":"1.9 November, 2019","text":""},{"location":"welsim/release_notes/#18-december-2018","title":"1.8 December, 2018","text":""},{"location":"welsim/release_notes/#17-july-2018","title":"1.7 July, 2018","text":""},{"location":"welsim/release_notes/#16-april-2018","title":"1.6 April, 2018","text":""},{"location":"welsim/release_notes/#15-february-2018","title":"1.5 February, 2018","text":""},{"location":"welsim/release_notes/#14-november-2017","title":"1.4 November, 2017","text":""},{"location":"welsim/release_notes/#13-september-2017","title":"1.3 September, 2017","text":""},{"location":"welsim/release_notes/#12-august-2017","title":"1.2 August, 2017","text":""},{"location":"welsim/release_notes/#11-july-2017","title":"1.1 July, 2017","text":""},{"location":"welsim/release_notes/#10-march-2017","title":"1.0 March 2017","text":""},{"location":"welsim/troubleshooting/","title":"Troubleshooting","text":"

If you encounter an issue that cannot be resolved here, please send the project file (*.wsdb and the associated folder), and the system information to info@welsim.com. Your computer information can be acquired by clicking About button on the toolbar.

"},{"location":"welsim/troubleshooting/#graphical-window-issue","title":"Graphical window issue","text":"

The graphics window fails to display items, and the context is all black. The screen capture of this issue is shown in Figure\u00a0below.

"},{"location":"welsim/troubleshooting/#result-data-matching-issue","title":"Result data matching issue","text":"

The result fails to display contours due to the dismatched mesh. The error message of this issue is shown in Figure below.

"},{"location":"welsim/get_started/quick_start/","title":"Quick start","text":"

This section demonstrates you the primary GUI features and workflow of WELSIM application.

"},{"location":"welsim/get_started/quick_start/#graphical-user-interface","title":"Graphical user interface","text":""},{"location":"welsim/get_started/quick_start/#overview","title":"Overview","text":"

The WELSIM application provides you an ease-of-use graphical interface to customize the finite element analysis settings. The primary components of graphical user interface include:

An overview of graphical user interface is shown in Figure below.

.

"},{"location":"welsim/get_started/quick_start/#menu-and-toolbar","title":"Menu and toolbar","text":"

Menus and toolbar contain primary commands of the application as shown in Figure below. Sections Main Menus and Toolbars of have more details.

.

"},{"location":"welsim/get_started/quick_start/#graphics-window","title":"Graphics window","text":"

The Graphics window displays the geometries and associated symbols, text, and annotations. In this window, you can pan, rotate, and zoom the 3D geometries using mouse and key. In addition to the geometries, this window may contain annotation, Graphics Toolbar, coordinate system symbol, ruler, logo, etc. A schematic view of the Graphics window is shown in Figure below.

.

"},{"location":"welsim/get_started/quick_start/#material-definition-spreadsheet","title":"Material definition spreadsheet","text":"

The material module provides a spreadsheet panel for you to define and review material properties. An overview of the material property spreadsheet is shown in Figure\u00a0below.

.

"},{"location":"welsim/get_started/quick_start/#geometry-display","title":"Geometry display","text":"

The Graphics window displays the 3D geometries, meshed elements, result contours, etc. A 3D geometry and object properties are shown in Figure below.

.

"},{"location":"welsim/get_started/quick_start/#mesh-display","title":"Mesh display","text":"

Graphics window displays the mesh as you select the mesh related objects in the tree. The Properties View shows the statistical data of the mesh as shown in Figure\u00a0below.

.

"},{"location":"welsim/get_started/quick_start/#boundary-condition-display","title":"Boundary condition display","text":"

For the boundary conditions, the Graphics window displays the highlighted entities (faces, edges, vertices), the Property View, Tabular Data, and Chart windows show the boundary values over time. The Properties View window also allows you to scope the geometry entities and set values, as shown in Figure\u00a0below.

.

"},{"location":"welsim/get_started/quick_start/#solution-display","title":"Solution display","text":"

After solving, the user interface displays the solution and results. The Graphics window displays the result contour and legend. The Properties View shows the Maximum and Minimum values of the result at the given Set Number. The Tabular Data and Chart Windows illustrate the maximum and minimum values over the time as shown in Figure \u00a0below.

.

"},{"location":"welsim/get_started/quick_start/#result-legend","title":"Result legend","text":"

You can adjust the result contour and legend by right clicking on the legend field and set the parameters in the context menu, as shown in Figure\u00a0below.

.

"},{"location":"welsim/get_started/quick_start/#workflow","title":"Workflow","text":"

Using WELSIM is straightforward. The following gives you the primary workflow steps in starting a finite element analysis project from scratch:

"},{"location":"welsim/get_started/quick_start/#create-a-new-project","title":"Create a new project","text":"

Clicking New command from Toolbar or File Menu creates a new simulation project. Several default objects are automatically generated in the tree, and the Graphics window is filled with the 3D modeling interface. The following shows the behaviors of creating a new project:

"},{"location":"welsim/get_started/quick_start/#defining-materials","title":"Defining materials","text":"

In addition to the default Structural Steel material, you can add new materials and define the properties. A Material object represents a material database. The following gives the behaviors of material definition.

"},{"location":"welsim/get_started/quick_start/#importing-or-creating-geometries","title":"Importing or creating geometries","text":"

You can add geometry data by importing a CAD file or creating primitive shapes using the commands from Toolbar or Geometry Menu.

"},{"location":"welsim/get_started/quick_start/#meshing","title":"Meshing","text":"

You can skip meshing at this moment because the system automatically meshes the domain at solving step if no mesh is generated. However, meshing at this step provides you an insight of the mesh quality and a chance to optimize the mesh. You can click the Mesh commands from the Toolbar or FEM Menu to perform the meshing operations.

"},{"location":"welsim/get_started/quick_start/#analysis-settings","title":"Analysis settings","text":"

You can define the analysis settings in the following order:

"},{"location":"welsim/get_started/quick_start/#imposing-initial-conditions","title":"Imposing initial conditions","text":"

For the transient analysis, you can define initial conditions. The available initial conditions are

"},{"location":"welsim/get_started/quick_start/#imposing-boundary-conditions","title":"Imposing boundary conditions","text":"

The boundary and body conditions are essential for the conducted analysis. Depending on the Physics Type and Analysis Type, you can insert various condition objects into the tree via the Toolbar or Menu. The following gives the behaviors of the body and boundary conditions.

"},{"location":"welsim/get_started/quick_start/#solve","title":"Solve","text":"

To solve the customized model, you can click the Compute command from the Toolbar or FEM Menu. The behaviors of solving are

"},{"location":"welsim/get_started/quick_start/#displaying-results","title":"Displaying results","text":"

Depending on the Physics Type and Analysis Type, you can insert various result objects into the tree via the Toolbar or Menu. The following gives the behaviors of the solution and results.

"},{"location":"welsim/get_started/quick_start/#completed","title":"Completed","text":"

The analysis is completed. You can Save the projects to an external \u201cwsdb\u201d file and close the application.

Note

The *.wsdb file and associated folder are the WELSIM database for project data persistence, you can open this project file later, on another computer, and on different operation systems.

"},{"location":"welsim/get_started/electromagnetics/electrostatic/","title":"Electrostatic analysis","text":"

This example shows you how to conduct a 3D electrostatic analysis for a unibody part.

"},{"location":"welsim/get_started/electromagnetics/electrostatic/#specifying-analysis","title":"Specifying analysis","text":"

In the Properties View of the FEM Project object, you set the Physics Type property to Electromagnetic and Analysis Type to Electrostatic. An Electro-Static analysis is defined as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/electromagnetics/electrostatic/#preparing-geometry","title":"Preparing geometry","text":"

Next, you can import the geometry file \u201ch_section_unibody.step\u201d by clicking the Import... command from the Toolbar or Geometry Menu. The imported geometry and material property are shown in Figure\u00a0below.

"},{"location":"welsim/get_started/electromagnetics/electrostatic/#setting-mesh","title":"Setting mesh","text":"

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 3e-3.

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 34,764 nodes, and 20,657 Tet10 elements generated as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/electromagnetics/electrostatic/#imposing-conditions","title":"Imposing conditions","text":"

Next, you impose two boundary conditions, a Ground, and Voltage by clicking the corresponding commands from the Toolbar and Electromagnetic Menu. In the Properties View of the Ground object, holding the Ctrl or Shift key and select left bottom and right top surfaces for the Geometry property, as shown in Figure\u00a0below.

In the Properties View of Voltage object, set the Voltage value to 5, and scope surfaces for the Geometry property, as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/electromagnetics/electrostatic/#solving-the-model","title":"Solving the model","text":"

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process. As shown in Figure\u00a0[fig:ch2_start_ex1_output_solver], this model is solved successfully.

"},{"location":"welsim/get_started/electromagnetics/electrostatic/#evaluating-results","title":"Evaluating results","text":"

To evaluate the deformation of the structure, you can add a Voltage object to the tree by clicking the Voltage item from the Toolbar, Electromagnetic Menu. Next, double-clicking the result object or clicking the Evaluate item from the Toolbar or FEM Menu, you display the contour in the Graphics window as shown in Figure\u00a0below.

Adding an electric field result object is similar. Clicking the Electric Field result from Toolbar or Electromagnetic Menu, you insert a Electric Field result object to the tree. Evaluating the default Total Electric Field Type, you obtain the magnitude of the electric field vector contour on the body in the Graphics window. The Maximum and Minimum values of field data are displayed in the Properties View window as shown in Figure\u00a0below.

Info

This project file is located at examples/quick_electrostatic_01.wsdb.

"},{"location":"welsim/get_started/structural/structural_modal/","title":"Structural modal analysis","text":"

This example shows you how to conduct a 3D transient structural analysis for an assembly.

"},{"location":"welsim/get_started/structural/structural_modal/#defining-materials","title":"Defining materials","text":"

In this multi-body analysis, we assign Structural Steel and Aluminum materials to different parts. Since a Structural Steel object is already added as you initialize a FEM Project, you only need to insert an aluminum material object by clicking Add Material from Toolbar or FEM Menu.

To edit the material properties, you can double-click the Material object, or right-click on the Material object and select the Edit command from the context menu. In the material editor, you select the Library tab > General Materials > Aluminum Alloy, then click Import button or double-click the Aluminum Alloy entry. Click the OK to save and exit the material editing.

You can rename this new material object to Aluminum by press F2 key or right-clicking.

"},{"location":"welsim/get_started/structural/structural_modal/#specifying-analysis","title":"Specifying analysis","text":"

In the Properties View of the FEM Project object, you set the Analysis Type property to Modal. A Modal Structural analysis is defined as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/structural/structural_modal/#preparing-geometry","title":"Preparing geometry","text":"

Next, you can import the geometry file \u201ch_section_multibody.step\u201d and assign the materials to the corresponding parts. Three Part objects in the Geometry group represent three bodies in the Graphics window, respectively. You assign the Aluminum material to the Part2, which is the connection body in the middle, the rest bodies are assigned with Structural Steel material.

"},{"location":"welsim/get_started/structural/structural_modal/#setting-mesh","title":"Setting mesh","text":"

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 3e-3, as shown in Figure\u00a0below.

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 42,329 nodes, and 25,920 Tet10 elements generated as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/structural/structural_modal/#specifying-contacts","title":"Specifying contacts","text":"

Next, you need to define two Contact Pairs to bond the three parts into one uni-body for the analysis. Clicking the Add Contact command from the Toolbar or FEM Menu, you add two Contact Pair objects into the tree. You can rename these two objects to Contact1 and Contact2, respectively. Then you select the surfaces for Master and Target Geometry properties.

"},{"location":"welsim/get_started/structural/structural_modal/#defining-analysis-settings","title":"Defining analysis settings","text":"

In the Properties View of Study Settings object, you can define the analysis details such as Number of Modes. Here, you can use the default settings as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/structural/structural_modal/#imposing-boundary-conditions","title":"Imposing boundary conditions","text":"

In this modal analysis, you impose a Constraint (Fixed Support) boundary condition, which can be processed by clicking the corresponding commands from the Toolbar and Structural Menu. In the Properties View of the Constraint object, select the left bottom surface for the Geometry property.

"},{"location":"welsim/get_started/structural/structural_modal/#solving-the-model","title":"Solving the model","text":"

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process.

"},{"location":"welsim/get_started/structural/structural_modal/#evaluating-results","title":"Evaluating results","text":"

To evaluate the deformation of the structure, you can add a Deformation object to the tree by clicking the Deformation item from the Toolbar, Structural Menu. A result object may provide multiple sub-result types. For example, a Deformation result object allows you to specify one deformation type from the candidates Deformation X, Y, Z, and Total.

After setting the Type property to Deformation Z, double-clicking on the result object displays the resulting contour in the Graphics window as shown in Figure\u00a0below. You also can click the Evaluate item from the Toolbar or FEM Menu to evaluate the result.

Info

This project file is located at examples/quick_structural_modal_solid_01.wsdb.

"},{"location":"welsim/get_started/structural/structural_static/","title":"Static structural analysis","text":"

This example shows you how to conduct a 3D static structural analysis for an assembly.

"},{"location":"welsim/get_started/structural/structural_static/#defining-materials","title":"Defining materials","text":"

In this multi-body analysis, we assign Structural Steel and Aluminum materials to different parts. Since a Structural Steel object is already added as you initialize a FEM Project, you only need to insert an aluminum material object by clicking Add Material from Toolbar or FEM Menu.

To edit the material properties, you can double-click the Material object, or right-click on the Material object and select the Edit command from the context menu. In the material editor, you select the Library tab > General Materials > Aluminum Alloy, then click Import button or double-click the Aluminum Alloy entry. The material properties are set as shown in Figure below. Click the OK to save and exit the material editing.

You can rename this new material object to Aluminum by press F2 key or right-clicking.

.

"},{"location":"welsim/get_started/structural/structural_static/#specifying-analysis","title":"Specifying analysis","text":"

Since the Static Structural analysis is the default settings at WELSIM application, you can keep the default settings as shown in Figure below.

"},{"location":"welsim/get_started/structural/structural_static/#preparing-geometry","title":"Preparing geometry","text":"

Next, you can import the geometry file \u201ch_section_multibody.step\u201d and assign the materials to the corresponding parts. As shown in Figure\u00a0below, three Part objects in the Geometry group represent three bodies in the Graphics window, respectively. You assign the Aluminum material to the Part2, which is the connection body in the middle, the rest bodies are assigned with Structural Steel material.

"},{"location":"welsim/get_started/structural/structural_static/#setting-mesh","title":"Setting mesh","text":"

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 5e-3, as shown in Figure\u00a0below.

Next, you add a Mesh Method object from the Toolbar or FEM Menu. In the property of this object, you select the left body for the Geometry property, and set Maximum Size value to 3e-3, , as shown in Figure\u00a0below.

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 21,117 nodes, and 12,427 Tet10 elements generated as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/structural/structural_static/#specifying-contacts","title":"Specifying contacts","text":"

Next, you need to define two Contact Pairs to bond the three parts into one uni-body for the analysis. Clicking the Add Contact command from the Toolbar or FEM Menu, you add two Contact Pair objects into the tree. You can rename these two objects to Contact1 and Contact2, respectively. Then you select the surfaces for Master and Target Geometry properties as shown in Figures\u00a0below.

"},{"location":"welsim/get_started/structural/structural_static/#imposing-conditions","title":"Imposing conditions","text":"

Next, you impose two boundary conditions, a Constraint (Fixed Support) and a Pressure by clicking the corresponding commands from the Toolbar and Structural Menu. In the Properties View of the Constraint object, select the left bottom surface for the Geometry property, as shown in Figure\u00a0below.

In the Properties View of Pressure object, set the Normal Pressure value to 1e7, and scope the right top surface for the Geometry property, as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/structural/structural_static/#solving-the-model","title":"Solving the model","text":"

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process. As shown in Figure\u00a0[fig:ch2_start_ex1_output_solver], this model is solved successfully.

"},{"location":"welsim/get_started/structural/structural_static/#evaluating-results","title":"Evaluating results","text":"

To evaluate the deformation of the structure, you can add a Deformation object to the tree by clicking the Deformation item from the Toolbar, Structural Menu. A result object may provide multiple sub-result types. For example, a Deformation result object allows you to specify one deformation type from the candidates Deformation X, Y, Z, and Total, as shown in Figure\u00a0below.

After setting the property Type to Total Deformation, double-clicking on the result object displays the resulting contour in the Graphics window. You can click the Evaluate item from the Toolbar or FEM Menu to evaluate the result.

Adding a stress result object is similar. Clicking the Stress result from Toolbar or Structural Menu, you insert a stress object to the tree. Evaluating the default von-Mises Stress Type, you obtain the von-Mises stress contour on bodies in the Graphics window. The Maximum and Minimum values of stress data are displayed in the Properties View, Tabular Data, and Chart windows.

Info

This project file is located at examples/quick_structural_static_solid_01.wsdb.

"},{"location":"welsim/get_started/structural/structural_transient/","title":"Transient structural analysis","text":"

This example shows you how to conduct a 3D transient structural analysis for an assembly.

"},{"location":"welsim/get_started/structural/structural_transient/#defining-materials","title":"Defining materials","text":"

In this multi-body analysis, we assign Structural Steel and Aluminum materials to different parts. Since a Structural Steel object is already added as you initialize a FEM Project, you only need to insert an aluminum material object by clicking Add Material from Toolbar or FEM Menu.

To edit the material properties, you can double-click the Material object, or right-click on the Material object and select the Edit command from the context menu. In the material editor, you select the Library tab > General Materials > Aluminum Alloy, then click Import button or double-click the Aluminum Alloy entry. The material properties are set as shown in Figure\u00a0below. Click the OK to save and exit the material editing.

You can rename this new material object to Aluminum by press F2 key or right-clicking.

"},{"location":"welsim/get_started/structural/structural_transient/#specifying-analysis","title":"Specifying analysis","text":"

In the Properties View of the FEM Project object, you set the Analysis Type property to Transient. A Transient Structural analysis is defined as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/structural/structural_transient/#preparing-geometry","title":"Preparing geometry","text":"

Next, you can import the geometry file \u201ch_section_multibody.step\u201d and assign the materials to the corresponding parts. As shown in Figure\u00a0below, three Part objects in the Geometry group represent three bodies in the Graphics window, respectively. You assign the Aluminum material to the Part2, which is the connection body in the middle, the rest bodies are assigned with Structural Steel material.

"},{"location":"welsim/get_started/structural/structural_transient/#setting-mesh","title":"Setting mesh","text":"

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 5e-3, as shown in Figure\u00a0below.

Next, you add a Mesh Method object from the Toolbar or FEM Menu. In the property of this object, you select the left body for the Geometry property, and set Maximum Size value to 3e-3, as shown in Figure\u00a0below.

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 21,117 nodes, and 12,427 Tet10 elements generated as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/structural/structural_transient/#specifying-contacts","title":"Specifying contacts","text":"

Next, you need to define two Contact Pairs to bond the three parts into one uni-body for the analysis. Clicking the Add Contact command from the Toolbar or FEM Menu, you add two Contact Pair objects into the tree. You can rename these two objects to Contact1 and Contact2, respectively. Then you select the surfaces for Master and Target Geometry properties as shown in Figures\u00a0below.

Note

Defining contacts is optional, adding a contact or not is up to your specific model.

"},{"location":"welsim/get_started/structural/structural_transient/#defining-analysis-settings","title":"Defining analysis settings","text":"

In this transient analysis, you define 18 steps and set the End Time for each step, as shown in Figure\u00a0below.

Next, you select the Study Settings object in the tree and set the Substeps property to 18, which determines the total number of substeps of the transient analysis. A screen capture of the defined properties is shown in Figure\u00a0below.

"},{"location":"welsim/get_started/structural/structural_transient/#imposing-conditions","title":"Imposing conditions","text":"

Next, you impose two boundary conditions, a Constraint (Fixed Support) and an Acceleration by clicking the corresponding commands from the Toolbar or Structural Menu. In the Properties View of the Constraint object, select the left bottom surface for the Geometry property, as shown in Figure\u00a0below.

In the Properties View of Acceleration object, set the Acceleration value for the current step, and repeat this value definition for each Step. After defining the acceleration values for all steps, you scope a surface on Part2 for the Geometry property, as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/structural/structural_transient/#solving-the-model","title":"Solving the model","text":"

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process. As shown in Figure\u00a0below, this model is solved successfully.

"},{"location":"welsim/get_started/structural/structural_transient/#evaluating-results","title":"Evaluating results","text":"

To evaluate the deformation of the structure, you can add a Deformation object to the tree by clicking the Deformation item from the Toolbar, Structural Menu. A result object may provide multiple sub-result types. For example, a Deformation result object allows you to specify one deformation type from the candidates Deformation X, Y, Z, and Total.

After setting the result Type to Deformation Z, double-clicking on the result object displays the resulting contour in the Graphics window as shown in Figure\u00a0below. You can click the Evaluate item from the Toolbar or FEM Menu to evaluate the result.

Adding a stress result object is similar. Clicking the Stress result from Toolbar or Structural Menu, you insert a stress object to the tree. Evaluating the default von-Mises Stress Type, you obtain the von-Mises stress contour on bodies in the Graphics window as shown in Figure\u00a0below. The Maximum and Minimum values of stress data are displayed in the Properties View, Tabular Data, and Chart windows.

Info

This project file is located at examples/quick_structural_transient_solid_01.wsdb.

"},{"location":"welsim/get_started/thermal/thermal_ss/","title":"Steady-state thermal analysis","text":"

This example shows you how to conduct a 3D static thermal analysis for an assembly.

"},{"location":"welsim/get_started/thermal/thermal_ss/#defining-materials","title":"Defining materials","text":"

In this multi-body analysis, we assign Structural Steel and Aluminum materials to different parts. Since a Structural Steel object is already added as you initialize a FEM Project, you only need to insert an aluminum material object by clicking Add Material from Toolbar or FEM Menu.

To edit the material properties, you can double-click the Material object, or right-click on the Material object and select the Edit command from the context menu. In the material editor, you select the Library tab > General Materials > Aluminum Alloy, then click Import button or double-click the Aluminum Alloy entry. The material properties are set as shown in Figure\u00a0below. Click the OK to save and exit the material editing.

You can rename this new material object to Aluminum by press F2 key or right-clicking.

"},{"location":"welsim/get_started/thermal/thermal_ss/#specifying-analysis","title":"Specifying analysis","text":"

In the Properties View of the FEM Project object, you set the Physics Type property to Thermal. A Steady-State Thermal analysis is defined as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/thermal/thermal_ss/#preparing-geometry","title":"Preparing geometry","text":"

Next, you can import the geometry file \u201ch_section_multibody.step\u201d and assign the materials to the corresponding parts. As shown in Figure, three Part objects in the Geometry group represent three bodies in the Graphics window, respectively. You assign the Aluminum material to the Part2, which is the connection body in the middle, the rest bodies are assigned with Structural Steel material.

"},{"location":"welsim/get_started/thermal/thermal_ss/#setting-mesh","title":"Setting mesh","text":"

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 3e-3.

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 42,329 nodes, and 25,920 Tet10 elements generated.

"},{"location":"welsim/get_started/thermal/thermal_ss/#specifying-contacts","title":"Specifying contacts","text":"

Next, you need to define two Contact Pairs to bond the three parts into one uni-body for the analysis. Clicking the Add Contact command from the Toolbar or FEM Menu, you add two Contact Pair objects into the tree. You can rename these two objects to Contact1 and Contact2, respectively. Then you select the surfaces for Master and Target Geometry properties.

"},{"location":"welsim/get_started/thermal/thermal_ss/#imposing-boundary-conditions","title":"Imposing boundary conditions","text":"

Next, you impose four boundary conditions, a Temperature, Heat Flux, Convection, and Radiation by clicking the corresponding commands from the Toolbar or Thermal Menu. In the Properties View of the Temperature object, select a left bottom surface for the Geometry property and set the Temperature value to 0, as shown in Figure\u00a0below.

In the Properties View of Heat Flux object, set the Heat Flux value to 5e3, and scope a surface for the Geometry property, as shown in Figure\u00a0below.

In the Properties View of Heat Radiation object, set the Radiation Coefficient value to 1e-6, Ambient Temperature value to 22.3, and scope a surface for the Geometry property, as shown in Figure\u00a0below.

In the Properties View of Heat Convection object, set the Convection Coefficient value to 1e3 and Ambient Temperature value to 22.3, and scope a surface for the Geometry property, as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/thermal/thermal_ss/#solving-the-model","title":"Solving the model","text":"

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process. As shown in Figure\u00a0below, this model is solved successfully.

"},{"location":"welsim/get_started/thermal/thermal_ss/#evaluating-results","title":"Evaluating results","text":"

To evaluate the deformation of the structure, you can add a Temperature object to the tree by clicking the Temperature item from the Toolbar or Thermal Menu. Next, double-clicking the result object or clicking the Evaluate item from the Toolbar or FEM Menu, you display the result contour in the Graphics window as shown in Figure\u00a0below.

Info

This project file is located at examples/quick_thermal_static_solid_01.wsdb.

"},{"location":"welsim/get_started/thermal/thermal_transient/","title":"Transient thermal analysis","text":"

This example shows you how to conduct a 3D transient thermal analysis for an assembly.

"},{"location":"welsim/get_started/thermal/thermal_transient/#defining-materials","title":"Defining materials","text":"

In this multi-body analysis, we assign Structural Steel and Aluminum materials to different parts. Since a Structural Steel object is already added as you initialize a FEM Project, you only need to insert an aluminum material object by clicking Add Material from Toolbar or FEM Menu.

To edit the material properties, you can double-click the Material object, or right-click on the Material object and select the Edit command from the context menu. In the material editor, you select the Library tab > General Materials > Aluminum Alloy, then click Import button or double-click the Aluminum Alloy entry. The material properties are set as shown in Figure\u00a0below. Click the OK to save and exit the material editing.

You can rename this new material object to Aluminum by press F2 key or right-clicking.

"},{"location":"welsim/get_started/thermal/thermal_transient/#specifying-analysis","title":"Specifying analysis","text":"

In the Properties View of the FEM Project object, you set the Physics Type property to Thermal and Analysis Type property to Transient. A Transient Thermal analysis is defined as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/thermal/thermal_transient/#preparing-geometry","title":"Preparing geometry","text":"

Next, you can import the geometry file \u201ch_section_multibody.step\u201d and assign the materials to the corresponding parts. As shown in Figure, three Part objects in the Geometry group represent three bodies in the Graphics window, respectively. You assign the Aluminum material to the Part2, which is the connection body in the middle, the rest bodies are assigned with Structural Steel material.

"},{"location":"welsim/get_started/thermal/thermal_transient/#setting-mesh","title":"Setting mesh","text":"

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 3e-3.

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 42,329 nodes, and 25,920 Tet10 elements generated.

"},{"location":"welsim/get_started/thermal/thermal_transient/#specifying-contacts","title":"Specifying contacts","text":"

Next, you need to define two Contact Pairs to bond the three parts into one uni-body for the analysis. Clicking the Add Contact command from the Toolbar or FEM Menu, you add two Contact Pair objects into the tree. You can rename these two objects to Contact1 and Contact2, respectively. Then you select the surfaces for Master and Target Geometry properties as shown in Figures\u00a0below.

"},{"location":"welsim/get_started/thermal/thermal_transient/#defining-analysis-settings","title":"Defining analysis settings","text":"

In this transient analysis, you define 1 step and set the Current End Time value to 600, as shown in Figure\u00a0below.

In the Properties View of Study Settings object in the tree, you can use the default settings as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/thermal/thermal_transient/#imposing-conditions","title":"Imposing conditions","text":"

Next, you can add an Initial Temperature object from the Toolbar or Thermal Menu. The initial temperature value is 300 as shown in Figure\u00a0below.

Next, you impose three boundary conditions, a Temperature, Heat Flux, and a Heat Convection by clicking the corresponding commands from the Toolbar and Thermal Menu. In the Properties View of the Temperature object, you select the bottom surface of Part1 for the Geometry property. Next set the Temperature value to 0, and define Initial Status to Equal to Step 1, as shown in Figure\u00a0below.

In the Properties View of Heat Flux object, set the Heat Flux value to -5000 and Initial Status to Equal to Step 1. Next, you scope a surface on Part1 for the Geometry property, as shown in Figure\u00a0below.

In the Properties View of Heat Convection object, set the Convection Coefficient value to 1000, Ambient Temperature value to 22.3, and Initial Status to Equal to Step 1. After defining these property values, you scope a surface on Part2 for the Geometry property, as shown in Figure\u00a0below.

"},{"location":"welsim/get_started/thermal/thermal_transient/#solving-the-model","title":"Solving the model","text":"

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process. As shown messages in Output window, this model is solved successfully.

"},{"location":"welsim/get_started/thermal/thermal_transient/#evaluating-results","title":"Evaluating results","text":"

To evaluate the temperature of the model, you can add a Temperature object to the tree by clicking the Temperature item from the Toolbar, Thermal Menu.

After inserting the result object and settings the Set Number to 15, double-clicking on the result object displays the resulting contour in the Graphics window as shown in Figure\u00a0below. You can click the Evaluate item from the Toolbar or FEM Menu to evaluate the result.

Info

This project file is located at examples/quick_thermal_transient_solid_01.wsdb.

"},{"location":"welsim/material/mat_overview/","title":"Overview","text":"

Material Module serves as a database for material properties used in analysis projects. The module not only provides a material library but allow you to create a material using the given properties. The properties view of a Material object is the primary user interface designed to let you create, save, and retrieve material models. The well-defined material object can be saved and used in the subsequent projects.

Note

The WELSIM Material module and MatEditor share the same features. For the completed and latest content, you can refer to the manual of MatEditor.

"},{"location":"welsim/material/mat_overview/#graphical-user-interface","title":"Graphical user interface","text":"

The ease-of-use Material Module contains the following graphical user interface components:

"},{"location":"welsim/material/mat_overview/#predefined-materials","title":"Predefined materials","text":"

WELSIM also provide predefined materials, which covers most of commonly used materials. Users can choose these materials and apply to the successive finite element analysis.

Category Materials General Materials Structural Steel, Stainless Steel, Aluminum Alloy, Concrete, Copper Alloy, Gray Cast Iron, Titanium Alloy Nonlinear Materials Aluminum Alloy NL, Concrete NL, Copper Alloy NL, Stainless Steel NL, Structural Steel NL, Titanium Alloy NL Hyperelastic Materials Elastomer Mooney-Rivlin, Elastomer Neo-Hookean, Elastomer Ogden, Elastomer Yeoh, Neoprene Rubber Thermal Materials Brass, Bronze, Copper, Diamond, Ferrite, Nodular Cast Iron, Solder, Teflon, Tungsten, Wood Electromagnetic Materials SS416, Supermendure Other Materials Water Liquid, Argon, Ash"},{"location":"welsim/material/mat_overview/#material-properties","title":"Material properties","text":"

The supported material properties are listed in the table below.

Category Materials Basic Density, Isotropic Thermal Expansion, Isotropic Instantaneous Thermal Expansion, Orthotropic Thermal Expansion, Orthotropic Instantaneous Thermal Expansion, Constant Damping Coefficient Linear Elastic Isotropic Elasticity, Orthotropic Elasticity, Viscoelastic Hyperelastic Test Data Uniaxial Test Data, Biaxial Test Data, Shear Test Data, Volumetric Test Data, SimpleShear Test Data, Uniaxial Tension Test Data, Uniaxial Compression Test Data Hyperelastic Arruda-Boyce, Blatz-Ko, Gent, Mooney-Rivlin 2, Mooney-Rivlin 3, Mooney-Rivlin 5, Mooney-Rivlin 9, Neo-Hookean, Ogden 1st Order, Ogden 2nd Order, Ogden 3rd Order, Polynomial 1st Order, Polynomial 2nd Order, Polynomial 3rd Order, Yeoh 1st Order, Yeoh 2nd Order, Yeoh 3rd Order Plasticity Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening, Anand Viscoplasticity Creep Strain Hardening, Time Hardening, Generalized Exponential, Generalized Graham, Generalized Blackburn, Modified Time Hardening, Modified Strain Hardening, Generalized Garofalo, Exponential Form, Norton, Combined Time Hardening, Rational Polynomial, Generalized Time Hardening Visco-elastic Prony Shear Relaxation, Prony Volumetric Relaxation Other Mechanical Strain Life Parameters, Compressive Ultimate Strength, Compressive Yield Strength, LaRc0304 Constants, Orthotropic Strain Limits, Orthotropic Stress Limits, Puck Constants, Tensile Ultimate Strength, Tensile Yield Strength, Tsai-Wu Constants, Shape Memory Effect, Drucker-Prager Strength Piecewise, Drucker-Prager Strength Linear, Ideal Gas EOS, Crushable Foam, Nonlinear Elastic Model Damage, Plakin Special Hardening, Tensile Pressure Failure, Crack Softening Failure Thermal Enthalpy, Isotropic Thermal Conductivity, Orthotropic Thermal Conductivity, Specific Heat Electromagnetics B-H Curve, Isotropic Relative Permeability, Orthotropic Relative Permeability, Isotropic Resistivity, Orthotropic Resistivity"},{"location":"welsim/material/mat_overview/#working-with-material-data","title":"Working with material data","text":""},{"location":"welsim/material/mat_overview/#exporting","title":"Exporting","text":"

You can export the complete material data to an external XML file. The following format is supported for export:

"},{"location":"welsim/mesh/mesh_usage/","title":"Usage in WELSIM","text":""},{"location":"welsim/mesh/mesh_usage/#basic-meshing-process","title":"Basic meshing process","text":"

The following steps provide the fundamental workflow for using the Meshing module as part of a finite element analysis in WELSIM.

  1. Create a finite element project and set the appropriate project type in the Properties of FEM Project object, such as Static Structural.

  2. Define appropriate material data for your analysis. The system provide a Structural Steel material, and you can create a new material object. Double-click, or Right click the material object. The Material Editing workspace appears, where you can add or edit material data as necessary.

  3. Import geometry to your system or build new geometry. Assign the material to the geometry.

  4. Click on the Mesh object in the Tree to access Meshing application functionality and apply mesh controls.

  5. Define loads and boundary conditions. Set up your analysis using that application's tools and features.

  6. You can solve your analysis by clicking solve button.

  7. Review your analysis results.

Note

You should save your data periodically (File>Save Project). The data will be saved as a .wsdb file and associated folder.

"},{"location":"welsim/mesh/meshing/","title":"Meshing Overview","text":""},{"location":"welsim/mesh/meshing/#philosophy","title":"Philosophy","text":"

The goal of meshing in WELSIM is to provide easy-to-use and stable meshing utilities that will simplify the mesh generation process.

"},{"location":"welsim/mesh/meshing/#physics-based-meshing","title":"Physics-based meshing","text":"

The WELSIM mesh generation is set based on the physics and engineering preferences. Particularly, the mesh system targets on the mechanical, thermal and electromagnetics physics.

"},{"location":"welsim/mesh/meshing/#meshing-application-interface","title":"Meshing application interface","text":"

The intuitive Meshing applicaiton interface, shown in the figure below, faciliates your use of all meshing controls and settings.

The funcational elements of the interface are described in the following table.

Window Component Description Main Menu This menu includes all basic menus such as File and Mesh. Standard Toolbar This toolbar contains commonly used application commands. Graphics Toolbar This toolbar contains commands that control pointer mode or cause an action in the graphics browser. Tree Outline Outline view of the project. Always visible. Location in the outline sets the context for other controls. Provides access to object's context menus. Allows renaming of objects. Establishes what details display in the Details View. Property Details View The Details View corresponds to the Outline selection. Displays a details window on the lower left panel (by default) which contains details about each object in the Outline. Geometry Window (also sometimes called the Graphics window) Displays and manipulates the visual representation of the object selected in the Outline. This window may display: <\\br> 3D Geometry<\\br> 2D/3D Graph<\\br> Spreadsheet<\\br> HTML Pages<\\br> Scale ruler<\\br> Triad control<\\br> Legend<\\br>"},{"location":"welsim/theory/contact/","title":"Structures with contact","text":"

As contact occurs among multiple bodies, the contact force \\(\\mathbf{t}_{c}\\) is transmitted via the contact surface. The principle equation of the virtual work can be rewritten as follows

\\[ \\begin{align} \\label{eq:ch5_contact_gov1} \\intop_{^{t'}V}\\thinspace^{t'}\\sigma\\colon\\delta^{t'}\\mathbf{A}_{(L)}d^{t'}v=\\intop_{^{t'}S_{t}}\\thinspace^{t'}\\mathbf{t}\\cdot\\delta\\mathbf{u}d^{t'}s+\\intop_{V}\\thinspace^{t'}\\mathbf{b}\\cdot\\delta\\mathbf{u}d^{t'}v+\\intop_{^{t'}S\\text{c}}\\thinspace^{t'}\\mathbf{t}_{c}[\\delta\\mathbf{u}^{(1)}-\\delta\\mathbf{u}^{(2)}] \\end{align} \\]

where notation \\(s_{c}\\) represents the contact area, \\(\\mathbf{u}^{(1)}\\) and \\(\\mathbf{u}^{(2)}\\) denotes the displacement of the contact object 1 and 2, respectively.

In the contact analysis, the surfaces involve contact are paired. One of these surfaces is called the master surface, and another type of surface is target surface. We also assume

The governing equations with contact term can be reduced to the finite element formation

\\[ \\intop_{^{t'}S_{c}}\\thinspace^{t'}\\mathbf{t}_{c}[\\delta\\mathbf{u}^{(1)}-\\delta\\mathbf{u}^{(2)}]\\approx\\delta\\mathbf{UK}_{C}\\triangle\\mathbf{U}+\\delta\\mathbf{UF}_{C} \\]

where \\(\\mathbf{K}_{c}\\) and \\(\\mathbf{F}_{c}\\) are contact rigid matrix, and the contact forces, respectively.

Remember that we introduced total Lagrange and update Lagrange methods, those formulation can be extended with the consideration of contact factors. The total Lagrange and updated Lagrange formulation with contact terms are given below

\\[ \\delta\\mathbf{U}^{T}(_{0}^{t}\\mathbf{K}_{L}+_{0}^{t}\\mathbf{K}_{NL}+\\mathbf{K}_{c})\\triangle\\mathbf{U}=\\delta\\mathbf{U}^{T}\\thinspace_{0}^{t'}\\mathbf{F}-\\delta\\mathbf{U}^{T}\\thinspace_{0}^{t}\\mathbf{Q}+\\delta\\mathbf{U}^{T}\\mathbf{F}_{c} \\] \\[ \\delta\\mathbf{U}^{T}(_{t}^{t}\\mathbf{K}_{L}+_{t}^{t}\\mathbf{K}_{NL}+\\mathbf{K}_{c})\\triangle\\mathbf{U}=\\delta\\mathbf{U}^{T}\\thinspace_{t}^{t'}\\mathbf{F}-\\delta\\mathbf{U}^{T}\\thinspace_{t}^{t}\\mathbf{Q}+\\delta\\mathbf{U}^{T}\\mathbf{F}_{c} \\]"},{"location":"welsim/theory/electromagnetic/","title":"Electromagnetic analysis","text":"

This section discuss the electromagnetic theories that are applied in the WELSIM application.

"},{"location":"welsim/theory/electromagnetic/#electromagnetic-field-fundamentals","title":"Electromagnetic field fundamentals","text":"

The electromagnetic fields are governed by the well-known Maxwell's equations\u00a0\\(\\eqref{eq:ch4_theory_maxwell1}\\)-\\(\\eqref{eq:ch4_theory_maxwell4}\\)12.

\\[ \\begin{align} \\label{eq:ch4_theory_maxwell1} \\nabla\\times\\mathbf{H}=\\mathbf{J}+\\dfrac{\\partial\\mathbf{D}}{\\partial t}=\\mathbf{J}_{S}+\\mathbf{J}_{e}+\\mathbf{J}_{V}+\\dfrac{\\partial\\mathbf{D}}{\\partial t} \\end{align} \\] \\[ \\begin{align} \\label{eq:ch4_theory_maxwell2} \\nabla\\times\\mathbf{E}=-\\dfrac{\\partial\\mathbf{B}}{\\partial t} \\end{align} \\] \\[ \\begin{align} \\label{eq:ch4_theory_maxwell3} \\nabla\\cdot\\mathbf{B}=0 \\end{align} \\] \\[ \\begin{align} \\label{eq:ch4_theory_maxwell4} \\nabla\\cdot\\mathbf{D}=\\rho \\end{align} \\]

where \\(\\mathbf{H}\\) is the magnetic field intensity vector, \\(\\mathbf{J}\\) is total current density vector, \\(\\mathbf{J}_{s}\\) is the applied source current density vector, \\(\\mathbf{J}_{e}\\) is the induced eddy current density vector, and \\(\\mathbf{J}_{VS}\\) is the velocity current density vector, \\(\\mathbf{D}\\) is the electric flux density vector (this term is also called electric displacement), \\(\\mathbf{E}\\) is the electric field intensity vector, \\(\\mathbf{B}\\) is the magnetic flux density vector, and \\(\\rho\\) is the electric charge density.

The above field governing equations contian the constitutive relations:

\\[ \\mathbf{D}=\\epsilon\\mathbf{E}+\\mathbf{P} \\]

and

\\[ \\mathbf{B}=\\mu\\mathbf{H} \\]

where \\(\\mathbf{P}\\) is the polarization density, and \\(\\mathbf{M}\\) is t he magnetization. In many materials the polarization density can be approximated as a scalar multiple of the electric field. \\(\\mu\\) is the magnetic permeability matrix. For example, if the magnetic permeability is a function of temperature,

\\[ \\mu=\\mu_{0}\\left[\\begin{array}{ccc} \\mu_{rx} & 0 & 0\\\\ 0 & \\mu_{ry} & 0\\\\ 0 & 0 & \\mu_{rz} \\end{array}\\right] \\]

For the permanent magnets, the constitutive relation of magnetic field becomes

\\[ \\mathbf{B}=\\mu\\mathbf{H}+\\mu_{0}\\mathbf{M}_{0} \\]

where \\(\\mathbf{M}_{0}\\) is the remanet intrinsic magnetization vector.

Similarly, the consitutive relations for the related electric fields are:

\\[ \\mathbf{J}=\\sigma[\\mathbf{E}+\\mathbf{v}\\times\\mathbf{B}] \\] \\[ \\sigma=\\left[\\begin{array}{ccc} \\sigma_{xx} & 0 & 0\\\\ 0 & \\sigma_{yy} & 0\\\\ 0 & 0 & \\sigma_{zz} \\end{array}\\right] \\] \\[ \\epsilon=\\left[\\begin{array}{ccc} \\epsilon_{xx} & 0 & 0\\\\ 0 & \\epsilon_{yy} & 0\\\\ 0 & 0 & \\epsilon_{zz} \\end{array}\\right] \\]

where \\(\\sigma\\) is the electrical conductivity matrix, \\(\\epsilon\\) is the permittivity matrix, and \\(v\\) is the velocity vector.

"},{"location":"welsim/theory/electromagnetic/#electrostatics","title":"Electrostatics","text":"

The WELSIM application introduces electric scalar potential to solve the electrostatic problems. When the time-derivetive of magnetic flux density is neglected from the full Maxwell's equations. The governing equations are reduced to

\\[ \\begin{align} \\label{eq:ch4_theory_govern_eqn_electrostatic} \\nabla\\times\\mathbf{H}=\\mathbf{J}+\\dfrac{\\partial\\mathbf{D}}{\\partial t} \\end{align} \\] \\[ \\nabla\\times\\mathbf{E}=\\mathbf{0} \\] \\[ \\nabla\\cdot\\mathbf{B}=0 \\] \\[ \\nabla\\cdot\\mathbf{D}=\\rho \\]

Since the electric field \\(\\mathbf{E}\\) is irrotational and can be expressed as the function of electric scalar potential

\\[ \\mathbf{E}=-\\nabla \\varphi \\]

where \\(\\varphi\\) is the electric scalar potential and has units of Volts in the SI system. Inserting this definition into the Gauss's Law gives:

\\[ -\\nabla \\cdot \\epsilon\\nabla\\varphi = \\rho - \\nabla \\cdot \\mathbf{P} \\]

which is Poisson's equation for the electric potential , where we have assumed a linear constitutive relation between \\(\\mathbf{D}\\) and \\(\\mathbf{E}\\) of the form \\(\\mathbf{D}=\\epsilon\\mathbf{E}+\\mathbf{P}\\).

"},{"location":"welsim/theory/electromagnetic/#boundary-conditions","title":"Boundary Conditions","text":"

For an electric material interface, the continuious conditions for \\(\\mathbf{E}\\), \\(\\mathbf{D}\\), and \\(\\mathbf{J}\\) are

\\[ E_{t1}-E_{t2}=0 \\] \\[ J_{1n}+\\dfrac{\\partial D_{1n}}{\\partial t}=J_{2n}+\\dfrac{\\partial D_{2n}}{\\partial t} \\] \\[ D_{1n}-D_{2n}=\\rho_{s} \\]

where \\(E_{t}\\) is the tangential components of \\(\\mathbf{E}\\), \\(J_{n}\\) is the normal components of \\(\\mathbf{J}\\), \\(D_{n}\\) is the normal components of \\(\\mathbf{D}\\), and \\(\\rho_{s}\\) is the surface charge density.

Since the solutons to the governing equation are non-unique, we must impose a Dirichlet boundary condition at least at one node in the domain to get the physical solution. The Dirichlet condition could be a fixed piecewise voltage value on certain nodes. In addition, the normal derivative boundary condition \\(\\hat{n}\\cdot\\mathbf{D}\\) such as surface charge density can be imposed on the boundary.

"},{"location":"welsim/theory/electromagnetic/#matrix-forms","title":"Matrix Forms","text":"

The electric scalar potential algorithm is applied in the WELSIM application for solving electrostatic problems. The governing equations are reduced to the following:

\\[ -\\nabla\\cdot\\left(\\epsilon\\nabla V\\right)=\\rho \\]

The matrix equation for an electrostatic analysis is derived from Equation \\(\\eqref{eq:ch4_theory_govern_eqn_electrostatic}\\):

\\[ \\left[K^{VS}\\right]\\left\\{ V_{e}\\right\\} =\\left\\{ L_{e}\\right\\} \\]

where

\\[ \\left[K^{VS}\\right]=\\intop_{V}\\left(\\nabla\\left\\{ N\\right\\} ^{T}\\right)^{T}\\epsilon\\left(\\nabla\\left\\{ N\\right\\} ^{T}\\right)dV \\] \\[ \\left\\{ L_{e}\\right\\} =\\left\\{ L_{e}^{n}\\right\\} +\\left\\{ L_{e}^{c}\\right\\} +\\left\\{ L_{e}^{SC}\\right\\} \\] \\[ \\left\\{ L_{e}^{c}\\right\\} =\\int_{V}\\rho\\left\\{ N\\right\\} ^{T}dV \\] \\[ \\left\\{ L_{e}^{sc}\\right\\} =\\int_{V}\\rho_{s}\\left\\{ N\\right\\} ^{T}dV \\]"},{"location":"welsim/theory/electromagnetic/#vector-magnetic-potential","title":"Vector magnetic potential","text":"

The WELSIM application applies the vector magnetic potential method for the magentostatic analysis. Considering the neglected electric displacement currents, the full Maxwell's equations can be reduced to

\\[ \\nabla\\times\\mathbf{H}=\\mathbf{J} \\] \\[ \\nabla\\times\\mathbf{E}=-\\dfrac{\\partial\\mathbf{B}}{\\partial t} \\] \\[ \\nabla\\cdot\\mathbf{B}=0 \\]

A numerical solution can be achieved by introducing potentials to the governing equations. The proposed magnetic vector potential\u00a0\\(\\mathbf{A}\\) and electric scalar potential\u00a0\\(V\\) have the following characteristics:

\\[ \\mathbf{B}=\\nabla\\times\\mathbf{A} \\] \\[ \\mathbf{E}=-\\dfrac{\\partial\\mathbf{A}}{\\partial t}-\\nabla V \\]

In addition, the Coulomb gauge condition is introduced to ensure the uniqueness of the vector potential, as shown in the following equations.

\\[ \\nabla\\times\\mathbf{v}\\nabla\\times\\mathbf{A}-\\nabla v_{e}\\nabla\\cdot\\mathbf{A}+\\sigma\\left\\{ \\dfrac{\\partial\\mathbf{A}}{\\partial t}\\right\\} +\\sigma\\nabla V-\\mathbf{v}\\times\\sigma\\nabla\\times\\mathbf{A}=\\mathbf{0} \\] \\[ \\nabla\\cdot\\left(\\sigma\\left\\{ \\dfrac{\\partial\\mathbf{A}}{\\partial t}\\right\\} -\\sigma\\nabla V+\\mathbf{v}\\times\\sigma\\nabla\\times\\mathbf{A}\\right)=\\mathbf{0} \\] \\[ \\nabla\\times\\mathbf{v}\\nabla\\times\\mathbf{A}-\\nabla v_{e}\\nabla\\cdot\\mathbf{A}=\\mathbf{J}_s+\\nabla\\times\\dfrac{1}{\\mathbf{v}_{0}}\\mathbf{v}\\mathbf{M}_{0} \\]

where matrix invarient \\(v_{e}\\) is \\(v_{e}=\\frac{1}{3}\\mathrm{tr}(v)=\\frac{1}{3}(v_{11}+v_{22}+v_{33})\\).

"},{"location":"welsim/theory/electromagnetic/#edge-element-magnetic-vector-potential","title":"Edge-element magnetic vector potential","text":"

Due to the limitation of node-based vector magnetic potential algorithm2, WELSIM application uses the edge-based finite element for the magnetic vector potential algorithm.

The governing equation for the edge finite element method is given below.

\\[ \\nabla\\times\\mathbf{v}\\nabla\\times\\mathbf{A}+\\sigma\\left\\{ \\dfrac{\\partial\\mathbf{A}}{\\partial t}+\\nabla V\\right\\} +\\epsilon\\left(\\left\\{ \\dfrac{\\partial^{2}\\mathbf{A}}{\\partial t^{2}}\\right\\} +\\nabla\\left\\{ \\dfrac{\\partial V}{\\partial t}\\right\\} \\right)=\\mathbf{0} \\] \\[ \\nabla\\cdot\\left(\\sigma\\left(\\left\\{ \\dfrac{\\partial\\mathbf{A}}{\\partial t}\\right\\} +\\nabla V\\right)+\\epsilon\\left(\\left\\{ \\dfrac{\\partial^{2}\\mathbf{A}}{\\partial t^{2}}\\right\\} +\\nabla\\left\\{ \\dfrac{\\partial V}{\\partial t}\\right\\} \\right)\\right)=\\mathbf{0} \\] \\[ \\nabla\\times\\mathbf{v}\\nabla\\times\\mathbf{A}=\\mathbf{J}_{s}+\\nabla\\times\\dfrac{1}{\\mathbf{v}_{0}}\\mathbf{v}\\mathbf{M}_{0} \\]

The uniqueness of these equations is ensured by the tree gauging procedure, which sets the edge-flux degrees of freedom related to the spanning tree of the finite element mesh to zero.

  1. John D. Jackson, Classical Electrodynamics, 3rd edition, Wiley.\u00a0\u21a9

  2. Jian-Ming Jin, The Finite Element Method in Electromagnetics, 2nd edition, Wiley-IEEE Press.\u00a0\u21a9\u21a9

"},{"location":"welsim/theory/elements/","title":"Element library","text":"

The WELSIM application supports several types of finite elements. This section discuss the details of element that is used in the program.

Element type Finite element type Description Plane element (Shell) Tri3 Three node triangular element Plane element (Shell) Tri6 Six node triangular element(quadratic) Solid element Tet4 Four node tetrahedral element Solid element Tet10 Ten node tetrahedral element(quadratic)

The element groups shown in Table\u00a0[tab:ch4_theory_elem_types] can be used for engineering analysis. The schematic views and the surface definition of those elements are given in Figures\u00a0[fig:ch4_theory_elem_views], [fig:ch4_theory_elem_triangles], and [fig:ch4_theory_elem_tet].

Surface No. Linear Quadratic 1 1-2-3 [front] 1-6-2-4-3-5 [front] 2 3-2-1 [back] 3-4-2-6-1-5 [back]

Surface No. Linear Quadratic 1 1-2-3 1-7-2-5-3-6 2 1-2-4 1-7-2-9-4-8 3 2-3-4 2-5-3-10-4-9 4 3-1-4 3-6-1-10-4-8"},{"location":"welsim/theory/geometricnl/","title":"Structures with geometric nonlinearity","text":"

In the analysis of finite deformation problems, the principle equation of virtual work becomes a nonlinear equation regarding the displacement-strain relation. To solve the nonlinear equation, an iterative algorithm is generally applied. When implementing an incremental analysis for a finite deformation problem, whether to refer to the initial status as a reference layout, or refer to the starting point of the increments can be selected. The former is called the total Lagrange method, and the latter is called the updated Lagrange method. Both the total Lagrange and updated Lagrange methods are available in the program. This section discusses the various geometrically nonlinear options available, including the large strain.

"},{"location":"welsim/theory/geometricnl/#decomposition-of-increments-of-virtual-work-equation","title":"Decomposition of increments of virtual work equation","text":"

Given the solid deformation at time t is known, the status at time t'=t+\\triangle t is unknown. The equilibrium equation, dynamic boundary condition, and external boundary condition can be expressed as

\\[ \\begin{align} \\label{eq:ch5_nonlinear_gov1} \\nabla_{t'\\mathbf{x}}\\cdot^{t'}\\sigma+^{t'}\\mathbf{b}=0\\quad\\text{in}V \\end{align} \\] \\[ ^{t'}\\sigma\\cdot^{t'}\\mathbf{n}=^{t'}\\mathbf{t}\\quad\\mathrm{on}\\thinspace^{t'}S \\] \\[ ^{t'}\\mathbf{u}=^{t'}\\bar{\\mathbf{u}} \\]

where \\(^{t'}\\sigma\\), \\(^{t'}\\mathbf{b}\\), \\(^{t'}\\mathbf{n}\\), \\(^{t'}\\mathbf{t}\\), \\(^{t'}\\mathbf{u}\\) are the Cauchy stress, body force, outward normal vector of the object's surface, fixed surface force, and fixed displacement in each time t'.

"},{"location":"welsim/theory/geometricnl/#principle-of-virtual-work","title":"Principle of virtual work","text":"

The principle of virtual work to the equation \\(\\eqref{eq:ch5_nonlinear_gov1}\\) is

\\[ \\begin{align} \\label{eq:ch5_nonlinear_gov2} \\int_{^{t'}V}^{t'}\\sigma:\\delta^{t'}\\mathbf{A}_{(L)}d^{t'}v=\\int_{^{t'}S_{t}}^{t'}\\mathbf{t}\\cdot\\delta\\mathbf{u}d^{t'}s+\\int_{V}^{t'}\\mathbf{b}\\cdot\\delta\\mathbf{u}d^{t'}v \\end{align} \\]

where \\(^{t'}\\mathbf{A}_{(L)}\\) is the linear portion of the Almansi strain tensor and can be calculated by

\\[ ^{t'}\\mathbf{A}_{(L)}=\\dfrac{1}{2}\\{\\dfrac{\\partial^{t'}\\mathbf{u}}{\\partial^{t'}\\mathbf{x}}+(\\dfrac{\\partial^{t'}\\mathbf{u}}{\\partial^{t'}\\mathbf{x}})^{T}\\} \\]

The equation \\(\\eqref{eq:ch5_nonlinear_gov2}\\) needs to be solved referring to layout V at time 0, or layout \\(^{t}v\\) at time t. The following sections will introduce these two algorithms: total Lagrange method and updated Lagrange method, respectively.

"},{"location":"welsim/theory/geometricnl/#formulation-of-total-lagrange-algorithm","title":"Formulation of total lagrange algorithm","text":"

The principle equation of the virtual work at time t' assuming the initial layout of time 0 is the reference domain, which is shown below.

\\[ \\begin{align} \\label{eq:ch5_nonlinear_total_lag_gov1} \\intop_{V}\\thinspace_{0}^{t'}\\mathbf{S}:\\delta_{0}^{t'}\\mathbf{E}dV=^{t'}\\delta\\mathbf{R} \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_nonlinear_total_lag_gov2} ^{t'}\\delta\\mathbf{R}=\\intop_{S_{t}}\\thinspace_{0}^{t'}\\mathbf{t}\\cdot\\delta dS+\\intop_{V}\\thinspace_{0}^{t'}\\mathbf{b}\\cdot\\delta\\mathbf{u}dV \\end{align} \\]

where \\(_{0}^{t'}\\mathbf{S}\\) and \\(_{0}^{t'}\\mathbf{E}\\) are the 2nd order Piola-Kirchhoff stress tensor and the Green-Lagrange strain tensor at time t', respectively. The initial domain at time 0 is called the reference domain. The body force \\(_{0}^{t'}\\mathbf{b}\\) and nominal surface force vector \\(_{0}^{t'}\\mathbf{t}\\) are

\\[ _{0}^{t'}\\mathbf{t}=\\dfrac{d^{t'}s}{dS}\\thinspace^{t'}\\mathbf{t} \\] \\[ _{0}^{t'}\\mathbf{b}=\\dfrac{d^{t'}v}{dV}\\thinspace^{t'}\\mathbf{b} \\]

The Green-Lagrange strain tensor at time t is defined by

\\[ _{0}^{t}\\mathbf{E}=\\dfrac{1}{2}\\{\\dfrac{\\partial^{t}\\mathbf{u}}{\\partial\\mathbf{X}}+(\\dfrac{\\partial^{t}\\mathbf{u}}{\\partial\\mathbf{X}})^{T}+(\\dfrac{\\partial^{t}\\mathbf{u}}{\\partial\\mathbf{X}})^{T}\\cdot\\dfrac{\\partial^{t}\\mathbf{u}}{\\partial\\mathbf{X}}\\} \\]

Then the displacement \\(^{t'}\\mathbf{u}\\) and 2nd order Piola-Kirchhoff stress \\(_{0}^{t'}\\mathbf{S}\\) at time t' are

\\[ \\begin{align} \\label{eq:ch5_nonlinear_total_lag_gov3} ^{t'}\\mathbf{u}=^{t}\\mathbf{u}+\\triangle\\mathbf{u} \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_nonlinear_total_lag_gov4} _{0}^{t'}\\mathbf{S}=_{0}^{t}\\mathbf{S}+\\triangle\\mathbf{S} \\end{align} \\]

Similarly, the incremental Green-Lagrange strain can be defined as

\\[ \\begin{align} \\label{eq:ch5_nonlinear_total_lag_gov5} ^{t'}\\mathbf{E}=^{t}\\mathbf{E}+\\triangle\\mathbf{E} \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_nonlinear_total_lag_gov6} \\triangle\\mathbf{E}=\\triangle\\mathbf{E}_{L}+\\triangle\\mathbf{E}_{NL} \\end{align} \\]

where

\\[ \\triangle\\mathbf{E}_{L}=\\dfrac{1}{2}\\{\\dfrac{\\partial\\triangle\\mathbf{u}}{\\partial\\mathbf{X}}+(\\dfrac{\\partial\\triangle\\mathbf{u}}{\\partial\\mathbf{X}})^{T}+(\\dfrac{\\partial\\triangle\\mathbf{u}}{\\partial\\mathbf{X}})^{T}\\cdot\\dfrac{\\partial^{t}\\mathbf{u}}{\\partial\\mathbf{X}}+(\\dfrac{\\partial^{t}\\mathbf{u}}{\\partial\\mathbf{X}})^{T}\\cdot\\dfrac{\\partial\\triangle\\mathbf{u}}{\\partial\\mathbf{X}}\\} \\] \\[ \\triangle\\mathbf{E}_{NL}=\\dfrac{1}{2}(\\dfrac{\\partial\\triangle\\mathbf{u}}{\\partial\\mathbf{X}})^{T}\\cdot\\dfrac{\\partial\\triangle\\mathbf{u}}{\\partial\\mathbf{X}} \\]

Substituting equations \\(\\eqref{eq:ch5_nonlinear_total_lag_gov3}\\), \\(\\eqref{eq:ch5_nonlinear_total_lag_gov4}\\), \\(\\eqref{eq:ch5_nonlinear_total_lag_gov5}\\), and \\(\\eqref{eq:ch5_nonlinear_total_lag_gov6}\\) into governing equations \\(\\eqref{eq:ch5_nonlinear_total_lag_gov1}\\) and \\(\\eqref{eq:ch5_nonlinear_total_lag_gov2}\\), we have

\\[ \\intop_{v}\\triangle\\mathbf{S}:(\\delta\\triangle\\mathbf{E}_{L}+\\delta\\triangle\\mathbf{E}_{NL})dV+\\intop_{V}\\thinspace_{0}^{t}\\mathbf{S}\\colon\\delta\\triangle\\mathbf{E}_{NL}dV=^{t'}\\delta\\mathbf{R}-\\intop_{V}\\thinspace_{0}^{t}\\mathbf{S}:\\delta\\triangle\\mathbf{E}_{L}dV \\]

where \\(\\triangle\\mathbf{S}\\) is assumed to be

\\[ \\triangle\\mathbf{S}=_{0}^{t}\\mathbf{C}\\colon\\triangle\\mathbf{E}_{L} \\]

then we have

\\[ \\begin{align} \\label{eq:ch5_nonlinear_total_lag_gov7} \\intop_{v}(\\mathbf{C}\\colon\\triangle\\mathbf{E}):\\delta\\triangle\\mathbf{E}_{L}dV+\\intop_{V}\\thinspace_{0}^{t}\\mathbf{S}\\colon\\delta\\triangle\\mathbf{E}_{NL}dV=^{t'}\\delta\\mathbf{R}-\\intop_{V}\\thinspace_{0}^{t}\\mathbf{S}:\\delta\\triangle\\mathbf{E}_{L}dV \\end{align} \\]

Equation \\(\\eqref{eq:ch5_nonlinear_total_lag_gov7}\\) can be discreted to finite element formulation

\\[ \\delta\\mathbf{U}^{T}(_{0}^{t}\\mathbf{K}_{L}+{}_{0}^{t}\\mathbf{K}_{NL})\\triangle\\mathbf{U}=\\delta\\mathbf{U}^{T}\\thinspace_{0}^{t'}\\mathbf{F}-\\delta\\mathbf{\\mathbf{U}}^{T}\\thinspace_{0}^{t'}\\mathbf{Q} \\]

where \\(_{0}^{t}\\mathbf{K}_{L}\\), \\(_{0}^{t}\\mathbf{K}_{NL}\\), \\(_{0}^{t'}\\mathbf{F}\\), \\(_{0}^{t}\\mathbf{Q}\\) are the initial material stiffness matrix, initial geometric stiffness (stress) matrix, external force vector, and internal force vector, respectively. The recursive algorithm to calculate the deformation status at time t' from time t is given:

Step 1: i = 0

\\[ \\quad\\quad_{0}^{t'}\\mathbf{K}^{(0)}=_{0}^{t}\\mathbf{K}_{L}+_{0}^{t}\\mathbf{K}_{NL} \\] \\[ \\quad\\quad_{0}^{t'}\\mathbf{Q}^{(0)}=_{0}^{t}\\mathbf{Q} \\] \\[ \\quad\\quad^{t'}\\mathbf{U}^{(0)}=^{t}\\mathbf{U} \\]

Step 2:

\\[ \\quad\\quad_{0}^{t'}\\mathbf{K}^{(i)}\\triangle\\mathbf{U}^{(i)}=_{0}^{t'}\\mathbf{F}-_{0}^{t'}\\mathbf{Q}^{(i-1)} \\]

Step 3:

\\[ \\quad\\quad^{t'}\\mathbf{U}^{(i)}=^{t'}\\mathbf{U}^{(i-1)}+\\triangle\\mathbf{U}^{(i)} \\]"},{"location":"welsim/theory/geometricnl/#formulation-of-updated-lagrange-algorithm","title":"Formulation of updated lagrange algorithm","text":"

In addition to the total Lagrange algorithm, the updated Lagrange algorithm is also widely applied in the nonlinear structural model computation. The principle virtual work equation at time t' uses the current domain at time t as reference domain.

\\[ \\begin{align} \\label{eq:ch5_nonlinear_updated_lag_gov1} \\intop_{V}\\thinspace_{t}^{t'}\\mathbf{S}:\\delta_{t}^{t'}\\mathbf{E}dV=^{t'}\\delta\\mathbf{R} \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_nonlinear_updated_lag_gov2} ^{t'}\\delta\\mathbf{R}=\\intop_{S_{t}}\\thinspace_{t}^{t'}\\mathbf{t}\\cdot\\delta dS+\\intop_{V}\\thinspace_{t}^{t'}\\mathbf{b}\\cdot\\delta\\mathbf{u}dV \\end{align} \\]

where

\\[ _{t}^{t'}\\mathbf{t}=\\dfrac{d^{t'}s}{d^{t}s}\\thinspace^{t'}\\mathbf{t} \\] \\[ _{t}^{t'}\\mathbf{b}=\\dfrac{d^{t'}v}{d^{t}v}\\thinspace^{t'}\\mathbf{b} \\]

The tensors \\(_{t}^{t'}\\mathbf{S}\\), \\(_{t}^{t'}\\mathbf{E}\\) and vectors \\(_{t}^{t'}\\mathbf{t}\\), \\(_{t}^{t'}\\mathbf{b}\\) are using the current time domain t as the reference domain. Therefore, the Green-Lagrange strain does not contain the initial displacement (the displacement at the time t) \\(^{t}\\mathbf{u}\\);

\\[ \\begin{align} \\label{eq:ch5_nonlinear_updated_lag_gov3} _{t}^{t'}\\mathbf{E}=\\triangle_{t}\\mathbf{E}_{L}+\\triangle_{t}\\mathbf{E}_{NL} \\end{align} \\]

where

\\[ \\begin{align} \\label{eq:ch5_nonlinear_updated_lag_gov4} \\triangle_{t}\\mathbf{E}_{L}=\\dfrac{1}{2}\\{\\dfrac{\\partial\\triangle\\mathbf{u}}{\\partial^{t}x}+(\\dfrac{\\partial\\triangle\\mathbf{u}}{\\partial^{t}x})^{T}\\} \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_nonlinear_updated_lag_gov5} \\triangle_{t}\\mathbf{E}_{NL}=\\dfrac{1}{2}(\\dfrac{\\partial\\triangle\\mathbf{u}}{\\partial^{t}x})^{T}\\cdot\\dfrac{\\partial\\triangle\\mathbf{u}}{\\partial^{t}x} \\end{align} \\]

Similarly,

\\[ _{t}^{t'}\\mathbf{S}=_{t}^{t}\\mathbf{S}+\\triangle_{t}\\mathbf{S} \\]

Substituting equations \\(\\eqref{eq:ch5_nonlinear_updated_lag_gov3}\\) and \\(\\eqref{eq:ch5_nonlinear_updated_lag_gov2}\\) into governing equations \\(\\eqref{eq:ch5_nonlinear_updated_lag_gov1}\\), we have

\\[ \\intop_{^{t}v}\\triangle_{t}\\mathbf{S}:(\\delta\\triangle_{t}\\mathbf{E}_{L}+\\delta\\triangle_{t}\\mathbf{E}_{NL})d^{t}v+\\intop_{V}\\thinspace_{t}^{t}\\mathbf{S}\\colon\\delta\\triangle_{t}\\mathbf{E}_{NL}d^{t}v=^{t'}\\delta\\mathbf{R}-\\intop_{^{t}v}\\thinspace_{t}^{t}\\mathbf{S}:\\delta\\triangle_{t}\\mathbf{E}_{L}d^{t}v \\]

where \\(\\triangle_{t}\\mathbf{S}\\) is assumed to be

\\[ \\triangle_{t}\\mathbf{S}=_{t}^{t}\\mathbf{C}\\colon\\triangle_{t}\\mathbf{E}_{L} \\]

then we have

\\[ \\begin{align} \\label{eq:ch5_nonlinear_updated_lag_gov7} \\intop_{v}(\\mathbf{C}\\colon\\triangle t\\mathbf{E}_{L}):\\delta\\triangle_{t}\\mathbf{E}_{L}dV+\\intop_{V}\\thinspace_{t}^{t}\\mathbf{S}\\colon\\delta\\triangle_{t}\\mathbf{E}_{NL}dV=^{t'}\\delta\\mathbf{R}-\\intop_{V}\\thinspace_{t}^{t}\\mathbf{S}:\\delta\\triangle_{t}\\mathbf{E}_{L}dV \\end{align} \\]

Equation \\(\\eqref{eq:ch5_nonlinear_updated_lag_gov7}\\) can be discreted to finite element formulation

\\[ \\delta\\mathbf{U}^{T}(_{t}^{t}\\mathbf{K}_{L}+{}_{t}^{t}\\mathbf{K}_{NL})\\triangle\\mathbf{U}=\\delta\\mathbf{U}^{T}\\thinspace_{t}^{t'}\\mathbf{F}-\\delta\\mathbf{\\mathbf{U}}^{T}\\thinspace_{t}^{t'}\\mathbf{Q} \\]

where \\(_{t}^{t}\\mathbf{K}_{L}\\), \\(_{t}^{t}\\mathbf{K}_{NL}\\), \\(_{t}^{t'}\\mathbf{F}\\), \\(_{t}^{t}\\mathbf{Q}\\) are the initial material stiffness matrix, initial geometric stiffness (stress) matrix, external force vector, and internal force vector, respectively. The recursive algorithm to calculate the deformation status at time t' from time t is given:

Step 1: i = 0

\\[ \\quad\\quad_{t}^{t'}\\mathbf{K}^{(i)}=_{t}^{t}\\mathbf{K}_{L}+_{t}^{t}\\mathbf{K}_{NL} \\] \\[ \\quad\\quad_{t}^{t'}\\mathbf{Q}^{(i)}=_{t}^{t}\\mathbf{Q} \\] \\[ \\quad\\quad^{t'}\\mathbf{U}^{(i)}=^{t}\\mathbf{U} \\]

Step 2:

\\[ \\quad\\quad_{0}^{t'}\\mathbf{K}^{(i)}\\triangle\\mathbf{U}^{(i)}=_{0}^{t'}\\mathbf{F}-_{0}^{t'}\\mathbf{Q}^{(i-1)} \\]

Step 3:

\\[ \\quad\\quad^{t'}\\mathbf{U}^{(i)}=^{t'}\\mathbf{U}^{(i-1)}+\\triangle\\mathbf{U}^{(i)} \\]"},{"location":"welsim/theory/introduction/","title":"Introduction","text":"

This theory reference presents theoretical descriptions of all algorithms, as well as many procedures and elements used in these products. It is useful to any of our users who need to understand how the software program calculates the output based on the inputs.

"},{"location":"welsim/theory/materialnl/","title":"Structures with material nonlinearities","text":"

Material nonlinearities occur because of the nonlinear relationship between stress and strain; that is, the stress is a nonlinear function of the strain. The relationship is also path-dependent (except for the case of nonlinear elasticity and hyperelasticity), so that the stress depends on the strain history as well as the strain itself.

The program can account for many material nonlinearities, as follows:

  1. Rate-independent plasticity is characterized by the irreversible instantaneous straining that occurs in a material.

  2. Rate-dependent plasticity allows the plastic-strains to develop over a time interval. It is also termed viscoplasticity.

  3. Creep is also an irreversible straining that occurs in a material and is rate-dependent so that the strains develop over time. The time frame for creep is usually much larger than that for rate-dependent plasticity.

  4. Nonlinear elasticity allows a nonlinear stress-strain relationship to be specified. All straining is reversible.

  5. Hyperelasticity is defined by a strain-energy density potential that characterizes elastomeric and foam-type materials. All straining is reversible.

  6. Viscoelasticity is a rate-dependent material characterization that includes a viscous contribution to the elastic straining.

When the material applicable for analysis is an elastoplastic material, the updated Lagrange method is applied, and the total Lagrange method is applied for hyperelastic material. Moreover, the Newton-Raphson method is applied to the repetitive analysis method.

"},{"location":"welsim/theory/materialnl/#strain-definitions","title":"Strain definitions","text":"

For the case of nonlinear materials, the definition of elastic strain given in Equation\u00a0\\(\\eqref{eq:ch4_theory_stress_strain_relation}\\) expands to

\\[ \\begin{align} \\label{eq:ch4_guide_strain_full} \\{\\epsilon\\}=\\{\\epsilon^{el}\\}+\\{\\epsilon^{th}\\}+\\{e^{pl}\\}+\\{\\epsilon^{cr}\\}+\\{\\epsilon^{sw}\\} \\end{align} \\]

where \\(\\epsilon\\) is the total strain vector, \\(\\epsilon^{el}\\) is elastic strain vector, \\(\\epsilon^{th}\\) is the thermal strain vector, \\(\\epsilon^{pl}\\) is the plastic strain vector, \\(\\epsilon^{cr}\\) is the creep strain vector, and \\(\\epsilon^{sw}\\) is the swelling strain vector.

"},{"location":"welsim/theory/materialnl/#hyperelasticity","title":"Hyperelasticity","text":"

The elastic potential energy in hyperelastic material can be obtained from the initial state with no stress activation. Therefore, we have the main invariable terms of the right Cauchy-Green deformation tensor C(\\(I_{1}\\), \\(I_{2}\\), \\(I_{3}\\)), or the main invariable of the deformation tensor excluding the volume changes (\\(\\bar{I}_{1}\\), \\(\\bar{I}_{2}\\), \\(\\bar{I}_{3}\\)). The potential can be expressed as \\(\\mathbf{W}=\\mathbf{W}(I_{1},I_{2},I_{3})\\), or \\(\\mathbf{W}=\\mathbf{W}(\\bar{I}_{1},\\bar{I}_{2},\\bar{I}_{3})\\).

The nonlinear constitutive relation of hyperelastic material is defined by the relation between the second order Piola-Kirchhoff stress and the Green-Lagrange strain, the total Lagrange method is more efficient in solving such models.

When the elastic potential energy \\(W\\) of the hyperelasticity is known, the second Piola-Kirchhoff stress and strain-stress relationship can be calculated as follows

\\[ S=2\\dfrac{\\partial W}{\\partial C} \\] \\[ C=4\\dfrac{\\partial^{2}W}{\\partial C\\partial C} \\]"},{"location":"welsim/theory/materialnl/#arruda-boyce-model","title":"Arruda-Boyce model","text":"

The form of the strain-energy potential for Arruda-Boyce model is

\\[ \\begin{array}{ccc} W & = & [\\dfrac{1}{2}(\\bar{I}_{1}-3)+\\dfrac{1}{20\\lambda_{m}^{2}}(\\bar{I_{1}^{2}}-9)+\\dfrac{11}{1050\\lambda_{m}^{4}}(\\bar{I_{1}^{3}}-27)\\\\ & + & \\dfrac{19}{7000\\lambda_{m}^{6}}(\\bar{I_{1}^{4}}-81)+\\dfrac{519}{673750\\lambda_{m}^{8}}(\\bar{I_{1}^{5}}-243)]+\\dfrac{1}{D_1}(\\dfrac{J^{2}-1}{2}-\\mathrm{ln}J) \\end{array} \\]

where \\(\\lambda_{m}\\) is limiting network stretch, and \\(D_1\\) is the material incompressibility parameter.

The initial shear modulus is

\\[ \\mu=\\dfrac{\\mu_{0}}{1+\\dfrac{3}{5\\lambda_{m}^{2}}+\\dfrac{99}{175\\lambda_{m}^{4}}+\\dfrac{513}{875\\lambda_{m}^{6}}+\\dfrac{42039}{67375\\lambda_{m}^{8}}} \\]

The initial bulk modulus is

\\[ K=\\dfrac{2}{D_1} \\]

As the parameter \\(\\lambda_L\\) goes to infinity, the model is equivalent to neo-Hookean form.

"},{"location":"welsim/theory/materialnl/#blatz-ko-foam-model","title":"Blatz-Ko foam model","text":"

The form of strain-energy potential for the Blatz-Ko model is:

\\[ W=\\frac{\\mu}{2}\\left(\\frac{I_{2}}{I_{3}}+2\\sqrt{I_{3}}-5\\right) \\]

where \\(\\mu\\) is initla shear modulus of material. The initial bulk modulus is defined as :

\\[ K = \\frac{5}{3}\\mu \\]"},{"location":"welsim/theory/materialnl/#extended-tube-model","title":"Extended tube model","text":"

The elastic strain-energy potential for the extended tube model is:

\\[ \\begin{array}{ccc} W & = & \\frac{G_{c}}{2}\\left[\\frac{\\left(1-\\delta^{2}\\right)\\left(\\bar{I}_{1}-3\\right)}{1-\\delta^{2}\\left(\\bar{I}_{1}-3\\right)}+\\mathrm{ln}\\left(1-\\delta^{2}\\left(\\bar{I}_{1}-3\\right)\\right)\\right]\\\\ & + & \\frac{2G_{e}}{\\beta^{2}}\\sum_{i=1}^{3}\\left(\\bar{\\lambda}_{i}^{-\\beta}-1\\right)+\\frac{1}{D_1}\\left(J-1\\right)^{2} \\end{array} \\]

where the initial shear modulus is \\(G\\)=\\(G_c\\) + \\(G_e\\), and \\(G_e\\) is constraint contribution to modulus, \\(G_c\\) is crosslinked contribution to modulus, \\(\\delta\\) is extensibility parameter, \\(\\beta\\) is empirical parameter (0\\(\\leq \\beta \\leq\\)1), and \\(D_1\\) is material incompressibility parameter.

Extended tube model is equivalent ot a two-term Ogden model with the following parameters:

\\[ \\begin{array}{cccc} \\alpha_1 = 2 &, & \\alpha_2=-\\beta\\\\ \\mu_1=G_c &, & \\mu_2=-\\dfrac{2}{\\beta}G_e, & \\delta=0 \\end{array} \\]"},{"location":"welsim/theory/materialnl/#gent-model","title":"Gent model","text":"

The form of the strian-energy potential for the Gent model is:

\\[ W=-\\frac{\\mu J_{m}}{2}\\mathrm{ln}\\left(1-\\frac{\\bar{I}_{1}-3}{J_{m}}\\right)+\\frac{1}{D_1}\\left(\\frac{J^{2}-1}{2}-\\mathrm{ln}J\\right) \\]

where \\(\\mu\\) is initial shear modulus of material, \\(J_m\\) is limiting value of \\(\\bar{I}_1-3\\), \\(D_1\\) is material incompressibility parameter.

The initial bulk modulus is

\\[ K=\\dfrac{2}{D_1} \\]

When the parameter \\(J_m\\) goes to infinity, the Gent model is equivalent to neo-Hookean form.

"},{"location":"welsim/theory/materialnl/#mooney-rivlin-model","title":"Mooney-Rivlin model","text":"

This model includes two-, three-, five-, and nine-terma Mooney-Rivlin models. The form of the strain-energy potential for a two-parameter Mooney-Rivlin model is

\\[ W=C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right)+\\frac{1}{D_1}\\left(J-1\\right)^{2} \\]

where \\(C_{10}\\), \\(C_{01}\\), and \\(D_{1}\\) are the material constants.

The form of strain-energy potential for a three-parameter Mooney-Rivlin model is

\\[ W=C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right)+C_{11}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right)+\\frac{1}{D_1}\\left(J-1\\right)^{2} \\]

where \\(C_{10}\\), \\(C_{01}\\), \\(C_{11}\\), and \\(D_1\\) are material ocnstants.

The form of strain-energy potential for a five-parameter Mooney-Rivlin model is

\\[ \\begin{array}{ccc} W & = & C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right)+C_{20}\\left(\\bar{I}_{1}-3\\right)^{2}\\\\ & + & C_{11}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right)+C_{02}\\left(\\bar{I}_{2}-3\\right)^{2}+\\frac{1}{D_1}\\left(J-1\\right)^{2} \\end{array} \\]

where \\(C_{10}\\), \\(C_{01}\\), \\(C_{20}\\), \\(C_{11}\\), \\(C_{02}\\), and \\(D_1\\) are material ocnstants.

The form of strain-energy potential for a nine-parameter Mooney-Rivlin model is

\\[ \\begin{array}{ccc} W & = & C_{10}\\left(\\bar{I}_{1}-3\\right)+C_{01}\\left(\\bar{I}_{2}-3\\right)+C_{20}\\left(\\bar{I}_{1}-3\\right)^{2}\\\\ & + & C_{11}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right)+C_{02}\\left(\\bar{I}_{2}-3\\right)^{2}+C_{30}\\left(\\bar{I}_{1}-3\\right)^{3}\\\\ & + & C_{21}\\left(\\bar{I}_{1}-3\\right)^{2}\\left(\\bar{I}_{2}-3\\right)+C_{12}\\left(\\bar{I}_{1}-3\\right)\\left(\\bar{I}_{2}-3\\right)^{2}+C_{03}\\left(\\bar{I}_{2}-3\\right)^{3}+\\frac{1}{D_1}\\left(J-1\\right)^{2} \\end{array} \\]

where \\(C_{10}\\), \\(C_{01}\\), \\(C_{20}\\), \\(C_{11}\\), \\(C_{02}\\), \\(C_{30}\\), \\(C_{21}\\), \\(C_{12}\\), \\(C_{03}\\), and \\(D_1\\) are material ocnstants.

The initial shear modulus is given by:

\\[ \\mu=2(C_{10}+C_{01}) \\]

The initial bulk modulus is

\\[ K=\\dfrac{2}{D_1} \\]"},{"location":"welsim/theory/materialnl/#neo-hookean-model","title":"Neo-Hookean model","text":"

The Neo-Hookean model is a well-known hyperelastic model with an expanded linear rule (Hooke rule) having isotropy so that it can respond to finite deformation problems. The elastic potential is as follows.

\\[ W=\\frac{\\mu}{2}(\\bar{I}_{1}-3)+\\dfrac{1}{D_{1}}(J-1)^{2} \\]

where \\(\\mu\\) is initial shear modulus of materials, \\(D_{1}\\) is the material constant.

The initial bulk modulus is given by:

\\[ K=\\dfrac{2}{D_1} \\]"},{"location":"welsim/theory/materialnl/#ogden-compressible-foam-model","title":"Ogden compressible foam model","text":"

The strain-energy potential of the Ogden compressible foam model is based on the principal stretches of left Cauchy strain tensor, which has the form:

\\[ W=\\sum_{i=1}^{N}\\frac{\\mu_{i}}{\\alpha_{i}}\\left(J^{\\alpha_{i}/3}\\left(\\bar{\\lambda}_{1}^{\\alpha_{i}}+\\bar{\\lambda}_{2}^{\\alpha_{i}}+\\bar{\\lambda}_{3}^{\\alpha_{i}}\\right)-3\\right)+\\sum_{i=1}^{N}\\frac{\\mu_{i}}{\\alpha_{i}\\beta_{i}}\\left(J^{-\\alpha_{i}\\beta_{i}}-1\\right) \\]

where N determines the order of the polynomial, \\(\\mu_i\\), \\(\\alpha_i\\) are material constants, \\(D_k\\) is incompressiblity parameter. The reduced principal strench is defined by:

\\[ \\bar{\\lambda}_{p}=J^{-\\frac{1}{3}}\\lambda_p,\\; J=(\\lambda_{1}\\lambda_{2}\\lambda_{3})^{\\frac{1}{2}} \\]

The initial shear modulus is given by:

\\[ \\mu=\\dfrac{\\sum_{i=1}^{N}\\mu_{i}\\alpha_{i}}{2} \\]

The initial bulk modulus K is defined by

\\[ K = \\sum_{i=1}^{N}\\mu_{i}\\alpha_{i}\\left(\\dfrac{1}{3}+\\beta_{i}\\right) \\]

When parameters N=1, \\(\\alpha_1\\)=-2, \\(\\mu_1\\)=-\\(\\mu\\), and \\(\\beta\\)=0.5, the Ogden compressible model is converted to the Blatz-Ko model.

"},{"location":"welsim/theory/materialnl/#ogden-model","title":"Ogden model","text":"

The strain-energy potential of the Ogden compressible foam model is based on the principal stretches of left Cauchy strain tensor, which has the form:

\\[ W=\\sum_{i=1}^{N}\\frac{\\mu_{i}}{\\alpha_{i}}\\left(\\bar{\\lambda}_{1}^{\\alpha_{i}}+\\bar{\\lambda}_{2}^{\\alpha_{i}}+\\bar{\\lambda}_{3}^{\\alpha_{i}}-3\\right)+\\sum_{k=1}^{N}\\frac{1}{D_{k}}\\left(J-1\\right)^{2k} \\]

where N determines the order of the polynomial, \\(\\mu_i\\), \\(\\alpha_i\\) are material constants, \\(D_k\\) is incompressiblity parameter. The reduced principal strench is defined by:

\\[ \\bar{\\lambda}_{p}=J^{-\\frac{1}{3}}\\lambda_p,\\; J=(\\lambda_{1}\\lambda_{2}\\lambda_{3})^{\\frac{1}{2}} \\]

The initial shear modulus is given by:

\\[ \\mu=\\dfrac{\\sum_{i=1}^{N}\\mu_{i}\\alpha_{i}}{2} \\]

The initial bulk modulus K is defined by

\\[ K = \\dfrac{2}{D_1} \\]

When parameters N=1, \\(\\alpha_1\\)=2, the Ogden model is converted to the neo-Hookean model. When parameters N=2, \\(\\alpha_1\\)=2 and \\(\\alpha_2\\)=-2, the Ogden model is converted to the 2-parameter Mooney-Rivlin model.

"},{"location":"welsim/theory/materialnl/#polynomial-form","title":"Polynomial form","text":"

The polynomial form of strain-energy potential is:

\\[ W=\\sum_{i+j=1}^{N}c_{ij}\\left(\\bar{I}_{1}-3\\right)^{i}\\left(\\bar{I_{2}}-3\\right)^{j}+\\sum_{k=1}^{N}\\frac{1}{D_{k}}\\left(J-1\\right)^{2k} \\]

where \\(N\\) determines the order of polynomial, \\(c_{ij}\\), \\(D_k\\) are material constants.

The initial shear modulus is given by:

\\[ \\mu=2\\left(C_{10}+C_{01}\\right) \\]

The initial bulk modulus K is defined by

\\[ K = \\dfrac{2}{D_1} \\]

The Polynomial model is converted to following models with specific paramters:

Parameters of Polynomial model Equivalent model N=1, \\(C_{01}\\)=0 neo-Hookean N=1 2-parameter Mooney-Rivlin N=2 5-parameter Mooney-Rivlin N=3 9-parameter Mooney-Rivlin"},{"location":"welsim/theory/materialnl/#yeoh-model","title":"Yeoh model","text":"

The Yeoh model is also called the reduced polynomial form. The strain-energy potential is

\\[ W=\\sum_{i=1}^{N}c_{i0}\\left(\\bar{I}_{1}-3\\right)^{i}+\\sum_{k=1}^{N}\\frac{1}{D_{k}}\\left(J-1\\right)^{2k} \\]

where N denotes the order of polynomial, \\(C_{i0}\\) and \\(D_k\\) are material constants. When N=1, Yeoh becomes neo-Hookean model.

The initial shear modulus is defined:

\\[ \\mu=2c_{10} \\]

The initial bulk modulus is:

\\[ K=\\frac{2}{D_1} \\]"},{"location":"welsim/theory/materialnl/#rate-independent-plasticity","title":"Rate-independent plasticity","text":"

The elastoplasticity based on the flow rule is applied in this program. The constitutive relation between Jaumman rate and the deformation rate tensor of the Kirchhoff stress is numerically solved using the updated Lagrange method.

"},{"location":"welsim/theory/materialnl/#elastoplastic-constitutive-equation","title":"Elastoplastic constitutive equation","text":"

The yield criteria of an elasto-plastic solid can be written into math formulas. The initial yield criteria are

\\[ F(\\sigma,\\sigma_{y0})=0 \\]

The Consecutive yield criteria are

\\[ F(\\sigma,\\sigma_{y}(e^{-p}))=0 \\]

where \\(F\\) is the yield function, \\(\\sigma_{y0}\\) is initial yield stress, \\(\\sigma_{y}\\) is consecutive yield stress, \\(\\sigma\\) is stress tensor, \\(\\mathbf{e}\\) is the infinitesimal strain tensor, \\(\\mathbf{e}^{p}\\) is the plastic strain tensor, \\(\\bar{\\mathbf{e}}^{p}\\) is equivalent plastic strain.

The yield stress-equivalent plastic strain relationship is assumed to conform to the stress-plastic strain relation in a single axis state. The stress-plastic strain relation about one single axis state is:

\\[ \\sigma=H(e^{p}) \\] \\[ \\dfrac{d\\sigma}{de^{p}}=H' \\]

where \\(H'\\) is the strain hardening factor. The equivalent stress-equivalent plastic strain relation is :

\\[ \\bar{\\sigma}=H(\\bar{e}^{p}) \\] \\[ \\dot{\\bar{\\sigma}}=H'\\dot{\\bar{e^{p}}} \\]

The consecutive yield function is generally a function of temperature and plastic strain work. In this program, this function is assumed to be related to the equivalent plastic strain \\bar{e}^{p}. Since condition F=0 holds during the plastic deformation, we have

\\[ \\begin{align} \\label{eq:ch5_plastic_gov1} \\dot{F}=\\dfrac{\\partial F}{\\partial\\sigma}\\colon\\dot{\\sigma}+\\dfrac{\\partial F}{\\partial\\mathbf{e}^{p}}\\colon\\dot{\\mathbf{e}}^{p}=0 \\end{align} \\]

where \\(\\dot{F}\\) is the time derivative function of \\(F\\).

In this case, we assume the existence of the plastic potential \\(\\Theta\\), the plastic strain rate is

\\[ \\dot{\\mathbf{e}}^{p}=\\dot{\\lambda}\\dfrac{\\partial\\Theta}{\\partial\\sigma} \\]

where \\(\\dot{\\lambda}\\) is the factor. Moreover, assuming the plastic potential \\(\\Theta\\) is equivalent to yield function \\(F\\), the associated flow rule is assumed as

\\[ \\dot{\\mathbf{e}}^{p}=\\dot{\\lambda}\\dfrac{\\partial F}{\\partial\\sigma} \\]

which is substituted with equation \\(\\eqref{eq:ch5_plastic_gov1}\\), we have

\\[ \\dot{\\lambda}=\\dfrac{\\mathbf{a}^{T}\\colon\\mathbf{d}_{D}}{A+\\mathbf{a}^{T}\\colon\\mathbf{D}\\colon\\mathbf{a}}\\mathbf{\\dot{\\mathbf{e}}} \\]

where \\(\\mathbf{D}\\) is the elastic matrix, and

\\[ \\mathbf{a}^{T}=\\dfrac{\\partial F}{\\partial\\sigma}\\quad\\mathbf{d}_{D}=\\mathbf{D}\\mathbf{a}^{T}\\quad A=-\\dfrac{1}{\\dot{\\lambda}}\\dfrac{\\partial F}{\\partial\\mathbf{\\mathbf{e}}^{p}}\\colon\\dot{\\mathbf{e}}^{p} \\]

The stress-strain relation for elastoplasicity can be rewritten to

\\[ \\begin{align} \\label{eq:ch5_plastic_yield_func1} \\dot{\\sigma}=\\{\\mathbf{D}-\\dfrac{\\mathbf{d}_{D}\\otimes\\mathbf{d}_{D}^{T}}{A+\\mathbf{d}_{D}^{T}\\mathbf{a}}\\}\\colon\\dot{\\mathbf{e}} \\end{align} \\]

Here we give the explicit form of several yield functions that are applied in the program.

"},{"location":"welsim/theory/materialnl/#von-mises-yield-function","title":"Von-Mises yield function","text":"\\[ F=\\sqrt{3\\mathbf{J}_{2}}-\\sigma_{y} = 0 \\]"},{"location":"welsim/theory/materialnl/#mohr-coulomb-yield-function","title":"Mohr-Coulomb yield function","text":"\\[ F=\\sigma_{1}-\\sigma_{3}+(\\sigma_{1}+\\sigma_{3})\\mathrm{sin}\\phi-2c\\mathrm{cos}\\phi = 0 \\]"},{"location":"welsim/theory/materialnl/#drucker-prager-yield-function","title":"Drucker-Prager yield function","text":"\\[ F=\\sqrt{\\mathbf{J}_{2}}-\\alpha\\sigma\\colon\\mathbf{I}-\\sigma_{y}=0 \\]

where material constant \\(\\alpha\\) and \\(\\sigma_{y}\\) are calculated from the viscosity and friction angle of the material as shown below

\\[ \\alpha=\\dfrac{2\\mathrm{sin}\\phi}{3+\\mathrm{sin}\\phi},\\quad\\sigma_{y}=\\dfrac{6c\\mathrm{cos}\\phi}{3+\\mathrm{sin}\\phi} \\]"},{"location":"welsim/theory/materialnl/#viscoelasticity","title":"Viscoelasticity","text":"

A material is viscoelastic if the material has both elastic (recoverable) and viscous (nonrecoverable) parts. Upon loads, the elastic deformation is instantaneous while the viscous part occurs over time. A viscoelastic model can depicts the deformation behavior of glass or glass-like materials and simulate heating and cooling processing of such materials.

"},{"location":"welsim/theory/materialnl/#constitutive-equations","title":"Constitutive Equations","text":"

A generalized Maxwell model is applied for viscoelasticity in this program. The constitutive equation becomes a function of deviatoric strain \\(\\mathbf{e}\\) and deviatoric viscosity strain \\(\\mathbf{q}\\),

\\[ \\sigma(t)=K\\thinspace tr(\\epsilon\\mathbf{I})+2G(\\mu_{0}\\mathbf{e}+\\mu\\mathbf{q}) \\]

where

\\[ \\mu\\mathbf{q}=\\sum_{m=1}^{M}\\mu_{m}\\mathbf{q}^{(m)};\\quad\\sum_{m=0}^{M}\\mu_{m}=1 \\]

moveover, the deviatoric viscosity strain \\(\\mathbf{q}\\) can be calculated by

\\[ \\dot{\\mathbf{q}}\\thinspace^{(m)}+\\dfrac{1}{\\tau_{m}}\\mathbf{q}^{(m)}=\\dot{\\mathbf{e}} \\]

where \\(\\tau_{m}\\) is the relaxation time. The shear and volumetric relaxation coefficient \\(G\\) is represented by the following Prony series:

\\[ G(t)=G[\\mu_{0}^{G}+\\sum_{i=1}^{M}\\mu_{i}^{G}e^{-(t/\\tau_{i}^{G})}] \\] \\[ K(t)=K[\\mu_{0}^{K}+\\sum_{i=1}^{M}\\mu_{i}^{K} e^{-\\frac{t}{\\tau_{i}^{K}}}] \\]

where \\(\\tau_{i}^{G}\\) and \\(\\tau_{i}^{K}\\) are relaxation times for each Prony component, \\(G_i\\) and \\(K_i\\) are shear and volumetric moduli, respectively.

"},{"location":"welsim/theory/materialnl/#themorheological-simplicity","title":"Themorheological Simplicity","text":"

Viscous material depends strongly on temperature. For instance, A glass-like material turninto viscous fluids at high temperatures and behave like a solid material at low temperatures. The thermorheological simplicity is proposed to assumes that material response to a load at a high temperature over a short duration is identical to that at lower temperature but over a longer duration. Essentially, the relaxation times in Prony components oby the scaling law:

\\[ \\tau_{i}^{G}(T) = \\dfrac{\\tau_{i}^{G}(T_r)}{A(T,T_r)} ,\\qquad \\tau_{i}^{K}(T) = \\dfrac{\\tau_{i}^{K}(T_r)}{A(T,T_r)} \\]

where \\(A(T,T_r)\\) is called the shift function.

"},{"location":"welsim/theory/materialnl/#shift-functions","title":"Shift Functions","text":"

WELSIM offers the following forms of the shift function:

"},{"location":"welsim/theory/materialnl/#williams-landel-ferry-shift-function","title":"Williams-Landel-Ferry Shift Function","text":"

The Williams-Landel-Ferry (WLF) shift function is defined by

\\[ log_{10}(A) = \\dfrac{C1(T-T_r)}{C2+T-T_r} \\]

where T is temperature, \\(T_r\\) is reference temperature, \\(C_1\\) and \\(C_2\\) are the WLF constants.

"},{"location":"welsim/theory/materialnl/#rate-dependent-plasticity-including-creep-and-viscoplasticity","title":"Rate-dependent plasticity (including creep and viscoplasticity)","text":"

The creep is a deformation phenomenon that the displacement depends on the time even under constant stress condition. The viscoelasticity can be viewed as linear creep. Several nonlinear creep are described in this section. In the mathematical theory, we define creep strain \\(\\epsilon^{c}\\) and creep strain rate \\(\\dot{\\epsilon}^{c}\\)

\\[ \\begin{align} \\label{eq:ch5_creep_gov1} \\dot{\\epsilon}^{c}=\\dfrac{\\partial\\epsilon^{c}}{\\partial t}=\\beta(\\sigma,\\epsilon^{c}) \\end{align} \\]

In this case, if the instantaneous strain is assumed as the elasticity strain \\(\\epsilon^{e}\\), the total strain can be expressed as the summary of elastic and creep strains

\\[ \\epsilon=\\epsilon^{e}+\\epsilon^{c} \\]

where the elastic strain can be calculated by

\\[ \\epsilon^{e}=\\mathbf{c}^{e-1}\\colon\\sigma \\]

When the creep occurs in the deformation, the stress becomes

\\[ \\sigma_{n+1}=\\mathbf{c}\\colon(\\epsilon_{n+1}-\\epsilon_{n+1}^{c}) \\] \\[ \\epsilon_{n+1}^{c}=\\epsilon_{n}^{c}+\\triangle t\\beta_{n+\\theta} \\]

where \\(\\beta_{n+\\theta}\\) becomes

\\[ \\beta_{n+\\theta}=(1+\\theta)\\beta_{n}+\\theta\\beta_{n+1} \\]

The incremental creep strain \\(\\triangle\\epsilon^{c}\\) can be simplified to a nonlinear equation

\\[ \\mathbf{R}_{n+1}=\\epsilon_{n+1}-\\mathbf{c}^{-1}\\colon\\sigma_{n+1}-\\epsilon_{n}^{c}-\\triangle t\\beta_{n+\\theta}=0 \\]

The Newton-Raphson method is applied to solve the nonlinear conditions. The iterative scheme in the finite element framework is

\\[ \\begin{align} \\label{eq:ch5_creep_gov2} \\mathbf{R}_{n+1}^{(k+1)}=0=\\mathbf{R}_{n+1}^{(k)}-(\\mathbf{c}^{-1}+\\triangle t\\mathbf{c}_{n+1}^{c})d\\sigma_{n+1}^{(k)} \\end{align} \\]

which yields

\\[ \\begin{align} \\label{eq:ch5_creep_gov3} \\mathbf{c}_{n+1}^{c}=\\dfrac{\\partial\\beta}{\\partial\\sigma}\\mid_{n+\\theta}=\\theta\\dfrac{\\partial\\beta}{\\partial\\sigma}\\mid_{n+1} \\end{align} \\]

The above equations \\(\\eqref{eq:ch5_creep_gov2}\\) and \\(\\eqref{eq:ch5_creep_gov3}\\) are used in the iterative scheme. As the residual \\(\\mathbf{R}\\) gets close to zero, the stress \\(\\sigma_{n+1}\\) and tangent tensile modulus are

\\[ \\mathbf{c}_{n+1}^{*}=[\\mathbf{c}^{-1}+\\triangle t\\mathbf{c}_{n+1}^{c}]^{-1} \\]

To solve the equation \\(\\eqref{eq:ch5_creep_gov1}\\), the following Norton model is applied in the program. The equivalent clip strain \\(\\dot{\\epsilon}^{cr}\\) is defined to be the function of Mises stress \\(q\\) and time \\(t\\).

\\[ \\dot{\\epsilon}^{cr}=Aq^{n}t^{m} \\]

where \\(A\\), \\(m\\), \\(n\\) are the material coefficients.

"},{"location":"welsim/theory/materialnl/#creep","title":"Creep","text":"

Creep is the inelastic, irreversible deformation of structures during time. It is a life limiting factor and depends on stress, strain, temperature and time. This dependency can be modeled as followed:

\\[ \\dot{\\epsilon}^{cr}=f(\\sigma,\\epsilon,T,t) \\]

Creep can occur in all crystalline materials, such as metal or glass, has various impacts on the behavior of the material.

"},{"location":"welsim/theory/materialnl/#three-types-of-creep","title":"Three types of creep","text":"

Creep can be divided in three different stages: primary creep, secondary creep and irradiation induced creep.

Primary creep (0<m<1) starts rapidly with an infinite creep rate at the initialization. Here is m the time index. It occurs after a certain amount of time and slows down constantly. It occurs in the first hour after applying the load and is essential in calculating the relaxation over time.

Secondary creep (m=1) follows right after the primary creep stage. The strain rate is now constant over a long period of time.

The strain rate in the irradiation induced creep stage is growing rapidly until failure. This happens in a short period of time and is not of great interest. Therefore only primary and secondary creep are modeled in WelSim.

"},{"location":"welsim/theory/materialnl/#creep-models","title":"Creep models","text":"

WELSIM supports implicit creep models including Strain Hardening, Time Hardening, Generalized Exponentia, Generalized Graham, Generalized Blackburn, Modified Time Hardening, Modified Strain Hardening, Generalized Garofalo, Exponential form, Norton, Combined Time Hardening, Rational polynomial, and Generalized Time Hardening. The details of these models are given in the table below.

Creep Model(index) Name Equations Parameters Type 1 Strain Hardening \\(\\dot{\\epsilon}_{cr}=C_{1}\\sigma^{C_2}\\epsilon_{cr}^{C_3}e^{-C_4/T}\\) \\(C_1>0\\) Primary 2 Time Hardening \\(\\dot{\\epsilon}_{cr}=C_{1}\\sigma^{C_2}t^{C_3}e^{-C_4/T}\\) \\(C_1>0\\) Primary 3 Generalized Exponential \\(\\dot{\\epsilon}_{cr}=C_{1}\\sigma^{C_2}re^{-rt}\\), \\(r=C_{5}\\sigma^{C_3}e^{-C4/T}\\) \\(C_1>0\\)\\(C_5>0\\) Primary 4 Generalized Graham \\(\\dot{\\epsilon}_{cr}=C_{1}\\sigma^{C_2}\\left( t^{C_3} + C_{4}t^{C_5} + C_{6}t^{C_7} \\right) e^{-C_8/T}\\) \\(C_1>0\\) Primary 5 Generalized Blackburn \\(\\dot{\\epsilon}_{cr} = f\\left(1-e^{-rt}\\right)+gt\\)\\(f=C_{1}e^{C_2\\sigma}\\), \\(r=C_3\\left(\\sigma/C_4\\right)^{C_5}\\), \\(g=C_{6}e^{C_{7}\\sigma}\\) \\(C_1>0\\)\\(C_3>0\\)\\(C_6>0\\) Primary 6 Modified Time Hardening \\(\\dot{\\epsilon}_{cr}=\\dfrac{C_{1}}{C_3+1}\\sigma^{C_2}t^{C_3+1}e^{-C_4/T}\\) \\(C_1>0\\) Primary 7 Modified Strain Hardening \\(\\dot{\\epsilon}_{cr}= \\{ C_{1} \\sigma^{C_2} \\left[\\left( C_3+1\\right)\\epsilon_{cr} \\right]^{C_3} \\}^{1/(C_3+1)} e^{-C_4/T}\\) \\(C_1>0\\) Primary 8 Generalized Garofalo \\(\\dot{\\epsilon}_{cr}=C_1\\left[ sinh(C_2\\sigma)\\right]^{C_3} e^{-C_4/T}\\) \\(C_1>0\\) Secondary 9 Exponential form \\(\\dot{\\epsilon}_{cr}=C_1 e^{\\sigma/C_2} e^{-C_3/T}\\) \\(C_1>0\\) Secondary 10 Norton \\(\\dot{\\epsilon}_{cr}=C_1 \\sigma^{C_2} e^{-C_3/T}\\) \\(C_1>0\\) Secondary 11 Combined Time Hardening \\(\\dot{\\epsilon}_{cr}=\\dfrac{C_1}{C_3+1} \\sigma^{C_2} t^{C_3+1} e^{-C_4/T} + C_5 \\sigma^{C_6}te^{-C_7/T}\\) \\(C_1>0\\), \\(C_5>0\\) Primary + Secondary 12 Rational Polynomial \\(\\dot{\\epsilon}_{cr}=C_1 \\dfrac{\\partial\\epsilon_c}{\\partial t}\\), \\(\\epsilon_{c}=\\dfrac{cpt}{1+pt}+\\dot{\\epsilon}_m t\\) \\(\\dot{\\epsilon}_m=C_2(10)^{C_3\\sigma}\\sigma^{C_4}\\) \\(c=C_7\\dot{\\epsilon}_m^{C_8}\\sigma^{C_9}\\), \\(p=C_{10}\\dot{\\epsilon}_{m}^{C_{11}}\\sigma^{C_{12}}\\) \\(C_2>0\\) Primary + Secondary 13 Generalized Time Hardening \\(\\dot{\\epsilon}_{cr}=ft^r e^{-C_6/T}\\) \\(f=C_1\\sigma+C_2\\sigma^2+C_3\\sigma^3\\) \\(r=C_4 + C_5\\sigma\\) - Primary

where \\(\\epsilon_{cr}\\) is equivalent creep strain, \\(\\dot{\\epsilon}_{cr}\\) is the change in equivalent creep strain with respect to time, \\(\\sigma\\) is equivalent stress. \\(T\\) is temperature. \\(C_1\\) through \\(C_{12}\\) are creep constants. \\(t\\) is time at end of substep. \\(e\\) is natural logarithm base.

"},{"location":"welsim/theory/modal/","title":"Modal analysis","text":""},{"location":"welsim/theory/modal/#generalized-eigenvalue-problem","title":"Generalized eigenvalue problem","text":"

When conducting a free oscillation analysis of the continuum, assuming no damping in the free vibration. The governing eqatuion is

\\[ \\begin{align} \\label{eq:ch5_modal_gov} \\mathbf{M}\\ddot{\\mathbf{u}}+\\mathbf{Ku}=0 \\end{align} \\]

where \\(\\mathbf{u}\\) is the generated displacement vector, \\(\\mathbf{M}\\) is the mass matrix and \\(\\mathbf{K}\\) is the stiffness matrix. The solution is assumed to

\\[ \\begin{align} \\label{eq:ch5_eigenvalue_vector} \\mathbf{u}(t)=(asin\\omega t+bcos\\omega t)\\mathbf{x} \\end{align} \\]

where \\(\\omega\\) is the natural angular frequency, \\(a\\) and \\(b\\) are the arbitrary constants. Herein, the second order differential of equation \\(\\eqref{eq:ch5_eigenvalue_vector}\\) is

\\[ \\begin{align} \\label{eq:ch5_modal_acceleration} \\ddot{\\mathbf{u}}(t)=\\omega(asin\\omega t-bsin\\omega t)\\mathbf{x} \\end{align} \\]

Combining equations \\(\\eqref{eq:ch5_modal_gov}\\), \\(\\eqref{eq:ch5_eigenvalue_vector}\\), and \\(\\eqref{eq:ch5_modal_acceleration}\\), we have

\\[ \\begin{align} \\label{eq:ch5_modal_gov3} \\mathbf{M}\\ddot{\\mathbf{u}}+\\mathbf{Ku}=(a\\mathrm{sin}\\omega t+b\\mathrm{cos}\\omega t)(-\\omega^{2}\\mathbf{M}+\\mathbf{K}\\mathbf{x})=(-\\lambda\\mathbf{M}\\mathbf{x}+\\mathbf{K}\\mathbf{x})=0 \\end{align} \\]

which simplifies

\\[ \\mathbf{K}\\mathbf{x}=\\lambda\\mathbf{M}\\mathbf{x} \\]

which indicates that if factor \\(\\lambda(=\\omega^{2})\\) and vector \\(\\mathbf{x}\\) satisfies equation \\(\\eqref{eq:ch5_modal_gov3}\\), function \\(\\mathbf{u}(t)\\) becomes the solution of equation \\(\\eqref{eq:ch5_modal_gov}\\). The factor \\(\\lambda\\) is called the eigenvalue, vector \\(\\mathbf{x}\\) is called the eigenvector.

"},{"location":"welsim/theory/modal/#problem-settings","title":"Problem settings","text":"

Equation \\(\\eqref{eq:ch5_modal_acceleration}\\) can be expanded to calculate arbitrary order frequencies, which may appear at real engineering practices. To solve various physical problems, we assume the system is Hermitian(Matrix Symmetrical). Thus, a complex matrix can be transposed into a conjugate complex number and a real symmetric matrix. The relationship can be expressed by the equation below

\\[ k_{ij}=\\bar{k}_{ji} \\]

In this manual, the matrix in modal analysis is assumed to be symmetrical and positive definite. A positively definite matrix always yields to positive eigenvalues. Thus a matrix in the modal system always satisfies the following equation

\\[ \\mathbf{x}^{T}\\mathbf{Ax}>0 \\]"},{"location":"welsim/theory/modal/#shifted-inverse-iteration-method","title":"Shifted inverse iteration method","text":"

In the practical structural modal analysis, not all eigen values are required. There are many cases that some low order eigenvalues are sufficient for the engineering analysis. In the large scale problem that contains large sparse matrix, efficiently calculate the eigenvalues of the low order modes becomes important.

When the lower limit of the eigenvalue is given, the equation \\(\\eqref{eq:ch5_modal_gov3}\\) can be derived to:

\\[ \\begin{align} \\label{eq:ch5_modal_gov4} (\\mathbf{K}-\\sigma\\mathbf{M})^{-1}\\mathbf{M}\\mathbf{x}=[1/(\\lambda-\\sigma)]\\mathbf{x} \\end{align} \\]

this formation of the equations has following advantages in numerical calculation:

In the computing practice, the maximum eigenvalue may be calculated by first. For this reason, we use the equation \\(\\eqref{eq:ch5_modal_gov4}\\) rather than equation \\(\\eqref{eq:ch5_modal_gov3}\\) to calculate the eigenvalues around \\sigma. This scheme is called the shifted inverse iteration.

"},{"location":"welsim/theory/modal/#lanczos-method","title":"Lanczos method","text":"

In the WELSIM application, the Lanczos method is applied to solve the eigenvalues. Lanczos method is a numerical method performing tridiagonalization of matrices. It has capabilities of :

The Lanczos method calculates the base of partial spaces by creating orthogonal vectors from the initial vectors. This method has advantages of computation speed over the subspace method. However, Lanczos method is easily affected by numerical errors. It is essential to check the solution with the numerical errors.

"},{"location":"welsim/theory/modal/#geometric-meaning-in-the-lanczos-method","title":"Geometric meaning in the lanczos method","text":"

Based on equation \\(\\eqref{eq:ch5_modal_gov4}\\), we define

\\[ \\begin{align} \\label{eq:ch5_modal_gov5} \\begin{cases} \\mathbf{A}=(\\mathbf{K}-\\sigma\\mathbf{M})^{-1}\\\\{} [1/(\\lambda-\\sigma)]=\\zeta \\end{cases} \\end{align} \\]

which can be rewritten to the following equation

\\[ \\mathbf{Ax}=\\zeta\\mathbf{x} \\]

The algorithm of the Lanczos method is the Gram-Schmidt orthogonalization for column vectors. Those column vectors are also called the columns of Krylov, and the space created by this scheme is called the Krylov subspace. When the Gram-Schmidt orthogonalization is performed in this space, the vectors can be acquired using the two nearest vectors. This is called the principle of Lanczos.

"},{"location":"welsim/theory/shapefunction/","title":"Shape functions","text":"

This chapter describes the shape functions for the finite elements.

"},{"location":"welsim/theory/shapefunction/#understanding-shape-function-notations","title":"Understanding shape function notations","text":"

The notations used in shape functions are listed below:

"},{"location":"welsim/theory/shapefunction/#3d-shell-elements","title":"3D shell elements","text":"

This section describes the shape functions for 3D shell elements that are applied in the WELSIM application.

"},{"location":"welsim/theory/shapefunction/#3-node-triangle","title":"3-Node triangle","text":"

The shape functions for the 3-node triangular shell elements are:

\\[ u=u_{0}L_{0}+u_{1}L_{1}+u_{2}L_{2} \\] \\[ v=v_{0}L_{0}+v_{1}L_{1}+v_{2}L_{2} \\] \\[ w=w_{0}L_{0}+w_{1}L_{1}+w_{2}L_{2} \\] \\[ A_{x}=A_{x0}L_{0}+A_{x1}L_{1}+A_{x2}L_{2} \\] \\[ A_{y}=A_{y0}L_{0}+A_{y1}L_{1}+A_{y2}L_{2} \\] \\[ A_{z}=A_{z0}L_{0}+A_{z1}L_{1}+A_{z2}L_{2} \\] \\[ T=T_{0}L_{0}+T_{1}L_{1}+T_{2}L_{2} \\] \\[ V=V_{0}L_{0}+V_{1}L_{1}+V_{2}L_{2} \\]"},{"location":"welsim/theory/shapefunction/#6-node-triangle","title":"6-Node triangle","text":"

The shape functions for the 6-node triangular shell elements are:

\\[ u=u_{0}(2L_{0}-1)L_{0}+u_{1}(2L_{1}-1)L_{1}+u_{2}(2L_{2}-1)L_{2}+u_{3}(4L_{0}L_{1})+u_{4}(4L_{1}L_{2})+u_{5}(4L_{2}L_{0}) \\] \\[ v=v_{0}(2L_{0}-1)L_{0}+v_{1}(2L_{1}-1)L_{1}+v_{2}(2L_{2}-1)L_{2}+v_{3}(4L_{0}L_{1})+v_{4}(4L_{1}L_{2})+v_{5}(4L_{2}L_{0}) \\] \\[ w=w_{0}(2L_{0}-1)L_{0}+w_{1}(2L_{1}-1)L_{1}+w_{2}(2L_{2}-1)L_{2}+w_{3}(4L_{0}L_{1})+w_{4}(4L_{1}L_{2})+w_{5}(4L_{2}L_{0}) \\]"},{"location":"welsim/theory/shapefunction/#3d-solid-elements","title":"3D solid elements","text":"

This section describes the shape functions for the 3D solid elements that are applied in the WELSIM application.

"},{"location":"welsim/theory/shapefunction/#4-node-tetrahedra","title":"4-Node tetrahedra","text":"

The 4-node tetrahedra is also called liner tetrahedra element. The shape functions are:

\\[ u=u_{0}L_{0}+u_{1}L_{1}+u_{2}L_{2}+u_{3}L_{3} \\] \\[ v=v_{0}L_{0}+v_{1}L_{1}+v_{2}L_{2}+v_{3}L_{3} \\] \\[ w=w_{0}L_{0}+w_{1}L_{1}+w_{2}L_{2}+w_{3}L_{3} \\]"},{"location":"welsim/theory/shapefunction/#10-node-tetrahedra","title":"10-Node tetrahedra","text":"

The 10-node tetrahedra is also called bilinear tetrahedra element. The shape functions are:

\\[ u=u_{0}(2L_{0}-1)L_{0}+u_{1}(2L_{1}-1)L_{1}+u_{2}(2L_{2}-1)L_{2}+u_{3}(2L_{3}-1)L_{3}+4u_{4}L_{0}L_{1}+u_{5}L_{1}L_{2}+u_{6}L_{0}L_{2}+u_{7}L_{0}L_{3}+u_{8}L_{1}L_{3}+u_{9}L_{2}L_{3} \\] \\[ v=...\\text{(analogous to u)} \\] \\[ w=...\\text{(analogous to u)} \\]"},{"location":"welsim/theory/structures/","title":"Structures","text":"

This section describes the mathematical and numerical theories used in this finite element analysis program. In the stress analysis of solids, the infinitesimal deformation linear elasticity static analysis method is discussed by first. The geometric nonlinearity and elastoplasticity are introduced to describe the finite deformation in solids.

"},{"location":"welsim/theory/structures/#infinitesimal-deformation-linear-elasticity-static-analysis","title":"Infinitesimal deformation linear elasticity static analysis","text":"

The infinitesimal deformation theory is the essential formulation for the linear elasticity, which assumes the stress-strain constitutive relation is linear. The equilibrium equation of solid mechanics, boundary conditions are given by the following equation.

\\[ \\begin{align} \\label{eq:ch5_equilibrium_eqn1} \\nabla\\cdot\\mathbf{\\sigma}+\\mathbf{b}=0\\quad\\mathrm{in}V \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_equilibrium_eqn2} \\sigma\\cdot\\mathbf{n}=\\mathbf{t}\\quad\\mathrm{on}\\thinspace S_{t} \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_equilibrium_eqn3} \\mathbf{u}=\\mathbf{u}_{0}\\quad\\mathrm{on}\\thinspace S_{u} \\end{align} \\]

where \\(\\sigma\\) is the stress, \\(\\mathbf{t}\\) is the surface force, \\(\\mathbf{b}\\) is the body force, and S_{t} expresses the dynamic boundary and the \\(S_{u}\\) expresses the geometric boundary. The strain and displacement relation in the infinitesimal deformation is given

\\[ \\epsilon=\\nabla_{s}\\mathbf{u} \\]

The stress and strain constitutive relation in the linear elastic body is given

\\[ \\sigma=\\mathbf{C}\\colon\\epsilon \\]

where \\(\\mathbf{C}\\) is the fourth order elasticity tensor.

"},{"location":"welsim/theory/structures/#principle-of-virtual-work","title":"Principle of virtual work","text":"

The principle of the virtual work regarding the equilibrium equations \\(\\eqref{eq:ch5_equilibrium_eqn1}\\), \\(\\eqref{eq:ch5_equilibrium_eqn2}\\), and \\(\\eqref{eq:ch5_equilibrium_eqn3}\\) is

\\[ \\begin{align} \\label{eq:ch5_equilibrium_virtual1} \\int_{V}\\sigma\\colon\\delta\\epsilon dV=\\int_{S_{t}}\\mathbf{t}\\cdot\\delta\\mathbf{u}dS+\\int_{V}\\mathbf{b}\\cdot\\delta\\mathbf{u}dV \\end{align} \\] \\[ \\delta\\mathbf{u}=0\\quad\\mathrm{on}\\quad S_{u} \\]

which can be rewritten into

\\[ \\begin{align} \\label{eq:ch5_equilibrium_virtual2} \\int_{V}(\\mathbf{C}\\colon\\epsilon)\\colon\\delta\\epsilon dV=\\int_{S_{t}}\\mathbf{t}\\cdot\\delta\\mathbf{u}dS+\\int_{V}\\mathbf{b}\\cdot\\delta\\mathbf{u}dV \\end{align} \\]

where \\(\\epsilon\\) is the strain tensor, \\(\\sigma\\) is the stress tensor, and \\(\\mathbf{C}\\) is the fourth order elasticity tensor. The strain tensor \\(\\epsilon\\) and stress tensor \\(\\sigma\\) can be rewritten into vector forms \\(\\hat{\\epsilon}\\) and \\(\\hat{\\sigma}\\), respectively. Then we have

\\[ \\begin{align} \\label{eq:ch4_theory_stress_strain_relation} \\hat{\\sigma}=\\mathbf{D}\\hat{\\epsilon} \\end{align} \\]

where \\(\\mathbf{D}\\) is the elasticity matrix. Given the strain and stress in the vector form, we can rewrite the governing equation ([eq:ch5_equilibrium_virtual1]) into

\\[ \\begin{align} \\label{eq:ch5_equilibrium_virtual3} \\int_{V}\\hat{\\epsilon}^{T}\\mathbf{D}\\delta\\hat{\\epsilon}dV=\\int_{S_{t}}\\delta\\mathbf{u^{T}}\\mathbf{t}dS+\\int_{V}\\delta\\mathbf{u}^{T}\\mathbf{b}dV \\end{align} \\]

Equation ([eq:ch5_equilibrium_virtual3]) is the principles of the virtual work applied in this software program.

"},{"location":"welsim/theory/structures/#finite-element-formulation","title":"Finite element formulation","text":"

The principle governing equation ([eq:ch5_equilibrium_virtual3]) of the virtual work can be discreted for each finite element:

\\[ \\begin{align} \\label{eq:ch5_equilibrium_fe_form1} \\sum_{e}\\int_{V^{e}}\\hat{\\epsilon}^{T}\\mathbf{D}\\delta\\hat{\\epsilon}dV=\\sum_{e}\\int_{S_{t}^{e}}\\delta\\mathbf{u}^{T}\\mathbf{t}dS+\\sum_{e}\\int_{V^{e}}\\delta\\mathbf{u}^{T}\\mathbf{b}dV \\end{align} \\]

where the displacement field is interpolated for each element

\\[ \\begin{align} \\label{eq:ch5_equilibrium_fe_form2} \\mathbf{u}=\\sum_{i=1}^{m}N_{i}\\mathbf{u}_{i}=\\mathbf{NU} \\end{align} \\]

Similarly, the strain component can be expressed as

\\[ \\begin{align} \\label{eq:ch5_equilibrium_fe_form3} \\hat{\\epsilon}=\\mathbf{BU} \\end{align} \\]

Substituting equations \\(\\eqref{eq:ch5_equilibrium_fe_form2}\\) and \\(\\eqref{eq:ch5_equilibrium_fe_form3}\\) into \\(\\eqref{eq:ch5_equilibrium_fe_form1}\\), we have

\\[ \\begin{align} \\label{eq:ch5_equilibrium_fe_form4} \\sum_{e}\\delta\\mathbf{U}^{T}(\\int_{V^{e}}\\mathbf{B}^{T}\\mathbf{DB}dV)\\mathbf{U}=\\sum_{e}\\delta\\mathbf{U}^{T}\\cdot\\int_{S_{t}^{e}}\\mathbf{N}^{T}\\mathbf{t}dS+\\sum_{e}\\delta\\mathbf{U}^{T}\\int_{V^{e}}\\mathbf{N}^{T}\\mathbf{b}dV \\end{align} \\]

The equation above can be summarized as

\\[ \\begin{align} \\label{eq:ch5_equilibrium_fe_form5} \\delta\\mathbf{U}^{T}\\mathbf{KU}=\\delta\\mathbf{U}^{T}\\mathbf{F} \\end{align} \\]

where

\\[ \\begin{align} \\label{eq:ch5_equilibrium_fe_form6} \\mathbf{K}=\\sum_{e}\\int_{V^{e}}\\mathbf{B}^{T}\\mathbf{DB}dV \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_equilibrium_fe_form7} \\mathbf{F}=\\sum\\int_{S_{t}^{e}}\\mathbf{N}^{T}\\mathbf{t}dS+\\int_{V^{e}}\\mathbf{N}^{T}\\mathbf{b}dV \\end{align} \\]

The components of the matrix and vectors defined by equations \\(\\eqref{eq:ch5_equilibrium_fe_form6}\\) and \\(\\eqref{eq:ch5_equilibrium_fe_form7}\\) can be calculated for each finite element. For arbitrary virtual displacement \\(\\delta\\mathbf{U}\\), equation \\(\\eqref{eq:ch5_equilibrium_fe_form5}\\) can be rewritten into

\\[ \\mathbf{KU=F} \\]"},{"location":"welsim/theory/thermal/","title":"Thermal analysis","text":"

This section discuss the theories used in the WESLIM thermal analysis.

"},{"location":"welsim/theory/thermal/#governing-equations","title":"Governing equations","text":"

The governing equations applied in thermal analysis are:

\\[ \\begin{align} \\label{eq:ch5_thermal_gov} \\rho c\\frac{\\partial T}{\\partial t}=\\nabla\\cdot(k\\nabla T) \\end{align} \\]

where \\(\\rho=\\rho(x)\\) is mass density, \\(c=c(x,T)\\) is the specific heat, \\(T=T(x,t)\\) is the temperature, \\(K=k(x,T)\\) is the thermal conductivity, \\(Q=Q(x,T,t)\\) is the calorific value. \\(x\\) is the position in the modeling domain, \\(T\\) is the temperature and \\(t\\) is the time.

The modeling domain is represented by S, and the boundary is represented by \\(\\varGamma\\). When assuming the boundary conditions of either the Dirichlet or Neumann type, those boundary conditions can be mathematically expressed as

\\[ T=T_{1}(x,t) \\qquad X\\in\\Gamma_{1} \\] \\[ k\\frac{\\partial T}{\\partial n}=q(x,T,t) \\qquad X\\in\\Gamma_{2} \\]

where the term \\(T_{1}\\), \\(q\\) is already known. \\(q\\) is the heat flux outflow from the boundary. Three types of heat flux can be considered in WELSIM thermal module.

\\[ q=-q_{s}+q_{c}+q_{r} \\] \\[ q_{s}=q_{s}(x,t) \\] \\[ q_{c}=hc(T-T_{c}) \\] \\[ q_{r}=hc(T^{4}-T_{r}^{4}) \\]

where \\(q_{s}\\) is the distributed heat flux, \\(q_{c}\\) is the heat flux by the convective heat transfer, and \\(q_{r}\\) is the heat flux by the radiant heat transfer. The other quantities are

"},{"location":"welsim/theory/thermal/#derivation-of-heat-flow-matrices","title":"Derivation of heat flow matrices","text":"

When equation \\(\\eqref{eq:ch5_thermal_gov}\\) is discreted by the Galerkin approximation, it becomes as follows,

\\[ \\begin{align} \\label{eq:ch5_thermal_gov2} [\\mathbf{K}]\\{T\\}+[\\mathbf{M}]\\frac{\\partial T}{\\partial t}=\\{F\\} \\end{align} \\]

where the matrices and vectors are

\\[ \\begin{array}{ccc} [\\mathbf{K}] & = & \\int(k_{xx}\\dfrac{\\partial\\{N\\}^{T}}{\\partial x}\\dfrac{\\partial\\{N\\}}{\\partial x}+k_{yy}\\dfrac{\\partial\\{N\\}^{T}}{\\partial y}\\dfrac{\\partial\\{N\\}}{\\partial y}+k_{zz}\\dfrac{\\partial\\{N\\}^{T}}{\\partial z}\\dfrac{\\partial\\{N\\}}{\\partial z})dV\\\\ & + & \\int h_{c}\\{N\\}^{T}\\{N\\}ds+\\int h_{r}\\{N\\}^{T}\\{N\\}ds \\end{array} \\] \\[ [\\mathbf{M}]=\\int\\rho c\\{N\\}^{T}\\{N\\}dV \\] \\[ \\{F\\}=\\int Q\\{N\\}^{T}dV-\\int q_{s}\\{N\\}^{T}dS+\\int h_{c}T_{c}\\{N\\}^{T}dS+\\int h_{r}T_{r}(T+T_{r})(T^{2}+T_{r}^{2})\\{N\\}^{T}dS \\]

where shape function

\\[ \\{N\\}=(N^{1},N^{2},.......),\\thinspace N_{i}=N_{i}(x) \\]

Equation \\(\\eqref{eq:ch5_thermal_gov2}\\) is nonlinear and unsteady. When the time is discretized by the backward Euler's rule and the temperature at time t=t_{0} is known, the temperature at t=t_{0+\\triangle t} is calculated using the following equation.

\\[ \\begin{align} \\label{eq:ch5_thermal_gov_disc1} [\\mathbf{K}]_{t=t_{0+\\triangle t}}\\{T\\}_{t=t_{0+\\triangle t}}+[\\mathbf{M}]_{t=t_{0+\\triangle t}}\\dfrac{\\{T\\}_{t=t_{0+\\triangle t}}-\\{T\\}_{t=t_{0}}}{\\triangle t}=\\{F\\}_{t=t_{0+\\triangle t}} \\end{align} \\]

The temperature vector can be expressed as

\\[ \\begin{align} \\label{eq:ch5_thermal_gov_disc2} \\{T\\}_{t=t_{0}+\\triangle t}=\\{T\\}_{t=t_{0}+\\triangle t}^{(i)}+\\{\\triangle T\\}_{t=t_{0}+\\triangle t}^{(i)} \\end{align} \\]

The product of the heat conduction matrix and temperature vector, mass matrix and etc. are expressed in approximation as in the following equation.

\\[ \\begin{align} \\label{eq:ch5_thermal_gov_disc3} [\\mathbf{K}]_{t=t_{0+\\triangle t}}\\{T\\}_{t=t_{0+\\triangle t}}\\cong[\\mathbf{K}]_{t=t_{0+\\triangle t}}^{(i)}\\{T\\}_{t=t_{0+\\triangle t}}^{(i)}+\\dfrac{\\partial[\\mathbf{K}]_{t=t_{0+\\triangle t}}^{(i)}\\{T\\}_{t=t_{0+\\triangle t}}^{(i)}}{\\partial\\{T\\}_{t=t_{0+\\triangle t}}^{(i)}}\\{\\triangle T\\}_{t=t_{0+\\triangle t}}^{(i)} \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_thermal_gov_disc4} [M]_{t=t_{0+\\triangle t}}\\cong[M]_{t=t_{0}+\\triangle t}^{(i)}+\\dfrac{\\partial[M]_{t=t_{0}+\\triangle t}^{(i)}}{\\partial\\{T\\}_{t=t_{0+\\triangle t}}^{\\{i\\}}}\\{\\triangle T\\}_{t=t_{0+\\triangle t}}^{(i)} \\end{align} \\]

Substituting equations \\(\\eqref{eq:ch5_thermal_gov_disc2}\\), \\(\\eqref{eq:ch5_thermal_gov_disc3}\\), and \\(\\eqref{eq:ch5_thermal_gov_disc4}\\) into equation \\(\\eqref{eq:ch5_thermal_gov_disc1}\\) and skipping the high order polynomial terms, we have

\\[ (\\dfrac{[\\mathbf{M}]_{t=t_{0+\\triangle t}}^{(i)}}{\\triangle t}+\\dfrac{\\partial[\\mathbf{M}]_{t=t_{0+\\triangle t}}^{(i)}\\{T\\}_{t=t_{0}+\\text{\\triangle t}}^{(i)}}{\\partial\\{T\\}_{t=t_{0}+\\triangle t}^{(i)}}\\dfrac{\\{T\\}_{t=t_{0}+\\triangle t}^{(i)}-\\{T\\}_{t=t0}}{\\triangle t}+\\dfrac{\\partial[\\mathbf{K}]_{t=t_{0}+\\triangle t}^{(i)}\\{T\\}_{t=t_{0}+\\triangle t}^{(i)}}{\\partial\\{T\\}_{t=t_{0}+\\triangle t}^{(i)}})\\{\\triangle T\\}_{t=t_{0}+\\triangle t}^{(i)}\\\\=\\{F\\}_{t=t_{0}+\\triangle t}-[\\mathbf{M}]_{t=t_{0}+\\triangle t}^{(i)}\\dfrac{\\{T\\}_{t=t_{0}+\\triangle t}^{(i)}-\\{T\\}_{t=t_{0}}}{\\triangle t}-[\\mathbf{K}]_{t=t_{0}+\\triangle t}^{(i)}\\{T\\}_{t=t_{0}+\\triangle t}^{(i)} \\]

Furthermore, an approximation evaluation for the left hand side factor is given below,

\\[ [\\mathbf{K}^{*}]^{(i)}=\\dfrac{[M]_{t=t_{0}+\\triangle t}^{(i)}}{\\triangle t}+\\dfrac{\\partial[\\mathbf{K}]_{t=t_{0}+\\triangle t}^{(t)}}{\\partial\\{T\\}_{t=t_{0}+\\triangle t}^{(i)}}\\{T\\}_{t=t_{0}+\\triangle t}^{(i)}=\\dfrac{[M]_{t=t_{0}+\\triangle t}^{(i)}}{\\triangle t}+[\\mathbf{K}_{T}]_{t=t_{0}+\\triangle t}^{(i)} \\]

where \\([\\mathbf{K}_{T}]_{t=t_{0}+\\triangle t}^{(i)}\\) tangent stiffness matrix.

Eventually, the temperature at time \\(t=t_{0}+\\triangle t\\) can be calculated by iterative solver using the following scheme:

\\[ \\begin{array}{cc} [\\mathbf{K}^{*}]^{(i)}\\{T\\}_{t=t_{0}+\\triangle t}^{(i)}=\\{F\\}_{t=t_{0}+\\triangle t}-[\\mathbf{M}]_{t=t_{0}+\\triangle t}^{(i)}\\dfrac{\\{T\\}_{t=t_{0}+\\triangle t}^{(i)}-\\{T\\}_{t=t_{0}}}{\\triangle t}-[\\mathbf{K}]_{t=t_{0}+\\triangle t}^{(i)}\\\\ \\{T\\}_{t=t_{0}+\\triangle t}^{(i+1)}=\\{T\\}_{t=t_{0}+\\triangle t}^{(i)}+\\{\\triangle T\\}_{t=t_{0}+\\triangle t}^{(i)} \\end{array} \\]

For the steady state analysis, the iteration algorithm is given below

\\[ \\begin{array}{cc} [\\mathbf{K}_{T}]^{(i)}\\{\\triangle T\\}_{t=\\infty}^{(i)}=\\{F\\}_{t=\\infty}-[\\mathbf{K}_{T}]^{(i)}\\{\\triangle T\\}_{t=\\infty}^{(i)}\\\\ \\{T\\}_{t=\\infty}^{(i+1)}=\\{T\\}_{t=\\infty}^{(i)}+\\{\\triangle T\\}_{t=\\infty}^{(i)} \\end{array} \\]

Since the implicit time solver is applied in the program, the selection of incremental time \\(\\triangle t\\) is relatively flexible. However, if the magnitude of \\(\\triangle t\\) is too large, the convergence frequency will be decreased in the iterative computation. The program contains automatic incremental functions to monitor the size of the residual vectors during the iterations. As the convergence rate becomes slow, the incremental time \\(\\triangle t\\) is automatically reduced. When the convergence rate becomes high, the program increases the incremental time \\(\\triangle t\\). Doing this automatic scheme can improve the numerical performance and saving computational time.

"},{"location":"welsim/theory/transient/","title":"Structures with transient analysis","text":"

The time integration method applied in structural transient analysis is described in the section.

"},{"location":"welsim/theory/transient/#formulation-of-implicit-method","title":"Formulation of implicit method","text":"

In the direct time integration, the equation of motion can be expressed as follows

\\[ \\begin{align} \\label{eq:ch5_time_solver_imp1} \\mathbf{M}(t+\\triangle t)\\ddot{\\mathbf{U}}(t+\\triangle t)+\\mathbf{C}(t+\\triangle t)\\dot{\\mathbf{U}}(t+\\triangle t)+\\mathbf{Q}(t+\\triangle t)=\\mathbf{F}(t+\\triangle t) \\end{align} \\]

where \\(\\mathbf{M}\\) and \\(\\mathbf{C}\\) is the mass matrix and damping matrix, respectively. The \\(\\mathbf{Q}\\) and \\(\\mathbf{F}\\) are the internal force vector, and external force vector, respectively. Note that, the mass density is consistent in the structural analysis, thus the mass matrix keep constants regardless of the deformation in non-linearity.

In the Newmark-\\(\\beta\\) method, the displacement, velocity, and acceleration at the each time incremental \\(\\triangle t\\) are

\\[ \\begin{align} \\label{eq:ch5_time_solver_imp2} \\dot{\\mathbf{U}}(t+\\triangle t)=\\dfrac{\\gamma}{\\beta\\triangle t}\\triangle\\mathbf{U}(t+\\triangle t)-\\dfrac{\\gamma-\\beta}{\\beta}\\dot{\\mathbf{U}}(t)-\\triangle t\\dfrac{\\gamma-2\\beta}{2\\beta}\\ddot{\\mathbf{U}}(t) \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_time_solver_imp3} \\ddot{\\mathbf{U}}(t+\\triangle t)=\\dfrac{\\text{1}}{\\beta\\triangle t^{2}}\\triangle\\mathbf{U}(t+\\triangle t)-\\dfrac{1}{\\beta\\triangle t}\\dot{\\mathbf{U}}(t)-\\dfrac{1-2\\beta}{2\\beta}\\ddot{\\mathbf{U}}(t) \\end{align} \\]

where \\(\\gamma\\) and \\(\\beta\\) are time solver parameters. Given the specific values, the numerical algorithm becomes linear acceleration method, or the trapezoid rule.

\\[ \\gamma=\\frac{1}{2},\\thinspace\\beta=\\frac{1}{6},\\quad\\mathrm{Linear}\\thinspace\\mathrm{acceleration\\thinspace\\mathrm{method}} \\] \\[ \\gamma=\\frac{1}{2},\\thinspace\\beta=\\frac{1}{4},\\quad\\mathrm{Trapezoid}\\thinspace\\mathrm{rule} \\]

substituting equations \\(\\eqref{eq:ch5_time_solver_imp2}\\) and \\(\\eqref{eq:ch5_time_solver_imp3}\\) into equation \\(\\eqref{eq:ch5_time_solver_imp1}\\), the following equation can be acquired

\\[ \\begin{array}{ccc} (\\dfrac{1}{\\beta\\triangle t^{2}}\\mathbf{M}+\\dfrac{\\gamma}{\\beta\\triangle t}\\mathbf{C}+\\mathbf{K})\\triangle\\mathbf{U}(t+\\triangle t) & = & \\mathbf{F}(t+\\triangle t)-\\mathbf{Q}(t+\\triangle t)\\\\ & + & \\dfrac{1}{\\beta\\triangle t}\\mathbf{\\mathbf{M}\\dot{\\mathbf{U}}}(t)+\\dfrac{1-2\\beta}{2\\beta}\\mathbf{M}\\ddot{\\mathbf{U}}(t)+\\dfrac{\\gamma-\\beta}{\\beta}\\mathbf{C}\\dot{\\mathbf{U}}(t)\\\\ & + & \\triangle t\\dfrac{\\gamma-2\\beta}{2\\beta}\\mathbf{C}\\ddot{\\mathbf{U}}(t) \\end{array} \\]

when we use linear stiffness matrix \\(\\mathbf{K}_{L}\\) for a linear problem, the equation above becomes \\(\\mathbf{Q}(t+\\triangle t)=\\mathbf{K}_{L}\\mathbf{U}(t+\\triangle t)\\). Substituting this term into the equation (), we have

\\[ \\begin{array}{ccc} \\{\\mathbf{M}(-\\dfrac{1}{(\\triangle t)^{2}\\beta}\\mathbf{U}(t)-\\dfrac{1}{(\\triangle t)\\beta}\\dot{\\mathbf{U}}(t)-\\dfrac{1-2\\beta}{2\\beta}\\ddot{\\mathbf{U}}(t))\\\\ +\\mathbf{C}(-\\dfrac{\\gamma}{(\\triangle t)\\beta}\\mathbf{U}(t)+(1-\\dfrac{\\gamma}{\\beta})\\dot{\\mathbf{U}}(t)+\\triangle t\\dfrac{2\\beta-\\gamma}{2\\beta}\\ddot{\\mathbf{U}}(t))\\}\\\\ +\\{\\dfrac{1}{(\\triangle t)^{2}\\beta}\\mathbf{M}+\\dfrac{\\gamma}{(\\triangle t)\\beta}\\mathbf{C}+\\mathbf{K}_{L}\\}\\mathbf{U}(t+\\triangle t) & = & \\mathbf{F}(t+\\triangle t) \\end{array} \\]

In the analysis practice, the acceleration and velocity boundary conditions are imposed. Then the displacement of the following equation can be derived from equation \\(\\eqref{eq:ch5_time_solver_imp1}\\).

\\[ u_{is}(t+\\triangle t)=u_{is}(t)+\\triangle t\\dot{u}_{is}(t)+(\\triangle t)^{2}(\\frac{1}{2}-\\beta)\\ddot{u}_{is}(t+\\triangle t) \\]

where \\(u_{is}(t+\\triangle t)\\) is the nodal displacement at time \\(t+\\triangle t\\), \\(\\dot{u}{}_{is}(t+\\triangle t)\\) is the nodal velocity, \\(\\ddot{u}{}_{is}(t+\\triangle t)\\) is the nodal acceleration, i is the degree of freedom per node, s is the node number.

The mass and damping terms are treated as follows

  1. The lumped mass matrix is used at most of cases in this program.
  2. The damping matrix is treated using Rayleigh algorithm \\(\\mathbf{C}=R_{m}\\mathbf{M}+R_{k}\\mathbf{K}_{L}\\).
"},{"location":"welsim/theory/transient/#formulation-of-explicit-method","title":"Formulation of explicit method","text":"

This section discuss how the explicit time solver is formulation to solve the governing equation below

\\[ \\begin{align} \\label{eq:ch5_time_solver_exp1} \\mathbf{M}\\ddot{\\mathbf{U}}(t)+\\mathbf{C}\\text{(t)}\\dot{\\mathbf{U}(t)+\\mathbf{Q}(t)=\\mathbf{F}(t)} \\end{align} \\]

where the displacement at the time \\(t+\\triangle t\\) and \\(t-\\triangle t\\) can be expressed by the Taylor's expansion at time t with the second order truncation.

\\[ \\begin{align} \\label{eq:ch5_time_solver_exp2} \\mathbf{U}(t+\\triangle t)=\\mathbf{U}(t)+\\dot{\\mathbf{U}}(t)(\\triangle t)+\\dfrac{1}{2!}\\ddot{\\mathbf{U}}(t)(\\triangle t)^{2} \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_time_solver_exp3} \\mathbf{U}(t-\\triangle t)=\\mathbf{U}(t)-\\dot{\\mathbf{U}}(t)(\\triangle t)+\\dfrac{1}{2!}\\ddot{\\mathbf{U}}(t)(\\triangle t)^{2} \\end{align} \\]

Differentiating equations \\(\\eqref{eq:ch5_time_solver_exp2}\\) and \\(\\eqref{eq:ch5_time_solver_exp3}\\), we have

\\[ \\begin{align} \\label{eq:ch5_time_solver_exp4} \\dot{\\mathbf{U}}(t)=\\dfrac{1}{2\\triangle t}(\\mathbf{U}(t+\\triangle t)-\\mathbf{U}(t-\\triangle t)) \\end{align} \\] \\[ \\begin{align} \\label{eq:ch5_time_solver_exp5} \\ddot{\\mathbf{U}}(t)=\\dfrac{1}{(\\triangle t)^{2}}(\\mathbf{U}(t+\\triangle t)-2\\mathbf{U}(t)+\\mathbf{U}(t-\\triangle t)) \\end{align} \\]

Substituting equations \\(\\eqref{eq:ch5_time_solver_exp4}\\) and \\(\\eqref{eq:ch5_time_solver_exp5}\\) into \\(\\eqref{eq:ch5_time_solver_exp1}\\), we have

\\[ (\\dfrac{1}{\\triangle t^{2}}\\mathbf{M}+\\dfrac{1}{2\\triangle t}\\mathbf{C})\\mathbf{U}(t+\\triangle t)=\\mathbf{F}(t)-\\mathbf{Q}(t)-\\dfrac{1}{\\triangle t^{2}}\\mathbf{M}[2\\mathbf{U}(t)-\\mathbf{U}(t-\\triangle t)]-\\dfrac{1}{2\\triangle t}\\mathbf{CU}(t-\\triangle t) \\]

For the linear problem, we also have condition \\(\\mathbf{Q}(t)=\\mathbf{K}_{L}\\mathbf{U}(t)\\) for equation. Finally, the displacement at \\(t+\\triangle t\\) is:

\\[ \\mathbf{U}(t+\\triangle t)=\\dfrac{1}{(\\frac{1}{\\triangle t^{2}}\\mathbf{M}+\\frac{1}{2\\triangle t}\\mathbf{C})}\\{\\mathbf{F}(t)-\\mathbf{Q}(t)-\\dfrac{1}{\\triangle t^{2}}\\mathbf{M}[2\\mathbf{U}(t)-\\mathbf{U}(t-\\triangle t)]-\\dfrac{1}{2\\triangle t}\\mathbf{C}(t-\\triangle t)\\mathbf{U}\\} \\]"},{"location":"welsim/users/analysistypes/","title":"Physics and analysis types","text":"

WELSIM supports several types of finite element analyses. This section describes those analysis types that you can perform in the WELSIM user interface.

"},{"location":"welsim/users/analysistypes/#static-structural-analysis","title":"Static structural analysis","text":"

As one of the most widely used analysis types, a static structural analysis discloses the structural displacements, stresses, strains, and forces caused by loads or other mechanical effects. In this static analysis, the constant loading and response are assumed.

The static structural analysis can be either linear or nonlinear. The non-linearity can be introduced by the large deformations, in-elasticity, contact, hyperelasticity, etc. For the nonlinear problem, it is recommended to set multiple substeps in the Study Settings.

"},{"location":"welsim/users/analysistypes/#conducting-a-static-structural-analysis","title":"Conducting a static structural analysis","text":"

The following lists the general and specifics steps in conducting static structural analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Structural and Analysis Type to Static. Since the static structural analysis is the default analysis type, you do not need to change these properties if the analysis is newly created. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, the default setting is Solid. You need to change this property value accordingly if the geometry is Shell or other types. See Defining Part Behaviors for details.

  5. Setting bonnections: Optional. Contacts are supported in a static structural analysis. See Setting Connections for details.

  6. Applying mesh: It is recommended to generate Tet10 elements for Solid analysis and the Tri6 element for the Shell analysis. See Applying Mesh for details.

  7. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analyses such as nonlinear models, the analysis controls you can tune: Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  8. Setting up boundary conditions: For a static structural analysis, the applicable boundary conditions are Fixed Supported, Fixed Rotation, Displacement, Force, and Pressure. The following body conditions are supported: Body Force, Acceleration, Earth Gravity, and Rotational Velocity. See Setting up Boundary Conditions for details.

  9. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  10. Evaluating results: For a static structural analysis, the applicable results are Deformations, Stresses, Strains, Rotations, Reaction Forces, and Reaction Moments. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

"},{"location":"welsim/users/analysistypes/#transient-structural-analysis","title":"Transient structural analysis","text":"

In the transient structural analysis, the dynamic response is updated and is a function of time. You can impose general time-dependent boundary conditions on the model and obtain the time-varying responded to these transient loads or constraints. The inertia or damping effects play important roles in this analysis type, if the inertia and damping effects are minimal, you could use the static analysis instead.

The transient structural analysis can be either linear or nonlinear. The non-linearity can be introduced by the large deformations, inelasticity, contact, hyperelasticity, etc. For the nonlinear problem, it is recommended to set multiple substeps for each load step in the Study Settings.

"},{"location":"welsim/users/analysistypes/#conducting-a-transient-structural-analysis","title":"Conducting a transient structural analysis","text":"

The following lists the general and specifics steps in conducting transient structural analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Structural and Analysis Type to Transient. You can choose either Implicit or Explicit time integration solver. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. You need to change this property value accordingly if the geometry is Shell or other types. See Defining Part Behaviors for details.

  5. Setting connections: Optional. Contacts are supported in a transient structural analysis. See Setting Connections for details.

  6. Applying mesh: It is recommended to generate Tet10 elements for Solid analysis and the Tri6 element for the Shell analysis. See Applying Mesh for details.

  7. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analyses such as nonlinear models, the analysis controls you can tune are Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  8. Defining initial conditions: Optional. In the transient structural analysis, you can define the initial status of boundary and body conditions. The Initial Status property provides two options: None and Equal to Step 1. The default option None set the initial value to zero, the option Equal to Step 1 set the initial value to that of step 1. See Defining Initial Conditions for details.

  9. Setting up boundary conditions: For the transient structural analysis, the applicable boundary conditions are Fixed Supported, Fixed Rotation, Displacement, Force, Pressure, Velocity, and Acceleration. The following body conditions are supported: Body Force, Acceleration, Earth Gravity, and Rotational Velocity. See Setting up Boundary Conditions for details.

  10. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  11. Evaluating results: For the transient structural analysis, the applicable results are: Deformations, Stresses, Strains, Rotations, Reaction Forces, Reaction Moments, Velocity, and Acceleration. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

"},{"location":"welsim/users/analysistypes/#modal-analysis","title":"Modal analysis","text":"

The modal analysis investigates the vibration characteristics of a structure or component. You can obtain the natural frequencies and mode shapes, which serve as a starting pointing for dynamic analysis of the target structure.

"},{"location":"welsim/users/analysistypes/#conducting-a-modal-structural-analysis","title":"Conducting a modal structural analysis","text":"

The following lists the general and specifics steps in conducting modal structural analysis:

  1. Creating analysis environment: From the properties view of FEM Project object, set the Physics Type to Structural and Analysis Type to Modal. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. However, the nonlinearity in the modal analysis is ignored due to the characteristics of eigen solver algorithms. You must define the sufficient properties that are required in the solving process. For example, the mass density parameter must be defined. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. You need to change this property value accordingly if the geometry is Shell or other types. See Defining Part Behaviors for details.

  5. Setting connections: Optional. The Bonded Contacts are supported in a modal structural analysis. See Setting Connections for details.

  6. Applying mesh: It is recommended to generate the Tet10 elements for Solid analysis and the Tri6 element for the Shell analysis. See Applying Mesh for details.

  7. Configuring study settings: You typically do not need to change these settings for simple modal analyses. The default number of modes is 6, increasing this value yields to calculate more natural frequency modes, while it requires more computational resources. See Configuring Study Settings for details.

  8. Setting up boundary conditions: For the modal structural analysis, the applicable boundary conditions are Fixed Supported, Fixed Rotation, zero Displacement. The following body conditions are supported: Body Force, Acceleration, Earth Gravity, and Rotational Velocity. Note that only constraint-type boundaries are applicable in modal analysis. See Setting up Boundary Conditions for details.

  9. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  10. Evaluating results: For the modal structural analysis, the applicable results are Deformations, and Frequencies. Note that deformation results here are just relative quantities intended to show the shape modes. The Tabular Data and Chart windows display the frequencies and related mode numbers. See Evaluating Results for details.

"},{"location":"welsim/users/analysistypes/#steady-state-thermal-analysis","title":"Steady-state thermal analysis","text":"

In the steady-state thermal analysis, you can determine the temperatures in objects that are impacted by the time-invariant thermal loads. Users are recommended to perform a steady-state analysis before conducting a transient study in a complex model.

The static thermal analysis can be either linear or nonlinear. The nonlinearity can be introduced by the temperature-depend material properties, or radiation and convection coefficient. For the nonlinear problem, it is recommended to set multiple substeps in the Study Settings.

"},{"location":"welsim/users/analysistypes/#conducting-a-static-structural-analysis_1","title":"Conducting a static structural analysis","text":"

The following lists the general and specifics steps in conducting static structural analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Thermal and Analysis Type to Static. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. You need to change this property value accordingly if the geometry is Shell or other types. See Defining Part Behaviors for details.

  5. Setting connections: Optional. The steady-state thermal analysis supports the Bonded Contact. See Setting Connections for details.

  6. Applying mesh: It is recommended to generate the Tet10 elements for Solid analysis, and the Tri6 element for the Shell analysis. See Applying Mesh for details.

  7. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analysis such as nonlinear models, the analysis controls you can tune are Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  8. Setting up boundary conditions: In the steady-state thermal analysis, the applicable boundary conditions are: Temperature, Heat Flux, Convection, and Radiation. See Setting up Boundary Conditions for details.

  9. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  10. Evaluating results: In steady-state thermal analysis, the applicable results are Temperature. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

"},{"location":"welsim/users/analysistypes/#transient-thermal-analysis","title":"Transient thermal analysis","text":"

In the transient thermal analysis, you can obtain the temperatures of objects that vary over time. Many heat transfer applications such as coiling or quenching problems, and so on involve transient thermal analysis. The transient thermal analysis can be either linear or nonlinear. The nonlinearity can be introduced by the temperature-dependent material properties or convection and radiation boundary conditions. For the nonlinear problem, it is recommended to define multiple substeps for each load step in the Study Settings.

"},{"location":"welsim/users/analysistypes/#conducting-a-transient-thermal-analysis","title":"Conducting a transient thermal analysis","text":"

The following lists the general and specifics steps in conducting transient thermal analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Thermal and Analysis Type to Transient. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. You need to change this property value accordingly if the geometry is Shell or other types. See Defining Part Behaviors for details.

  5. Setting connections: Optional. In the transient thermal analysis, the Bonded Contact is supported. See Setting Connections for details.

  6. Applying mesh: It is recommended to generate the Tet10 elements for Solid analysis and the Tri6 element for the Shell analysis. See Applying Mesh for details.

  7. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analysis such as nonlinear models, the analysis controls you can tune are Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  8. Setting up boundary conditions: In the transient thermal analysis, the applicable boundary conditions are: Temperature, Heat Flux, Convection, and Radiation. See Setting up Boundary Conditions for details.

  9. Defining initial conditions: You can define the global initial temperature condition for the analysis. In the transient thermal analysis, you can define the initial status of boundary and body conditions. The Initial Status property provides two options: None and Equal to Step 1. The default option None set the initial value to zero, the option Equal to Step 1 set the initial value to that of step 1. See Defining Initial Conditions for details.

  10. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  11. Evaluating results: In the transient thermal analysis, the applicable results are Temperature. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

"},{"location":"welsim/users/analysistypes/#electrostatic-analysis","title":"ElectroStatic Analysis","text":"

The electrostatic analysis can be applied to determine the distribution of electric potential in a conducting body under voltage or current conditions. You can obtain the solution results such as voltage, electric field, etc. The electrostatic analysis supports the single body analysis.

An electrostatic analysis could be either linear or nonlinear. The electric field dependent material properties can introduce the nonlinearity. For the nonlinear problem, it is recommended to set multiple substeps in the Study Settings.

"},{"location":"welsim/users/analysistypes/#conducting-an-electrostatic-analysis","title":"Conducting an electrostatic analysis","text":"

The following lists the general and specifics steps in conducting electrostatic analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Electromagnetic and Analysis Type to ElectroStatic. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. An electrostatic analysis only supports the Solid geometry type. See Defining Part Behaviors for details.

  5. Applying mesh: It is recommended to generate Tet10 elements for Solid analysis. See Applying Mesh for details.

  6. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analysis such as nonlinear models, the analysis controls you can tune are Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  7. Setting up boundary conditions: In the electrostatic analysis, the applicable boundary conditions are Ground, Voltage, Symmetry, Zero Charge, Surface Charge Density, and Electric Displacement. See Setting up Boundary Conditions for details.

  8. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  9. Evaluating results: In the electrostatic analysis, the applicable results are Voltage, Electric Field, Electric Displacement, and Energy Density. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

"},{"location":"welsim/users/analysistypes/#magnetostatic-analysis","title":"MagnetoStatic analysis","text":"

The magnetostatic analysis determines the magnetic field in and around a magnetic body.

A magnetostatic analysis requires the medium such as air surrounding the geometry be included as part of the entire simulation domain. In many cases, the full model can be reduced to the symmetric model by applying a symmetric boundary condition on the symmetric surface.

"},{"location":"welsim/users/analysistypes/#conducting-a-magnetostatic-analysis","title":"Conducting a magnetostatic analysis","text":"

The following lists the general and specifics steps in conducting magnetostatic analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Electromagnetic and Analysis Type to MagnetoStatic. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. A magnetostatic analysis only supports the Solid geometry type. See Defining Part Behaviors for details.

  5. Applying mesh: It is recommended to generate the Tet10 elements for magnetostatic analysis. See Applying Mesh for details.

  6. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analysis such as nonlinear models, the analysis controls you can tune are Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  7. Setting up boundary conditions: In the magnetostatic analysis, the applicable boundary conditions are Insulating, Symmetry, Magnetic Potential, and Magnetic Flux Density. See Setting up Boundary Conditions for details.

  8. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  9. Evaluating results: In the magnetostatic analysis, the applicable results are Magnetic Potential, Magnetic Field, Magnetic Induction Field, and Energy Density. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

The following describes the widget components in the material editor interface:

"},{"location":"welsim/users/analysistypes/#library-outline-tab","title":"Library outline tab","text":"

The Library Outline Tab shows an outline of the contents of the selectable material sources. You can directly load a material data from this pre-defined source by one of the methods below:

"},{"location":"welsim/users/bcs/","title":"Setting up boundary conditions","text":"

Boundary or Body conditions are essential conditions for the most analyses. A boundary condition is imposed on the boundary of the geometry. For example, a displacement condition imposed on the face of the 3D solid geometry. A body condition is imposed on the entire body. For example, the rotational velocity imposed on the body.

Each analysis type has its boundary and body conditions. These boundary and body conditions will be described separately regarding structural, thermal, and electromagnetic analyses.

Note

The boundary condition here includes both boundary and body conditions.

"},{"location":"welsim/users/bcs/#add-boundary-condition","title":"Add boundary condition","text":"

Adding boundary and body conditions in WELSIM application is straightforward. The following describes the adding method and its behaviors.

"},{"location":"welsim/users/bcs/#scoping-method","title":"Scoping method","text":"

The scoping method supports the geometry selection, and you can select the target geometry entities and set to the properties. A voltage boundary condition scoping is illustrated in Figure\u00a0below. You can select multiple geometry entities such as bodies, faces, edges, or vertices to a Geometry property, but all these entities must be the same type.

"},{"location":"welsim/users/bcs/#tips-in-geometry-selection","title":"Tips in geometry selection","text":"

The following describes the tips in selecting geometries for boundary and body conditions:

"},{"location":"welsim/users/bcs/#types-of-boundary-conditions","title":"Types of boundary conditions","text":"

This section describes the boundary conditions that are provided in the WELSIM application.

"},{"location":"welsim/users/bcs/#displacement","title":"Displacement","text":"

Displacement determines the spatial motion of one or more faces, edges, or vertices for their original location. This boundary condition is available for all structural analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application","title":"Boundary condition application","text":"

To apply Displacement:

  1. On the menu or toolbar of the Structural, click Displacement button. Or, right-click the Study object in the tree and select Impose Conditions > Displacement.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Displacement components on X, Y, and Z directions.
"},{"location":"welsim/users/bcs/#properties-view","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#displacement-example","title":"Displacement example","text":"

Displacement boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#fixed-support","title":"Fixed support","text":"

Fixed Support is a special case of Displacement boundary condition. It essentially sets the displacement to zero at the scoped geometries. This boundary condition is available for all structural analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_1","title":"Boundary condition application","text":"

To apply the Fixed Support:

  1. On the menu or toolbar of the Structural, click Fixed Support button. Or, right-click the Study object in the tree and select Impose Conditions > Fixed Support.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Determine the constraint status on X, Y, and Z directions.
"},{"location":"welsim/users/bcs/#properties-view_1","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#fixed-support-example","title":"Fixed support example","text":"

Fixed support boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#fixed-rotation","title":"Fixed rotation","text":"

Fixed Rotation constrains the rotation of the scoped geometry entities. This boundary condition is only available for Shell structural analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_2","title":"Boundary condition application","text":"

To apply Fixed Rotation: 1. On the menu or toolbar of the Structural, click Fixed Rotation button. Or, right-click the Study object in the tree and select Impose Conditions > Fixed Rotation. 2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window. 3. Determine the constraint status on X, Y, and Z directions.

"},{"location":"welsim/users/bcs/#properties-view_2","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#fixed-rotation-example","title":"Fixed Rotation example","text":"

Fixed Rotation boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#pressure","title":"Pressure","text":"

A pressure boundary condition imposes a constant normal pressure to one or more surfaces. A positive pressure acts into the surface, which compresses the scoped body. Similarly, a negative pressure pulling away from the scoped surface. This boundary condition is available for all structural analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_3","title":"Boundary condition application","text":"

To apply Pressure:

  1. On the menu or toolbar of the Structural, click Pressure button. Or, right-click the Study object in the tree and select Impose Conditions > Pressure.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Input the magnitude of normal pressure. A positive pressure acts into the surface, and a negative pressure pulls away from the surface.
"},{"location":"welsim/users/bcs/#properties-view_3","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#pressure-example","title":"Pressure example","text":"

Pressure boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#force","title":"Force","text":"

A force boundary condition imposes a constant force to one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for all structural analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_4","title":"Boundary condition application","text":"

To apply Force:

  1. On the menu or toolbar of the Structural, click Force button. Or, right-click the Study object in the tree and select Impose Conditions>Force.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Force components on X, Y, and Z directions.
"},{"location":"welsim/users/bcs/#properties-view_4","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#force-example","title":"Force example","text":"

Force boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#velocity","title":"Velocity","text":"

A velocity boundary condition imposes a constant velocity to one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for transient structural analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_5","title":"Boundary condition application","text":"

To apply Velocity:

  1. On the menu or toolbar of the Structural, click Velocity button. Or, right-click the Study object in the tree and select Impose Conditions > Velocity.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Velocity components on X, Y, and Z directions.
"},{"location":"welsim/users/bcs/#properties-view_5","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#velocity-example","title":"Velocity example","text":"

Velocity boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#acceleration","title":"Acceleration","text":"

An acceleration boundary condition imposes a constant acceleration to one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for transient structural analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_6","title":"Boundary condition application","text":"

To apply Acceleration:

  1. On the menu or toolbar of the Structural, click Acceleration button. Or, right-click the Study object in the tree and select Impose Conditions>Acceleration.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Acceleration components on X, Y, and Z directions.
"},{"location":"welsim/users/bcs/#properties-view_6","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#acceleration-example","title":"Acceleration example","text":"

Acceleration boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#temperature","title":"Temperature","text":"

A temperature boundary condition imposes a constant temperature to one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for all thermal analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_7","title":"Boundary condition application","text":"

To apply Temperature:

  1. On the menu or toolbar of the Thermal, click Temperature button. Or, right-click the Study object in the tree and select Impose Conditions>Temperature.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Temperature scalar value.
"},{"location":"welsim/users/bcs/#properties-view_7","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#temperature-example","title":"Temperature example","text":"

Temperature boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#heat-flux","title":"Heat flux","text":"

A Heat Flux boundary condition imposes a constant flux to one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for all thermal analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_8","title":"Boundary condition application","text":"

To apply Heat Flux:

  1. On the menu or toolbar of the Thermal, click Heat Flux button. Or, right-click the Study object in the tree and select Impose Conditions>Heat Flux.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Heat Flux scalar value.
"},{"location":"welsim/users/bcs/#properties-view_8","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#heat-flux-example","title":"Heat flux example","text":"

Heat Flux boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#heat-convection","title":"Heat convection","text":"

A heat convection boundary condition imposes a constant convection onto one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for all thermal analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_9","title":"Boundary condition application","text":"

To apply Heat Convection:

  1. On the menu or toolbar of the Thermal, click Heat Convection button. Or, right-click the Study object in the tree and select Impose Conditions > Heat Convection.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Convection Coefficient and Ambient Temperature scalar values.
"},{"location":"welsim/users/bcs/#properties-view_9","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#heat-convection-example","title":"Heat convection example","text":"

Heat Convection boundary condition is applied in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#heat-radiation","title":"Heat radiation","text":"

A heat radiation boundary condition imposes a constant radiation onto one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for all thermal analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_10","title":"Boundary condition application","text":"

To apply Heat Radiation:

  1. On the menu or toolbar of the Thermal, click Heat Radiation button. Or, right-click the Study object in the tree and select Impose Conditions>Heat Radiation.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Radiation Coefficient and Ambient Temperature scalar values.
"},{"location":"welsim/users/bcs/#properties-view_10","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#heat-radiation-example","title":"Heat radiation example","text":"

Heat Radiation boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#initial-temperature","title":"Initial temperature","text":""},{"location":"welsim/users/bcs/#boundary-condition-application_11","title":"Boundary condition application","text":"

To apply Initial Temperature:

  1. On the Menu or Toolbar of the Thermal, click Initial Temperature button. Or, right-click the Study object in the tree and select Impose Conditions > Heat Radiation.
  2. Set the Initial Temperature value or use the default value.
"},{"location":"welsim/users/bcs/#properties-view_11","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#initial-temperature-example","title":"Initial temperature example","text":"

Initial Temperature boundary condition is applied as shown in Figure\u00a0below.

Note

Initial Temperature should be added before any other boundary conditions in all kinds of thermal analyses.

"},{"location":"welsim/users/bcs/#heat-flow","title":"Heat flow","text":""},{"location":"welsim/users/bcs/#boundary-condition-application_12","title":"Boundary condition application","text":"

To apply Heat Flow:

  1. On the Menu or Toolbar of the Thermal, click Heat Flow button. Or, right-click the Study object in the tree and select Impose Conditions > Heat Flow.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Set the Heat Flow value.
"},{"location":"welsim/users/bcs/#properties-view_12","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#heat-flow-example","title":"Heat flow example","text":"

Heat Flow boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#perfectly-insulated","title":"Perfectly insulated","text":""},{"location":"welsim/users/bcs/#boundary-condition-application_13","title":"Boundary condition application","text":"

To apply Perfectly Insulated:

  1. On the Menu or Toolbar of the Thermal, click Heat Flow button. Or, right-click the Study object in the tree and select Impose Conditions > Heat Flow.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
"},{"location":"welsim/users/bcs/#properties-view_13","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#perfectly-insulated-example","title":"Perfectly insulated example","text":"

Perfectly Insulated boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#voltage","title":"Voltage","text":"

Voltage determines the electric potential to one or more faces or edges, or vertices. This boundary condition is available for the electrostatic analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_14","title":"Boundary condition application","text":"

To apply Voltage:

  1. On the menu or toolbar of the Electromagnetic, click Voltage button. Or, right-click the Study object in the tree and select Impose Conditions>Voltage.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Voltage value.
"},{"location":"welsim/users/bcs/#properties-view_14","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#voltage-example","title":"Voltage example","text":"

Voltage boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#ground","title":"Ground","text":"

A Ground boundary condition is a special case of Voltage boundary condition. It essentially sets the voltage to zero at the scoped geometries. This boundary condition is available for the electrostatic analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_15","title":"Boundary condition application","text":"

To apply Ground:

  1. On the menu or toolbar of the Electromagnetic, click Ground command. Or, right-click the Study object in the tree and select Impose Conditions>Ground.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
"},{"location":"welsim/users/bcs/#properties-view_15","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#ground-example","title":"Ground example","text":"

Ground boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#symmetry","title":"Symmetry","text":"

A Symmetry boundary condition defines the symmetric boundary for the scoped geometry. This boundary condition is available for electromagnetic analyses.

"},{"location":"welsim/users/bcs/#boundary-condition-application_16","title":"Boundary condition application","text":"

To apply Symmetry:

  1. On the menu or toolbar of the Electromagnetic, click Symmetry button. Or, right-click the Study object in the tree and select Impose Conditions>Symmetry.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
"},{"location":"welsim/users/bcs/#properties-view_16","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#symmetry-example","title":"Symmetry example","text":"

Symmetry boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#zero-charge","title":"Zero charge","text":"

A Zero Charge boundary condition defines the zero surface charge for the scoped geometry. This boundary condition is available for electrostatic analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_17","title":"Boundary condition application","text":"

To apply Zero Charge:

  1. On the menu or toolbar of the Electromagnetic, click Zero Charge button. Or, right-click the Study object in the tree and select Impose Conditions>Zero Charge.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
"},{"location":"welsim/users/bcs/#properties-view_17","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#zero-charge-example","title":"Zero charge example","text":"

Zero Charge boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#surface-charge-density","title":"Surface charge density","text":"

A Surface Change Density boundary condition defines the surface charge density for the scoped geometry. This boundary condition is available for electrostatic analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_18","title":"Boundary condition application","text":"

To apply Surface Charge Density:

  1. On the menu or toolbar of the Electromagnetic, click Surface Charge Density button. Or, right-click the Study object in the tree and select Impose Conditions>Surface Charge Density.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
"},{"location":"welsim/users/bcs/#properties-view_18","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#surface-charge-density-example","title":"Surface charge density example","text":"

Surface Charge Density boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#electric-displacement","title":"Electric displacement","text":"

An Electric Displacement boundary condition defines the electric displacement vector for the scoped geometry. This boundary condition is available for electrostatic analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_19","title":"Boundary condition application","text":"

To apply Electric Displacement:

  1. On the menu or toolbar of the Electromagnetic, click Electric Displacement button. Or, right-click the Study object in the tree and select Impose Conditions>Electric Displacement.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Determine the values of Electric Displacement.
"},{"location":"welsim/users/bcs/#properties-view_19","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#electric-displacement-example","title":"Electric displacement example","text":"

Electric Displacement boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#insulating","title":"Insulating","text":"

An Insulating boundary condition defines the zero magnetic field for the scoped geometry. This boundary condition is available for the magnetic analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_20","title":"Boundary condition application","text":"

To apply Insulating:

  1. On the menu or toolbar of the Electromagnetic, click Insulating command. Or, right-click the Study object in the tree and select Impose Conditions>Insulating.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
"},{"location":"welsim/users/bcs/#properties-view_20","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#insulating-example","title":"Insulating example","text":"

Insulating boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#vector-magnetic-potential","title":"Vector magnetic potential","text":"

A Vector Magnetic Potential boundary condition defines the magnetic potential vector for the scoped geometry. This boundary condition is available for magnetic analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_21","title":"Boundary condition application","text":"

To apply Vector Magnetic Potential:

  1. On the menu or toolbar of the Electromagnetic, click Magnetic Potential button. Or, right-click the Study object in the tree and select Impose Conditions>Magnetic Potential.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Determine the value of Vector Magnetic Potential.
"},{"location":"welsim/users/bcs/#properties-view_21","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#magnetic-potential-example","title":"Magnetic potential example","text":"

Magnetic Potential boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#magnetic-flux-density","title":"Magnetic flux density","text":"

A Magnetic Flux Density boundary condition defines the magnetic flux density for the scoped geometry. This boundary condition is available for magnetic analysis.

"},{"location":"welsim/users/bcs/#boundary-condition-application_22","title":"Boundary condition application","text":"

To apply Magnetic Flux Density:

  1. On the menu or toolbar of the Electromagnetic, click Magnetic Flux Density button. Or, right-click the Study object in the tree and select Impose Conditions>Magnetic Flux Density.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
"},{"location":"welsim/users/bcs/#properties-view_22","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#magnetic-flux-density-example","title":"Magnetic flux density example","text":"

Magnetic Flux Density boundary condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#types-of-body-conditions","title":"Types of body conditions","text":"

This section describes the Body Conditions that are provided in the WELSIM application.

"},{"location":"welsim/users/bcs/#acceleration_1","title":"Acceleration","text":"

The Acceleration body condition defines a linear acceleration of a structure in a particular direction. This body condition is available for all structural analysis.

If desired, acceleration body condition can be used to mimic the Earth Gravity. For example, the standard earth gravity is 9.80665 m/s\\(^{2}\\) toward the ground, you can add an acceleration body condition object and apply to all or the target bodies to represent the earth gravity.

"},{"location":"welsim/users/bcs/#body-condition-application","title":"Body condition application","text":"

To apply Acceleration:

  1. On the menu or toolbar of the Structural, click Acceleration button. Or, right-click the Study object in the tree and select Impose Conditions>Acceleration.
  2. Keep the All bodies Scoping Method, or choose the Geometry Selection and scope the geometric entities from Graphics window.
  3. Define the Acceleration magnitude on X, Y, and Z directions.
"},{"location":"welsim/users/bcs/#properties-view_23","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#acceleration-example_1","title":"Acceleration example","text":"

Acceleration is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#earth-gravity","title":"Earth gravity","text":"

The earth gravity condition defines gravitational effects on structure bodies. This body condition is available for all structural analysis. This condition is equivalent to the Acceleration body condition.

"},{"location":"welsim/users/bcs/#body-condition-application_1","title":"Body condition application","text":"

To apply Acceleration:

  1. On the menu or toolbar of the Structural, click Earth Gravity button. Or, right-click the Study object in the tree and select Impose Conditions>Earth Gravity.
  2. Keep the All bodies Scoping Method, or choose the Geometry Selection and scope the geometric entities from Graphics window.
  3. Define the Earth Gravity magnitude on X, Y, and Z directions.
"},{"location":"welsim/users/bcs/#properties-view_24","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#earth-gravity-example","title":"Earth gravity example","text":"

The Earth Gravity body condition is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#body-force","title":"Body force","text":"

The body force condition defines a linear force acting structure bodies. This body condition is available for all structural analysis. The contribution of body force to the governing equation can be seen at Infinitesimal deformation linear elasticity static analysis.

"},{"location":"welsim/users/bcs/#body-condition-application_2","title":"Body condition application","text":"

To apply Body Force:

  1. On the menu or toolbar of the Structural, click Body Force button. Or, right-click the Study object in the tree and select Impose Conditions>Body Force.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Body Force magnitude on X, Y, and Z directions.
"},{"location":"welsim/users/bcs/#properties-view_25","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#body-force-example","title":"Body force example","text":"

The Body Force is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#rotational-velocity","title":"Rotational velocity","text":"

The Rotational Velocity condition determines the centrifugal force generated from a part spinning at a constant rate. This body condition is available for all structural analysis.

"},{"location":"welsim/users/bcs/#body-condition-application_3","title":"Body condition application","text":"

To apply Rotational Velocity:

  1. On the menu or toolbar of the Structural, click Rotational Velocity button. Or, right-click the Study object in the tree and select Impose Conditions>Rotational Velocity.
  2. Keep the All bodies Scoping Method, or choose the Geometry Selection and scope the geometric entities from Graphics window.
  3. Define the coefficients of Angular Velocity, Rotating Axis.
"},{"location":"welsim/users/bcs/#properties-view_26","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#rotational-velocity-example","title":"Rotational velocity example","text":"

The Rotational Velocity is applied as shown in Figure\u00a0below.

"},{"location":"welsim/users/bcs/#internal-heat-generation","title":"Internal heat generation","text":"

The Internal Heat Generation condition determines the heat flow generated from the body. This body condition is available for all thermal analysis.

"},{"location":"welsim/users/bcs/#internal-heat-generation-application","title":"Internal heat generation application","text":"

To apply Internal Heat Generation:

  1. On the menu or toolbar of the Thermal, click Internal Heat Generation button. Or, right-click the Study object in the tree and select Impose Conditions > Internal Heat Generation.
  2. Keep the All bodies Scoping Method, or choose the Geometry Selection and scope the geometric entities from Graphics window.
  3. Define the coefficients of Heat Flow value.
"},{"location":"welsim/users/bcs/#properties-view_27","title":"Properties view","text":"

The available settings in the Properties View are described below.

"},{"location":"welsim/users/bcs/#internal-heat-generation-example","title":"Internal heat generation example","text":"

The Internal Heat Generation is applied as shown in Figure below.

"},{"location":"welsim/users/connections/","title":"Setting connections","text":"

The Connections object acts as a group folder includes all connecting related settings, such as Contact Pair.

"},{"location":"welsim/users/connections/#connections-group","title":"Connections group","text":"

The Connections group is a unique container in WELSIM application for all types of connection objects. As illustrated in Figure\u00a0below, the Connections object includes multiple Contact Pair objects.

"},{"location":"welsim/users/connections/#contact-pairs","title":"Contact pairs","text":"

Contact Pairs are applied when two separate parts (solid, surface, and line bodies) in an assembly touch one another (they are mutually tangent). The contact bodies/surfaces:

As shown in Figure\u00a0below, the Contact for structure analysis support three types of contact: Bonded, Frictionless, and Frictional. For the Frictionless and Frictional types, the contact pairs (surfaces, edges) are free to separate and move away from one another, which is called to have status-changing nonlinearity. The stiffness matrice in the solving change dramatically as the parts are touching or separated.

"},{"location":"welsim/users/connections/#formulation-of-contact","title":"Formulation of contact","text":"

Since the contact algorithms are complicated, it is recommended to use the default formulation method for your contact analysis. This section describes the theory of contact formulations: Lagrange and Augmented Lagrange methods. Those methods only exist in the structural analysis.

"},{"location":"welsim/users/connections/#bonded","title":"Bonded","text":"

For the Non-Separated Bonded contact, the MPC algorithm is applied internally to add constraint equations to the tied nodes on the contact entities (surfaces, edges). The bonded contact has no penetration, no separation behaviors during the motion.

"},{"location":"welsim/users/connections/#lagrange-method","title":"Lagrange method","text":"

This formulation adds an extra contact pressure term to satisfy the contact compatibility. Thus the contact force is solved explicitly as an unknown degree of freedom.

"},{"location":"welsim/users/connections/#augmented-lagrange-method","title":"Augmented lagrange method","text":"

Augmented Lagrange method is a penalty-based contact formulation. The finite contact force is

\\[ F_{Normal}=k_{Normal}x_{Penetration}+\\lambda \\]

where \\(k_{Normal}\\) is the contact stiffness, \\(x_{Penetration}\\) is the penetration depth along the normal direction. The smaller the penetration depth, the more accurate numerical solutions. The exist of term \\(\\lambda\\) is the difference between the traditional penalty method and the augmented Lagrange method.

"},{"location":"welsim/users/connections/#contact-settings","title":"Contact settings","text":"

When you select a Contact Pair object in the tree, the contact settings become available in the Properties view. The Target Geometry and Master Geometry properties allow you to scope the contact pairs from the Graphics window. Note that the valid Target and Master Geometries show in different colors. You can change the highlight color in the Display tab of the contact Properties View.

When you choose the Frictionless or Frictional option in the Contact Type property, the following properties shows:

"},{"location":"welsim/users/connections/#supported-contact-types","title":"Supported contact types","text":"

The Table below identifies the supported formulations for the various contact geometries.

Contact Geometry Face (Master) Edge (Master) Vertex (Master) Face (Target) Yes Yes Not Supported for solving Edge (Target) Yes Yes Not Supported for solving Vertex (Target) Not Supported for solving Not Supported for solving Not Supported for solving"},{"location":"welsim/users/connections/#ease-of-use-contact","title":"Ease of use contact","text":""},{"location":"welsim/users/connections/#flipping-master-and-target-scoping-geometries","title":"Flipping master and target scoping geometries","text":"

This feature provides you a command to quickly swap master and target geometries that are already scoped in the Properties View. You can achieve this by right clicking on the specific Contact Pair, and choosing Switch Target/Master Contacts from the context menu as shown in Figure\u00a0below.

Note

This feature is not applicable to Face to Edge contact where faces and edges are always designated as targets and masters, respectively.

"},{"location":"welsim/users/geometry/","title":"Specifying geometry","text":""},{"location":"welsim/users/geometry/#geometry-fundamentals","title":"Geometry fundamentals","text":"

Part is the fundamental object carries the geometry data. An assembly model may contain one or multiple parts. There is no limit of parts in WELSIM application, and large assemblie require more hardware resources to process the geometric operations. All parts object are grouped in the Geometry Group object.

"},{"location":"welsim/users/geometry/#working-with-parts","title":"Working with parts","text":"

The part has these attributes:

"},{"location":"welsim/users/geometry/#color-scheme-of-parts","title":"Color scheme of parts","text":"

The geometry is assigned with predefined random color. However, you can define the color of part to visually identify different components in an assembly. Click the Display tab from the Properties view of the Part Object, and click the Color By property to determine the color scheme. The following lists the available color schemes:

You can reset the colors back to the default color scheme by right click on the Geometry object in the tree and selecting Reset Body Colors.

"},{"location":"welsim/users/geometry/#overview","title":"Overview","text":"

The WELSIM geometry module's interface is similar to that most other features. The graphical user interface of geometry commands is consist of three regions:

  1. Toolbars: Located at the top of the interface, there is a toolbar.
  2. Geometry Menu: Located at the Menu, the Geometry Menu provides all geometry related commands.
  3. Context Menu: Popped up at Geometry tree objects, the context menu provides geometry related commands as shown in Figure\u00a0below.

"},{"location":"welsim/users/geometry/#creating-primitive-geometry","title":"Creating primitive geometry","text":"

The system provides built-in commands to allow you to create primitive geometries. The following describes the supported geometries: Box, Cylinder, Plate, and Line.

"},{"location":"welsim/users/geometry/#box","title":"Box","text":"

An example of a created box shape is shown in Figure\u00a0[fig:ch3_guide_geom_box].

"},{"location":"welsim/users/geometry/#cylinder","title":"Cylinder","text":"

An example of a created cylinder shape is shown in Figure\u00a0[fig:ch3_guide_geom_cylinder].

"},{"location":"welsim/users/geometry/#plate","title":"Plate","text":"

An example of a created plate shape is shown in Figure\u00a0[fig:ch3_guide_geom_plate].

"},{"location":"welsim/users/geometry/#line","title":"Line","text":"

An example of a created Line shape is shown in Figure\u00a0[fig:ch3_guide_geom_line].

"},{"location":"welsim/users/geometry/#importing-and-exporting-geometry","title":"Importing and exporting geometry","text":""},{"location":"welsim/users/geometry/#importing","title":"Importing","text":"

The geometry importing feature supports the STEP and IGES format files, and the STEP file is recommended. The following lists the behaviors of importing geometry:

"},{"location":"welsim/users/geometry/#exporting","title":"Exporting","text":"

The geometries in the tree can be exported to an external STEP file. The following methods show you how to export:

"},{"location":"welsim/users/geometry/#boolean-operations","title":"Boolean operations","text":"

The WELSIM geometry module supports fundamental Boolean operations, which allow users to manipulate the shape of geometries. The available operations are Union, Intersection, and Difference. You can select multiple geometry objects from the tree list and press the Boolean commands to implement the operations. You can hold Ctrl or Shift keys to select multiple geometry objects from the project tree.

"},{"location":"welsim/users/geometry/#union","title":"Union","text":"

The union operation consolidates two or more geometry into one geometry. An example of Union geometry of a box and cylinder shape is shown in Figure\u00a0below.

"},{"location":"welsim/users/geometry/#intersection","title":"Intersection","text":"

The intersection operation keeps the commonly shared portions of two or more geometries. An example of Intersection geometry of a box and cylinder shape is shown in Figure\u00a0below.

"},{"location":"welsim/users/geometry/#difference","title":"Difference","text":"

The Difference operation subtracts the secondly selected geometry from the first selected geometry. Thus the selection order plays an important role in the final generated geometry. You can see the results of two different selection orders in Figures\u00a0below.

"},{"location":"welsim/users/geometry/#geometry-commands","title":"Geometry commands","text":"

In addition to the fundamental geometry commands, the following lists the commands that may be applied in the geometry modeling:

"},{"location":"welsim/users/geometry/#generate-solid","title":"Generate solid","text":"

In the most of analysis, the model needs to be solid to generate the 3D solid finite element. If the imported geometry only contains the surface data, the mesher cannot generate solid elements. In this scenario, you need to convert a surface geometry to solid geometry. The Generate Solid command provides you with a tool to complete this conversion.

To convert a surface to solid geometry, you can follow the steps below:

  1. Select the surface geometry objects from the tree.
  2. Click the Generate Solid command from the Geometry Menu, or right click on the selected geometry objects, and select the Generate Solid command from the context menu.
"},{"location":"welsim/users/geometry/#part-structure-types","title":"Part structure types","text":""},{"location":"welsim/users/geometry/#solid-bodies","title":"Solid bodies","text":"

The solid bodies including parts and assembly support all simulation features of WELSIM application.

"},{"location":"welsim/users/geometry/#surface-bodies","title":"Surface bodies","text":"

The surface bodies are treated as Shell structure in the structural and thermal analyses. In the Properties View of the Shell part, you need to specify the thickness of the shell, as shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/","title":"Application user interface","text":"

This section describes the fundamental components of the WELSIM application interface, their usage, and behaviors.

"},{"location":"welsim/users/gui/#welsim-application-window","title":"WELSIM application window","text":"

The functional components of the graphical user interface include the following as listed in Table\u00a0below.

Window Component Description Main Menus This menu includes all application level actions such as File and About Standard Toolbar This toolbar contains commonly used actions such as Mesh and Solve Graphics Toolbar This toolbar contains graphics related actions such as Zoom and Selection Project Explorer (Tree) Window This window contains a list of simulation objects that represents the modeling settings. Since it contains the branches and trunk, this windows is also called tree outline. The context menu for each object could vary. The object can be renamed, deleted, duplicated, copied and pasted Properties Window This window displays the properties of each object in the tree list. The user can view or edit the property values Graphics View This window shows and manipulates the visual content of the simulation entities. This window can display: 3D geometry, mesh, annotation, coordinate system symbol, spreadsheet, etc Output Window This window display the messages from the system or solvers Tabular Data Window This window lists the data that is input from user or output from the solvers. The listed data is always consistent with the curves in the Chart window Chart Window This window plots the graphics that is input from user or output from the solvers. The curves are always consistent with the table data in the Tabular Data window Context Menu This menu shows up as user right mouse button click on objects, graphics, toolbars, etc. Different entities may show different context Status Bar This widget shows the message and status on the bottom area of the application interface"},{"location":"welsim/users/gui/#windows-management","title":"Windows management","text":"

The WELSIM window owns panes that can carry project objects, properties, graphics, output, tabular data, and chart views.Window management functionalities enable you to dock, hide, show, move, and resize the windows.

"},{"location":"welsim/users/gui/#hiding-and-showing","title":"Hiding and showing","text":"

The windows can be hidden or shown by setting the view controller. As shown in Figure\u00a0[tab:ch3_guide_gui_windows], there are two ways to control the window views:

  1. Browse the View Menu > Windows, toggle the windows that you would show or hide.
  2. Right mouse button clicks on the Toolbar, you can toggle the windows.

You also can click the cross button on the title bar to hide the window.

"},{"location":"welsim/users/gui/#docking-and-undocking","title":"Docking and undocking","text":"

You can drag a window's title bar to move a window pane. Once you start to drag the window, the activated window is moving with your mouse. You can release the button on the target area to settle the new docking area. You can double-click a window's title bar to move it around the screen. The size of the window can be adjusted easily by dragging the borders or corners. You also can click the undocking button on the title bar to undock the window.

"},{"location":"welsim/users/gui/#moving-and-resizing","title":"Moving and resizing","text":"

You can drag a window's title bar to move and undock a window pane. Once you start to drag the window, the potential dock target area appears in the allowed space. At this moment, you can release the button to dock the window on the target area.

"},{"location":"welsim/users/gui/#main-windows","title":"Main windows","text":"

Besides the menu and toolbar widgets of the user interface, some other widgets are available. Those windows appear by default or when specific options are activated. The availability of those windows is controlled by the VIEW\u202f>\u202fWindows menu. This section discusses the following windows:

As the user selects a tree object in the Project Explorer window, all attributes for the selected object in Properties View, Tabular Data, and Chart Window are displayed or updated. The Properties window contains two tabs, and the Data tab shows the attributes about the object data, the Display tab lists the specifications about the graphics. The Graphics window shows the three-dimensional geometry model, depending on the tree object selection, shows information about the object details, highlighted areas, and annotations. The Output window displays the messages from the system or solvers. The Spreadsheet window shows the worksheet data for specific tree objects.

Those user interface components are described in the following sections:

"},{"location":"welsim/users/gui/#project-explorer","title":"Project explorer","text":"

The object Tree list represents the logical steps of the conducted simulation study. All branches relate to the parenting object. For instance, a key object called Study contains Study Settings and boundary condition objects. The user can right click on an object to activate a context menu that relates to the clicked object. The objects can be copied, pasted, duplicated, and renamed.

An example of the Project Explorer window is shown in Figure\u00a0below.

Note

The tree outline contains all elements that applied in the simulation study. The root object displays the number of projects in the solution. The Material project node includes all material specification. The FEM project contains the analysis settings, multiple FEM projects are allowed in the solution.

"},{"location":"welsim/users/gui/#knowing-the-tree-objects","title":"Knowing the tree objects","text":"

The tree objects in the Project Explorer window have the following conventions:

"},{"location":"welsim/users/gui/#object-status-symbols","title":"Object status symbols","text":"

The status icons are smaller than the tree object icon and located to the right bottom corner of the object icon. These symbols are intend to provide a quick visual reference to the status of the object. The details of the status symbols are described in Table\u00a0below.

Status Name Symbol Icon Description Underdefined A study object or its child objects requires user input values Error A fixed supported object may stop the simulation due to the confliction with other settings, user needs to resolve the confliction to continue the modeling OK A mesh settings object is well defined or any action about this object is succeed Suppressed An object is suppressed, such object becomes deactivated and won't participate the simulation. User can unsuppress the object Needs to be Updated An answers object or its child objects are not evaluated. Waiting for user to update"},{"location":"welsim/users/gui/#suppressingunsuppressing-objects","title":"Suppressing/Unsuppressing objects","text":"

Most of the objects in the Project Explorer window can be suppressed or unsuppressed by users. A suppressed object means that it is excluded from the further analysis. For example, suppressing a boundary condition excludes the boundary condition from the study and the further solutions. You also can unsuppress the object with the restored object attributes.

There are two ways to suppress/unsuppress an object:

"},{"location":"welsim/users/gui/#properties-view","title":"Properties view","text":"

The Properties View is located in the bottom left corner of the main user interface by default, and the user can change the location by dragging the window pane. This view window provides the user with details and information that relate to the selected object in the Project Explorer. Some properties are read-only that cannot be changed by the users, and some properties allow users to input values. An example of Properties View of the object is shown in Figures\u00a0below.

"},{"location":"welsim/users/gui/#features","title":"Features","text":"

The features of the Properties View include:

"},{"location":"welsim/users/gui/#group-property","title":"Group property","text":"

The Group Property is a read-only and occupy the entire row of the Properties pane, as shown in Figure below.

The group provides you better user experience by organizing the properties into distinct categories.

"},{"location":"welsim/users/gui/#undefined-or-invalid-properties","title":"Undefined or invalid properties","text":"

In the Properties View, the undefined or invalid fields are highlighted in yellow as shown in Figure\u00a0below.

Once the property is well defined and becomes valid, highlight yellow color disappears.

"},{"location":"welsim/users/gui/#drop-down-list","title":"Drop-down list","text":"

The combo property shows the drop-down list as user clicks the attribute as shown in Figure below.

Note

You can adjust the width of the columns by dragging the separator between the columns.

"},{"location":"welsim/users/gui/#text-entry","title":"Text entry","text":"

In the text entry field, you can input strings, numbers, or integers, depending on the type of the cell as shown in Figure\u00a0below.

The invalid value for the specific cell will be discarded, or the cell shows red background.

"},{"location":"welsim/users/gui/#geometry-selection","title":"Geometry selection","text":"

Geometry Selection allows users to scope topological entities from the graphics window. An example of Geometry Selection property is shown in Figure\u00a0below.

After selecting appropriate geometry entities, you can click the OK button to set the current selection into the field. Clicking the Cancel button does not change the pre-existing selection.

"},{"location":"welsim/users/gui/#graphics-window","title":"Graphics window","text":"

The Graphics window displays the geometry, annotation, mesh, result, etc. The components in the graphics window could be:

An example view of the Grpahics window is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#tabular-data-window","title":"Tabular data window","text":"

Tabular Data window is designed in better reviewing the input and output data. When you select the following objects in the tree window, both Tabular Data and Chart windows display data on the interface.

The listed data in Tabular Data window is consistent with the curves in the Chart window. As an example shown in Figure below, you can see the maximum and minimum values at all time steps are consistent between those two windows.

"},{"location":"welsim/users/gui/#chart-window","title":"Chart window","text":"

The Chart window displays the curves for the selected tree object. The curves are consistent with the data in the Tabular Data window. An example of Chart window drawing the maximum and minimum values along time is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#spreadsheet-window","title":"Spreadsheet window","text":"

The spreadsheet window provides object data in the form of tables, charts, or text to you. This widget usually contains the summarized data for a collection of properties. Note that not all objects contain a spreadsheet window, only the object that has large data may own a spreadsheet window. The behaviors of the spreadsheet window are:

  1. A spreadsheet designed to show large data on one field does not automatically display the data. You can open the spreadsheet window by double-clicking specific objects, such as Material and Study Setting objects.
  2. A new tab shows up as the spreadsheet window is open. You can close the window by clicking the cross button on the tab, or by pressing the OK button on the spreadsheet.

An example of the spreadsheet window is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#output-window","title":"Output window","text":"

The output window prompts you with feedback concerning the results of your actions in using WELSIM. In the current version, the output window mainly displays the message from the solvers. An example of output window displaying the solver messages is shown in Figure\u00a0below.

The Output window pane contains several buttons, there are:

"},{"location":"welsim/users/gui/#main-menus","title":"Main menus","text":"

The main menus contain the following items as shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#file-menu","title":"File menu","text":"

The FILE menu includes the following actions:

The items of the File menu is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#view-menu","title":"View menu","text":"

The VIEW menu includes the following actions:

The items of the View menu is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#material-menu","title":"Material menu","text":"

The MATERIAL menu includes the following actions:

The items of the Material Menu is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#geometry-menu","title":"Geometry menu","text":"

The GEOMETRY menu includes the following actions:

The items of the Geometry Menu is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#fem-menu","title":"FEM menu","text":"

The FEM Menu includes the following actions:

The items of the FEM Menu is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#structural-menu","title":"Structural menu","text":"

The STRUCTURAL menu includes the following actions:

The items of the Structural menu is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#thermal-menu","title":"Thermal menu","text":"

The THERMAL menu includes the following actions:

The items on the Thermal menu is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#electromagnetic-menu","title":"Electromagnetic menu","text":"

The ELECTROMAGNETIC menu includes the following actions:

The items of the Electromagnetic menu is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#tools-menu","title":"Tools menu","text":"

The TOOLS menu includes the following actions:

The items of the Tools menu is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#help-menu","title":"Help menu","text":"

The HELP menu includes the following actions:

The items of the Help menu is shown in Figure\u00a0below.

"},{"location":"welsim/users/gui/#toolbars","title":"Toolbars","text":"

Toolbars are displayed across the top of the main user interface. Toolbars are dockable, and you can drag the toolbar to your preferred field.

"},{"location":"welsim/users/gui/#file-toolbar","title":"File toolbar","text":"

The File toolbar contains application-level commands as shown in Figure\u00a0below. Each icon button and its description follows:

"},{"location":"welsim/users/gui/#material-toolbar","title":"Material toolbar","text":"

The Material toolbar contains material-related simulation commands as shown in Figure\u00a0below. Each icon button and its description follows:

"},{"location":"welsim/users/gui/#geometry-toolbar","title":"Geometry toolbar","text":"

The Geometry toolbar contains geometry-related commands as shown in Figure below. Each icon button and its description follows:

"},{"location":"welsim/users/gui/#fem-toolbar","title":"FEM toolbar","text":"

The FEM toolbar contains finite element analysis commands as shown in Figure\u00a0below. Each icon button and its description follows:

"},{"location":"welsim/users/gui/#structural-toolbar","title":"Structural toolbar","text":"

The Structural toolbar contains structural analysis commands as shown in Figure\u00a0below. Each icon button and its description follows:

"},{"location":"welsim/users/gui/#thermal-toolbar","title":"Thermal toolbar","text":"

The Thermal toolbar contains thermal analysis commands as shown in Figure\u00a0below. Each icon button and its description follows:

"},{"location":"welsim/users/gui/#electromagnetic-toolbar","title":"Electromagnetic toolbar","text":"

The Electromagnetic toolbar contains electric and magnetic analyses commands as shown in Figure\u00a0below. Each icon button and its description follows:

"},{"location":"welsim/users/gui/#tool-toolbar","title":"Tool toolbar","text":"

The Tool toolbar contains assistance commands as shown in Figure below. Each icon button and its description follows:

To be added ...\n
"},{"location":"welsim/users/gui/#help-toolbar","title":"Help toolbar","text":"

The Help toolbar contains assistance commands as shown in Figure\u00a0below. Each icon button and its description follows:

"},{"location":"welsim/users/gui/#graphics-toolbar","title":"Graphics toolbar","text":"

The Graphics toolbar contains graphical operation commands as shown in Figure\u00a0below. Each icon button and its description follows:

"},{"location":"welsim/users/gui/#working-with-graphics","title":"Working with graphics","text":"

The following lists the tips for working with WELSIM graphics:

"},{"location":"welsim/users/gui/#preselecting-geometry","title":"PreSelecting geometry","text":"

This section discusses the pre-selection features in the Graphics window.

"},{"location":"welsim/users/gui/#highlighting","title":"Highlighting","text":"

As you hover the cursor over a geometry entity, the graphics highlights the selection and shows the location of the pointer. The pre-selection is controlled by the selection filter, and only the allowed entity types can be pre-selected and highlighted.

As shown in Figure\u00a0below, the face are highlighted in green color at pre-selection mode.

"},{"location":"welsim/users/gui/#selecting-geometry","title":"Selecting geometry","text":"

This section discusses how to select and pick geometry in the Graphics window.

"},{"location":"welsim/users/gui/#picking","title":"Picking","text":"

You can pick visible geometries by left clicking on the entities. A valid picking sets the geometry selection property for specific objects, such as boundary conditions.

You can hold the Ctrl or Shift key down to add or remove multiple selections from the current selections. A pick in the free space clears the current selection.

"},{"location":"welsim/users/gui/#selection-filters","title":"Selection filters","text":"

The selection filters control the user selection mode and provide an easy interface for users to pick or select the geometry entities. A pressed button in the selection filter toolbar denotes a selectable geometry type. The following describes the filters.

"},{"location":"welsim/users/gui/#controlling-graphical-view","title":"Controlling graphical view","text":"

The section describes the controlling and manipulating the graphical view with mouse and keys.

"},{"location":"welsim/users/gui/#view-annotations","title":"View annotations","text":"

Graphics window may contain these types of annotations:

"},{"location":"welsim/users/objects/","title":"Objects reference","text":"

This reference provides a specification for the objects in the tree.

"},{"location":"welsim/users/objects/#answers","title":"Answers","text":"

The Answers object customizes the solution properties and contains all result-level objects. The Properties View of the Answers object is shown in Figure\u00a0below.

"},{"location":"welsim/users/objects/#tree-dependencies","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options","title":"Insertion options","text":"

Appears by default when you create a new FEM project.

"},{"location":"welsim/users/objects/#object-properties","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Solver Method A drop-down field allows you to select a solver from the options: CG(Conjugate Gradient), BiCGStab, GMRES, GPBiCG, MUMPS, Direct, DIRECTmkl, where MUMPS, Direct, and DIRECTmkl are direct solvers, and the rest are iterative solvers. The default solver is MUMPS Number of Iterations A number field defines the maximum number of the linear algebra solver iterations. The default is 10000 Residual Threshold A number field defines the residual threshold for the linear algebra solver. The default is 1e-7 Output Time Log A Boolean field outputs the log for each time step. The default is False Output Iteration Log A Boolean field outputs the log each iteration step. The default is False Generate Result Files A Boolean field generates ASCII format result file. The default is False Output Frequency A number field determines the frequency of the result data output. The default value is 1, which outputs result data every step."},{"location":"welsim/users/objects/#body-conditions","title":"Body conditions","text":"

Body condition type objects enable you to impose the body condition onto the geometry bodies.

"},{"location":"welsim/users/objects/#application-objects","title":"Application objects","text":"

Body Force, Acceleration, Earth Gravity, Rotational Velocity

"},{"location":"welsim/users/objects/#tree-dependencies_1","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_1","title":"Insertion options","text":"

You can use any of the following methods to insert body conditions:

"},{"location":"welsim/users/objects/#object-properties_1","title":"Object properties","text":"

The properties may vary for different body conditions. See the Setting Up Boundary Conditions section for more information about body conditions.

"},{"location":"welsim/users/objects/#boundary-conditions","title":"Boundary conditions","text":"

Boundary condition type objects enable you to impose the boundary condition onto the geometry entities, such as faces, edges, and vertices.

"},{"location":"welsim/users/objects/#application-objects_1","title":"Application objects","text":"

Displacement, Fixed Support, Fixed Rotation, Pressure, Force, Velocity, Acceleration, Temperature, Heat Flux, Convection, Radiation, Voltage, Ground, Symmetry, Zero Charge, Surface Charge Density, Electric Displacement, Insulating, Magnetic Potential, Magnetic Flux Density

"},{"location":"welsim/users/objects/#tree-dependencies_2","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_2","title":"Insertion options","text":"

You can use any of the following methods to insert boundary condition:

"},{"location":"welsim/users/objects/#object-properties_2","title":"Object properties","text":"

The properties may vary for different body conditions. See the Setting up Boundary Conditions section for more information about Boundary Conditions.

"},{"location":"welsim/users/objects/#box","title":"Box","text":"

The Box object defines a shape that is generated by the built-in modeler. An example of Box object and properties are illustrated in Figure\u00a0below.

"},{"location":"welsim/users/objects/#tree-dependencies_3","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_3","title":"Insertion options","text":"

Appears when you create a box shape. You can use any of the following methods to insert a Box:

"},{"location":"welsim/users/objects/#object-properties_3","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Suppressed Include (False - default) or exclude (True) the geometry from the analysis Length A vector component field to determine the length, width, and height of the box. The default value is 10 Origin A vector component field to determine the location of origin. The default vector is 0 Material A drop-down field to assign the material for the selected part. The available material candidates are defined in the Material Project Source A read-only field indicates the shape is generated internally"},{"location":"welsim/users/objects/#connections","title":"Connections","text":"

The Connections object is a group-type object that may contain the connection objects between two or more parts. The currently supported children object types are Contact Pair.

"},{"location":"welsim/users/objects/#tree-dependencies_4","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_4","title":"Insertion options","text":"

Connections object is automatically inserted as you add a contact pair object to the tree.

"},{"location":"welsim/users/objects/#object-properties_4","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Suppressed A Boolean field to include (False - Default) or exclude (True) the object in the analysis"},{"location":"welsim/users/objects/#contact-pair","title":"Contact pair","text":"

This object defines a contact pair between parts.

"},{"location":"welsim/users/objects/#tree-dependencies_5","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_5","title":"Insertion options","text":"

You can use any of the following methods to insert contact pairs:

"},{"location":"welsim/users/objects/#object-properties_5","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Suppressed A Boolean field to include (False - Default) or exclude (True) the object in the analysis Master Geometry A Geometry Selection field to scope geometry entities, such as faces, edges Target Geometry A Geometry Selection field to scope geometry entities, such as faces, edges Contact Type A drop-down enumeration field to select a type from three options: Bonded, Frictionless, and Frictional Formulation A drop-down enumeration field to selection contact formulation from two options: Lagrange and Augmented Lagrange. This property is only available for Frictionless or Frictional contact type Finite Sliding A Boolean field to turn on (True) or off (False - default) the finite sliding algorithm. This property is only available for Frictionless or Frictional contact type Normal Direction Tolerance A number field to determine the distance tolerance in the normal direction. The default value is 1e-5 Tangential Direction Tolerance A number field to determine the distance tolerance in the tangential direction. The default value is 1e-5 Normal Direction Penalty A number field to determine the penalty value in the normal direction. The default value is 1e3 Tangential Direction Penalty A number field to determine the penalty value in the tangential direction. The default value is 1e3"},{"location":"welsim/users/objects/#cylinder","title":"Cylinder","text":"

The Cylinder object defines a shape that is generated by the built-in modeler. An example of Cylinder object and properties are illustrated in Figure\u00a0below.

"},{"location":"welsim/users/objects/#tree-dependencies_6","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_6","title":"Insertion options","text":"

Appears when you create a Cylinder shape. You can use any of the following methods to insert a Cylinder:

"},{"location":"welsim/users/objects/#object-properties_6","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Suppressed Include (False - default) or exclude (True) the geometry from the analysis Normal A vector component field to determine the direction of the cylinder. The default value is (0,0,1) Radius A number component field to determine the radius of the cylinder base. The default value is 10 Height A number component field to determine the height of the cylinder. The default value is 30 Angle A number component field to determine the sweeping angle of the cylinder circle. The default value 360 gives a full cylinder Origin A vector component field to determine the location of origin. The default vector is 0 Material A drop-down field to assign the material for the selected part. The available material candidates are defined in the Material Project Source A read-only field indicates the shape is generated internally"},{"location":"welsim/users/objects/#fem-project","title":"FEM project","text":"

The FEM Project object represents an independent analysis, which contains Geometry, Mesh, Study, and Answers objects. The Connections object is not created until you add a contact pair object. An example of FEM Project and properties are illustrated in Figure\u00a0[fig:ch3_guide_obj_fem_proj].

"},{"location":"welsim/users/objects/#tree-dependencies_7","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_7","title":"Insertion options","text":"

Appears by default when you create a new FEM project.

"},{"location":"welsim/users/objects/#object-properties_7","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Numerical Method A read-only field to indicate the Finite Element Method applied in this project Dimension A read-only field to indicate a 3D analysis of this project Physics Type A drop-down enumeration field for you to select the physics type. The available options are Structural, Thermal, and Electromagnetic. The default is Structural. Note that change this property may change the validation of existing objects and display of object's properties Analysis Type A drop-down enumeration field for you to select the analysis type. Depending on the Physics Type, the available options vary. For the Structural analysis, the options are Static, Transient, and Modal. For the Thermal analysis, the options are Steady-State and Transient. For the Electromagnetic analysis, the options are ElectroStatic and MagnetoStatic Ambient Temperature A number field to determine the environment temperature for the analysis, the default value is 22.3"},{"location":"welsim/users/objects/#geometry-group","title":"Geometry group","text":"

Geometry Group object contains the geometries in the form of a part or assembly. All imported and created geometries are included in this group-level object as shown in Figure\u00a0below.

"},{"location":"welsim/users/objects/#tree-dependencies_8","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_8","title":"Insertion options","text":"

Appears by default when you create a new FEM project.

"},{"location":"welsim/users/objects/#object-properties_8","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name"},{"location":"welsim/users/objects/#initial-temperature","title":"Initial temperature","text":"

Initial Temperature defines the temperature status at the beginning of the simulation for transient thermal analysis. An example of Initial Temperature and its properties are shown in Figure\u00a0below.

"},{"location":"welsim/users/objects/#tree-dependencies_9","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_9","title":"Insertion options","text":"

You can use any of the following methods to insert initial temperature:

Note

Inserting initial condition command is only applicable when the Physics Type and Analysis Type properties of FEM Project object are Thermal and Transient, respectively.

"},{"location":"welsim/users/objects/#object-properties_9","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Suppressed A Boolean field to include (False - Default) or exclude (True) the object in the analysis Scoping Method A read-only field shows All Initial Temperature A number field to define the temperature value. The default is 22.3"},{"location":"welsim/users/objects/#line","title":"Line","text":"

The Line object defines a shape that is generated by the built-in modeler. An example of Line object and properties are illustrated in Figure\u00a0below.

"},{"location":"welsim/users/objects/#tree-dependencies_10","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_10","title":"Insertion options","text":"

Appears when you create a line shape. You can use any of the following methods to insert a Line:

"},{"location":"welsim/users/objects/#object-properties_10","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Suppressed Include (False - default) or exclude (True) the geometry from the analysis Start Point A vector component field to determine one point of a line. The default value is 0 End Point A vector component field to determine another point of a line. The default value is (10, 10, 0) Material A drop-down field to assign the material for the selected part. The available material candidates are defined in the Material Project Source A read-only field indicates the shape is generated internally"},{"location":"welsim/users/objects/#material","title":"Material","text":"

A Material object defines a material data using the associated properties and spreadsheet data. You can define multiple material objects in the WELSIM application. An example of a Material object and its properties and spreadsheet are shown in Figure\u00a0below.

"},{"location":"welsim/users/objects/#tree-dependencies_11","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_11","title":"Insertion options","text":"

You can use any of the following methods to insert material:

"},{"location":"welsim/users/objects/#object-properties_11","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Suppressed A Boolean field to include (False - Default) or exclude (True) the object in the analysis"},{"location":"welsim/users/objects/#spreadsheet","title":"Spreadsheet","text":"

The Material object is able to display the Spreadsheet window, which provides a friendly user interface for defining all material properties as shown in Figure\u00a0below. You can double click or right click on the Material object and select the Edit command to display the spreadsheet window.

"},{"location":"welsim/users/objects/#material-project","title":"Material project","text":"

The Material Project object holds all material definition objects.

"},{"location":"welsim/users/objects/#tree-dependencies_12","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_12","title":"Insertion options","text":"

Appears by default when you create a new FEM project.

"},{"location":"welsim/users/objects/#object-properties_12","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name"},{"location":"welsim/users/objects/#mesh-group","title":"Mesh group","text":"

Mesh Group manages all meshing features and tools for the project. An example of mesh object and properties is shown in Figure\u00a0below.

"},{"location":"welsim/users/objects/#tree-dependencies_13","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_13","title":"Insertion options","text":"

Appears by default when you create a new FEM project.

"},{"location":"welsim/users/objects/#object-properties_13","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Number of Nodes A read-only output field to show the number of generated nodes. The value is automatically updated as the mesh is completed Number of Elements A read-only output field to show the number of generated elements. The value is automatically updated as the mesh is completed Number of Tetrahedrons A read-only output field to show the number of generated tetrahedrons. The value is automatically updated as the mesh is completed Number of Triangles A read-only output field to show the number of generated triangles. The value is automatically updated as the mesh is completed"},{"location":"welsim/users/objects/#mesh-method","title":"Mesh method","text":"

In the multi-body analysis, different parts may need different mesh density due to the various sizes of geometries. Mesh Method object helps you fine tuning the mesh for the specifically scoped geometries. An example of Mesh Method object is shown in Figure\u00a0below.

"},{"location":"welsim/users/objects/#tree-dependencies_14","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_14","title":"Insertion options","text":"

You can use any of the following methods to insert Mesh Method:

"},{"location":"welsim/users/objects/#object-properties_14","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Scoping Method A read-only field indicates the scoping method Geometry A geometry selection field to scope the geometry entities (volume/body only) Maximum Size A number field determines the maximum size of the generated finite element Quadratic A read-only field to show the order of the generated element. This property is determined by the Quadratic property in the global Mesh Settings object Mesh Density A drop-down enumeration field to determine the mesh density for the scoped geometries. The options are Very Coarse, Coarse, Regular, Fine, Very Fine, and User Defined. The default is Regular. If you select User Defined, additional properties Growth Rate, Segments per Edge, and Segments per Radius are shown Growth Rate A number field determines the change of mesh density in spatial. The default value is 0.3 Segments per Edge A number field determines the number of element segments per edge. The default value is 1. The higher value, the more dense mesh Segments per Radius A number field determines the number of element segments per radius. The default value is 2. The higher value, the more dense mesh Number of Nodes A read-only output field to show the number of generated nodes. The value is updated as the mesh is completed Number of Elements A read-only output field to show the number of generated elements. The value is updated as the mesh is completed Number of Tetrahedrons A read-only output field to show the number of generated tetrahedrons. The value is updated as the mesh is completed Number of Triangles A read-only output field to show the number of generated triangles. The value is updated as the mesh is completed"},{"location":"welsim/users/objects/#mesh-settings","title":"Mesh settings","text":"

The Mesh Settings object is a global setting for the meshing operations. You change the global mesh settings by tuning the properties of this object. An example of Mesh Settings object is shown in Figure\u00a0[fig:ch3_guide_obj_mesh_settings].

"},{"location":"welsim/users/objects/#tree-dependencies_15","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_15","title":"Insertion options","text":"

Appears by default when you create a new FEM project.

"},{"location":"welsim/users/objects/#object-properties_15","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Maximum Size A number field to determine the maximum size of the generated finite element Quadratic A Boolean field to determine the linear element (False) or bilinear element (True) Mesh Density A drop-down enumeration field to determine the mesh density for the scoped geometries. The options are Very Coarse, Coarse, Regular, Fine, Very Fine, and User Defined. The default is Regular. If you select User Defined, additional properties Growth Rate, Segments per Edge, and Segments per Radius are shown Growth Rate A number field indicate the change of mesh density in spatial. The default value is 0.3 Segments per Edge A number field indicate the element segment per edge. The default value is 1. The higher value, the more dense mesh Segments per Radius A number field indicate the element segment per radius. The default value is 2. The higher value, the more dense mesh"},{"location":"welsim/users/objects/#part","title":"Part","text":"

The Part object defines a component of the geometry that is imported from an external CAD file. An example of Part object and properties are illustrated in Figure\u00a0[fig:ch3_guide_obj_part].

"},{"location":"welsim/users/objects/#tree-dependencies_16","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_16","title":"Insertion options","text":"

Appears when you import geometry from external files. You can use any of the following methods to insert Part:

"},{"location":"welsim/users/objects/#object-properties_16","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Suppressed Include (False - default) or exclude (True) the part from the analysis Scale A number field to manipulate the size of the imported geometry. The default value is 1 Origin A vector component field to determine the location of origin. The default vector is 0 Material A drop-down field to assign the material for the selected part. The available material candidates are defined in the Material Project Structure Type A drop-down field to define the structure type. The available options are Solid, Shell, Beam, and Truss. The default is Solid Source A read-only field indicates the name of the imported geometry file"},{"location":"welsim/users/objects/#plate","title":"Plate","text":"

The Plate object defines a shape that is generated by the built-in modeler. An example of Plate object and properties are illustrated in Figure\u00a0[fig:ch3_guide_obj_part].

"},{"location":"welsim/users/objects/#tree-dependencies_17","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_17","title":"Insertion options","text":"

Appears when you create a plate shape. You can use any of the following methods to insert a Plate:

"},{"location":"welsim/users/objects/#object-properties_17","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Suppressed Include (False - default) or exclude (True) the geometry from the analysis Length A vector component field to determine the length vector of the plate. The default value is (10, 0, 0) Width A vector component field to determine the width vector from the origin. The default vector is (0, 5, 0) Material A drop-down field to assign the material for the selected part. The available material candidates are defined in the Material Project Thickness A number field to determine the thickness of the plate. The default value is 0.01 Source A read-only field indicates the shape is generated internally"},{"location":"welsim/users/objects/#results","title":"Results","text":"

The Result objects define the simulation output for displaying and analyzing the results from a solution.

"},{"location":"welsim/users/objects/#application-objects_2","title":"Application objects","text":"

Deformation, Stress, Strain, Acceleration, Velocity, Rotation, Reaction Force, Reaction Moment, Temperature, Voltage, Electric Field, Electric Displacement, Electromagnetic Energy Density, Magnetic Potential, Magnetic Flux Density, Magnetic Field, User-Defined Result.

"},{"location":"welsim/users/objects/#tree-dependencies_18","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_18","title":"Insertion options","text":"

Appears by default when you start the WELSIM application.

"},{"location":"welsim/users/objects/#object-properties_18","title":"Object properties","text":"

The properties may vary for different result types. The following lists the properties that may be shown for the most of Result objects. See the Using results section for more information.

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Suppressed Include (False - default) or exclude (True) the result object from the analysis Result By Determines the result loading type Set Number Determines the set number to retrieve the result data Maximum Value The maximum result value at the current step Minimum Value The minimum result value at the current step"},{"location":"welsim/users/objects/#solution","title":"Solution","text":"

The Solution object acts as a root object in the WELSIM application. Only one Solution can exist per simulation session, and one solution can contain multiple FEM projects.

"},{"location":"welsim/users/objects/#tree-dependencies_19","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_19","title":"Insertion options","text":"

Appears by default when you create a new FEM project.

"},{"location":"welsim/users/objects/#study","title":"Study","text":"

The Study object holds all analysis related objects such as Study Settings, Boundary Conditions, Body Conditions, and Initial Conditions. An example of Study object is shown in Figure\u00a0[fig:ch3_guide_obj_study].

"},{"location":"welsim/users/objects/#tree-dependencies_20","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_20","title":"Insertion options","text":"

Appears by default when you create a new FEM project.

"},{"location":"welsim/users/objects/#object-properties_19","title":"Object properties","text":"

The Properties View for this object include the following:

Property Name Description ID A read-only field denotes the ID of this object Class Label A read-only field denotes the class name Number of Steps A number field to determine the total number of steps. The default value is 1. The input value must be positive Current Step A number field to determine the current step for the successive settings. The default value is 1. The input value must be less than or equal to the Number of Steps. Note that Current Step property of Study object is adjustable, and determines the Current Step properties in other objects such as Study Settings, and Boundary Conditions Current End Time a number field to determine the end time of the current step. The value must be larger than that of the last step"},{"location":"welsim/users/objects/#study-settings","title":"Study Settings","text":"

The Study Settings object allows you to define analysis and solving settings to customize a specific simulation model. An example of Study Settings object is shown in Figure\u00a0[fig:ch3_guide_obj_study_settings].

"},{"location":"welsim/users/objects/#tree-dependencies_21","title":"Tree dependencies","text":""},{"location":"welsim/users/objects/#insertion-options_21","title":"Insertion options","text":"

Appears by default when you create a new FEM project.

"},{"location":"welsim/users/objects/#object-properties_20","title":"Object properties","text":"

The properties of Study Settings vary for different Physics and Analysis types. The following lists the available properties according to Analysis Type:

"},{"location":"welsim/users/objects/#spreadsheet_1","title":"Spreadsheet","text":"

The Study Settings object can display the Spreadsheet window, which provides a friendly user interface to review properties at all steps as shown in Figure\u00a0[fig:ch3_guide_obj_study_settings]. You can double click or right click on the Study Settings object and select the Edit command to display the Spreadsheet window.

"},{"location":"welsim/users/overview/","title":"Overview","text":"

This chapter is the user guide for working with WELSIM application, which is used to perform various types of structural, thermal, and electromagnetic analyses. The entire simulation process is tied together by a unified graphical user interface.

"},{"location":"welsim/users/overview/#overview","title":"Overview","text":"

WELSIM application enables you to investigate design alternative efficiently. You can modify any aspect of analysis or vary parameters, then update the project to the see results of the change in the modeling. A typical modeling process is composed of defining the model, and boundary conditions applied to it, computing for the simulation's response to the conditions, then evaluating the solutions with a variety of tools.

The WELSIM software application has a tree structure that consists of \u201cobjects\u201d that enable you to define simulation conditions. By clicking the objects, you activate the associated properties in the property window, and you can use the corresponding command and tools to conduct the simulation study. The following sections describe in details to use the WELSIM to set up and implement simulation studies.

"},{"location":"welsim/users/results/","title":"Using results","text":"

This section describes the details of a result. The help for Results is classified by the physics and analysis types.

"},{"location":"welsim/users/results/#introduction-to-the-results","title":"Introduction to the results","text":"

You can generate results to understand the behaviors of the analyzed model. The advantages of using results in WELSIM application are:

"},{"location":"welsim/users/results/#result-application","title":"Result application","text":"

Applying results can be achieved by

"},{"location":"welsim/users/results/#result-definitions","title":"Result definitions","text":"

This section describes the fundamental features in result definitions.

"},{"location":"welsim/users/results/#result-controller","title":"Result controller","text":"

In the multi-step or transient analysis, the solution contains result data at various steps. Result By property provides a controller to select the desired step data to display. You can determine to show the result by Set Number or Time/Frequency. The default is by Set Number. Additional properties such as Set Number, Time, or Frequency shows up as you define the Result By property.

"},{"location":"welsim/users/results/#clear-generated-data","title":"Clear generated data","text":"

You can clear results data from the database using the Clear Result command from the Toolbar, Menu, or the right-click context menu on a result object.

You also can clear entire solution data from the database using the Clear Calculated Data command from the Toolbar, Menu, or the right-click context menu on an Answers object. These two commands from the context menu are shown in Figure\u00a0[fig:ch3_guide_rst_clear_data].

"},{"location":"welsim/users/results/#display-controller","title":"Display controller","text":"

You can select the Graphics tab on the result Properties View pane. As shown in Figure\u00a0[fig:ch3_guide_rst_display_prop], the following properties are available to adjust the contour display:

"},{"location":"welsim/users/results/#structural-results","title":"Structural results","text":"

The following structural results are described in this section.

"},{"location":"welsim/users/results/#deformation","title":"Deformation","text":"

Physical deformation of the modeling geometries can be calculated and plotted in the form of contour. This result is available for all structural analysis. The following gives the properties of result object:

"},{"location":"welsim/users/results/#stress","title":"Stress","text":"

The stress quantities provide mechanical insights to the given model and material of a part or an assembly under a specific structural loading environment. A general 3D stress state contains three normal and three shear stresses. The stress quantities in WELSIM application are the nodal values and available for all structural analysis. The equivalent stress (also called von-Mises stress) is related to the principal stresses by the equation:

\\[ \\sigma_{VM}=\\left[\\dfrac{(\\sigma_{11}-\\sigma_{22})^{2}+(\\sigma_{22}-\\sigma_{33})^{2}+(\\sigma_{33}-\\sigma_{11})^{2}+6(\\sigma_{12}^{2}+\\sigma_{23}^{2}+\\sigma_{31}^{2})}{2}\\right]^{1/2} \\]

The following gives the properties of result object:

"},{"location":"welsim/users/results/#strain","title":"Strain","text":"

The strain quantities provide deformation insights to the given model and material of a part or an assembly under a specific structural loading environment. This result is available for all structural analysis.

The available properties for strain result are:

"},{"location":"welsim/users/results/#acceleration","title":"Acceleration","text":"

The acceleration quantities demonstrate the acceleration of the given model and material of a part or an assembly under a specific structural loading environment. This result is available for transient structural analysis.

The available properties for acceleration result are:

Note

Acceleration result is only available for the transient structural analysis.

"},{"location":"welsim/users/results/#velocity","title":"Velocity","text":"

The velocity quantities demonstrate the velocity of the given model and material of a part or an assembly under a specific structural loading environment. This result is available for transient structural analysis.

The available properties for velocity result are:

Note

Velocity result is only available for the transient structural analysis.

"},{"location":"welsim/users/results/#rotation","title":"Rotation","text":"

The rotation quantities demonstrate the rotation of the given model and material of a part or an assembly under a specific structural loading environment. This result is available for only shell structure.

The available properties for rotation result are:

Note

Rotation result is only available for the shell structural analysis.

"},{"location":"welsim/users/results/#reaction-force-probe","title":"Reaction Force Probe","text":"

The reaction force provides an insight to abstract reaction force of the given model and material of a part or an assembly under a specific structural loading environment. This result is available for structural analysis.

The available properties for a reaction force probe are:

Note

This probe result does not show contour on the geometry. The primary output data is the Maximum Value and Minimum Value displayed in the Properties View window.

"},{"location":"welsim/users/results/#reaction-moment-probe","title":"Reaction Moment Probe","text":"

The reaction moment provides an insight to abstract quantities of the given model and material of a part or an assembly under a specific structural loading environment. This result is available for only shell structure.

The available properties for reaction moment probe are:

Note

Reaction moment probe result is only available for the shell structural analysis.

Reaction moment probe result does not show contour on the geometry. The primary output data is the Maximum Value and Minimum Value displayed in the Properties View window.

"},{"location":"welsim/users/results/#thermal-results","title":"Thermal results","text":"

The following thermal results are described in this section:

"},{"location":"welsim/users/results/#temperature","title":"Temperature","text":"

The temperature, a scalar quantity, provides an insight to the temperature distribution throughout the structure. Temperature results can be displayed as a contour plot.

The available properties for temperature are:

"},{"location":"welsim/users/results/#electric-results","title":"Electric results","text":""},{"location":"welsim/users/results/#voltage","title":"Voltage","text":"

The voltage, a scalar quantity, provides an insight to the electric potential distribution throughout the conductor bodies.

The available properties for voltage are:

"},{"location":"welsim/users/results/#electric-field","title":"Electric Field","text":"

The electric field, a vector component quantity, provides an insight to the electric field intensity distribution throughout the bodies.

The available properties for Electric Field are:

"},{"location":"welsim/users/results/#current-density","title":"Current Density","text":""},{"location":"welsim/users/results/#electric-displacement","title":"Electric Displacement","text":"

The electric displacement, a vector component quantity, provides an insight to the electric displacement intensity distribution throughout the bodies. This quantity has the constitutive relation with Electric Field as shown in equation below:

\\[ D=\\epsilon E \\]

where D is the electric displacement, E is the electric field, and \\(\\epsilon\\) is the electric permittivity. The available properties for Electric Displacement are:

"},{"location":"welsim/users/results/#energy-density","title":"Energy Density","text":"

The energy density, a scalar quantity, provides an insight to the electromagnetic energy throughout the simulation bodies.

The available properties for energy density are:

"},{"location":"welsim/users/results/#magnetic-results","title":"Magnetic results","text":"

The magnetostatic analysis provides fundamental result quantities for you to investigate the field.

"},{"location":"welsim/users/results/#electric-potential","title":"Electric Potential","text":""},{"location":"welsim/users/results/#magnetic-potential","title":"Magnetic Potential","text":"

Magnetic Potential vector components are computed throughout the simulation domain. The available properties for Magnetic Potential are:

"},{"location":"welsim/users/results/#magnetic-flux-density","title":"Magnetic Flux Density","text":"

Magnetic Flux Density vector components are computed throughout the simulation domain. The available properties for Magnetic Flux Density are:

"},{"location":"welsim/users/results/#magnetic-field","title":"Magnetic Field","text":"

Magnetic Field vector components are computed throughout the simulation domain. The available properties for Magnetic Field are:

"},{"location":"welsim/users/results/#user-defined-results","title":"User-Defined Results","text":"

This section describes the use of the User-Defined Result feature in WELSIM application. The user-defined result provides you with more flexible result evaluation methods. In addition to the system-provided result types, the User-Defined Result allows you to plot more broad kinds of results with the given expression.

Like other result types that display contours, chart, and data, the User-Defined results:

Applying a User-Defined Result can be done using one of the following methods:

An example of User Defined Result properties view is shown in Figure\u00a0[fig:ch3_guide_user_defined_rst_prop].

"},{"location":"welsim/users/results/#user-defined-result-expressions","title":"User Defined Result expressions","text":"

The property Expression accepts the capital string values, and the lower case letters are converted automatically to the capital letters. The following lists the supported Expressions used in the WELSIM application:

Expression Result description UVW Total deformation for structural analysis U Directional deformation X for structural analysis V Directional deformation Y for structural analysis W Directional deformation Z for structural analysis SIGVM von-Mises stress for the structural analysis SIG00 Normal stress X for the structural analysis SIG11 Normal stress Y for the structural analysis SIG22 Normal stress Z for the structural analysis SIG01 Shear stress XY for the structural analysis SIG12 Shear stress YZ for the structural analysis SIG02 Shear stress XZ for the structural analysis EPS00 Normal strain X for the structural analysis EPS11 Normal strain Y for the structural analysis EPS22 Normal strain Z for the structural analysis EPS01 Shear strain XY for the structural analysis EPS12 Shear strain YZ for the structural analysis EPS02 Shear strain XZ for the structural analysis RFT Total reaction force for the structural analysis RFX Directional reaction force X for the structural analysis RFY Directional reaction force Y for the structural analysis RFZ Directional reaction force Z for the structural analysis RMT Total reaction moment for the shell structural analysis RMX Directional reaction moment X for the shell structural analysis RMY Directional reaction moment Y for the shell structural analysis RMZ Directional reaction moment Z for the shell structural analysis ENEEL Total energy for the structural analysis V123 Total velocity for the transient structural analysis V1 Directional velocity X for the transient structural analysis V2 Directional velocity Y for the transient structural analysis V3 Directional velocity Z for the transient structural analysis A123 Total acceleration for the transient structural analysis A1 Directional acceleration X for the transient structural analysis A2 Directional acceleration Y for the transient structural analysis A3 Directional acceleration Z for the transient structural analysis ROTT Total rotation for shell structural analysis ROTX Directional rotation X for shell structural analysis ROTY Directional rotation Y for shell structural analysis ROTZ Directional rotation Z for shell structural analysis TEMP Temperature for thermal analysis EM_U Voltage for electromagnetic analysis EM_ET Total electric field intensity for electromagnetic analysis EM_EX Directional electric field intensity X for electromagnetic analysis EM_EY Directional electric field intensity Y for electromagnetic analysis EM_EZ Directional electric field intensity Z for electromagnetic analysis EM_DT Total electric displacement for electromagnetic analysis EM_DX Directional electric displacement X for electromagnetic analysis EM_DY Directional electric displacement Y for electromagnetic analysis EM_DZ Directional electric displacement Z for electromagnetic analysis EM_EN Energy density for electromagnetic analysis EM_HT Total magnetic field intensity for electromagnetic analysis EM_HX Directional magnetic field intensity X for electromagnetic analysis EM_HY Directional magnetic field intensity Y for electromagnetic analysis EM_HZ Directional magnetic field intensity Z for electromagnetic analysis EM_BT Total magnetic flux density for electromagnetic analysis EM_BX Directional magnetic flux density X for electromagnetic analysis EM_BY Directional magnetic flux density Y for electromagnetic analysis EM_BZ Directional magnetic flux density Z for electromagnetic analysis EM_AT Magnitude of a magnetic potential vector for electromagnetic analysis EM_A_x Magnetic potential vector component X for electromagnetic analysis EM_A_y Magnetic potential vector component Y for electromagnetic analysis EM_A_z Magnetic potential vector component Z for electromagnetic analysis"},{"location":"welsim/users/results/#result-tools","title":"Result tools","text":""},{"location":"welsim/users/results/#result-legend","title":"Result legend","text":"

The result legend feature helps you display the result range and contour colors in a specific design. The legend component is shown in the left of the Graphics window. As shown in Figure below, the legend displays the following information:

The Legend style can be adjusted by right-clicking on the Legend field. As shown in Figure\u00a0below, the Context Menu contains items:

Note

For the option of user-defined max/min settings, the input maximum value must be greater than the minimum value.

"},{"location":"welsim/users/results/#exporting-results","title":"Exporting results","text":"

The data associated with result objects can be exported in ASCII (.txt or .dat) file format by right-clicking on the desired result object and selecting the Export Result option. Once executed, you are asked to define a filename and select the directory to save the file.

Note

The desired result object must have been successfully evaluated before exporting the result data.

"},{"location":"welsim/users/steps/","title":"Steps for using the application","text":"

This section discusses the workflow in performing simulation analysis in the WELSIM application.

"},{"location":"welsim/users/steps/#creating-analysis-environment","title":"Creating analysis environment","text":"

All analyses in WELSIM are represented by one independent analysis environment. After creating a new project environment, you can choose the analysis type and define the parameters to conduct the simulation study.

"},{"location":"welsim/users/steps/#unit-system-behavior","title":"Unit system behavior","text":"

The WELSIM provides eight types of unit systems for you to chose. You can select the preferred unit system from File > Preferences > General > Units. Once the unit system is chosen, quantity units of FEM objects are fixed. However, user still can select different unit for the quantity defined in material module. The material quantity will be converted to the system units at solve.

"},{"location":"welsim/users/steps/#defining-materials","title":"Defining materials","text":"

In simulation analysis, a geometry's attribute is influenced by the material properties that are assigned to the body. When you create a new FEM project, a material project and a structural steel material object are created automatically. This material project can include multiple material objects, which contains the material properties for the successive analysis. The system-generated structural steel can be used directly.

You can add new materials by either one of the methods below:

"},{"location":"welsim/users/steps/#editing-material-properties","title":"Editing material properties","text":"

To manage material properties, you can

"},{"location":"welsim/users/steps/#defining-material-properties","title":"Defining material properties","text":"

In the material definition panel, two tabs display on the left sub-window as shown in Figure\u00a0below. The Library tab gives you a quick method to add a bundle of properties for the specific type of material. The Build allows you to add each preferred property one by one.

"},{"location":"welsim/users/steps/#defining-analysis-type","title":"Defining analysis type","text":"

There are several analysis types are supported in WELSIM. You can define the analysis type while performing an analysis. For example, if the temperature is to be calculated, you would choose a thermal analysis. In the FEM project object, you can set the Physics Type and Analysis Type from the Properties View window as shown in Figure\u00a0below. The currently available physics and analysis types are:

"},{"location":"welsim/users/steps/#generating-geometries","title":"Generating geometries","text":"

There are two ways of generating geometries in the WELSIM application. You can either create primitive shapes using built-in tools or import an existing STEP/IGES file. Since the built-in tool only can create primitive shapes such as box and cylinder, it is recommended to create your complex geometry in an external application and import the CAD file into WELSIM.

"},{"location":"welsim/users/steps/#create-primitive-shapes","title":"Create primitive shapes","text":"

The following lists the primitive shapes that WELSIM build-in tool can create:

"},{"location":"welsim/users/steps/#import-geometry-files","title":"Import geometry files","text":"

For the complex geometry or practical designs, you can create your geometry in an external CAD application, and import to WELSIM application via STEP or IGES file. The properties view of the imported geometry allows you to define the geometry attributes, as shown in Figure\u00a0below.

"},{"location":"welsim/users/steps/#defining-part-behaviors","title":"Defining part behaviors","text":"

The primitive and imported parts have slightly different behaviors, but the primary attributes are the same. This section describes the behaviors of the imported part.

"},{"location":"welsim/users/steps/#geometry-scale","title":"Geometry scale","text":"

The Scale determines the size change of the imported geometry, and the current geometry size is the original size multiplied by the scale value. The default value is 1. Increasing the scale value enlarges the geometry, reducing this value causes the geometry smaller. The scale ruler on the bottom of the Graphics Window provides a reference for users to recognize the current size of the geometry.

"},{"location":"welsim/users/steps/#spatial-parameters","title":"Spatial parameters","text":"

For the imported geometry, the Spatial Parameters allows the user to adjust the origin of geometries. The default value is the origin of global coordinates (0, 0, 0).

"},{"location":"welsim/users/steps/#material-assignment","title":"Material assignment","text":"

Once you have defined the material objects and created the geometry, you can assign the specific material to the selected geometry object. Click Material property, and the cell displays all candidate materials in the drop-down list as shown in Figure\u00a0below. Each entry includes the material object name and ID.

"},{"location":"welsim/users/steps/#structure-type","title":"Structure type","text":"

The Structure Type provides a topological reference for you to differentiate the solid, shell, and beam geometries. The default structural type is Solid.

"},{"location":"welsim/users/steps/#source-file-name","title":"Source file name","text":"

The read-only Source property shows the information of the imported geometry file name. It provides a reference for you to identify the specific imported CAD file.

"},{"location":"welsim/users/steps/#applying-mesh","title":"Applying mesh","text":"

Meshing is the process that your geometry is spatially discretized into finite elements and nodes. The quality of the mesh directly influences the final solutions. You can automatically mesh the geometry domains, and generate 3D tetrahedral elements (Tet10 and Tet4), or 3D triangle elements (Tri6 and Tri3).

If your model does not mesh, the system applies the default settings and automatically meshes the domains at solve time. However, it is recommended to mesh the domain before solving since the system provides a reference for you to examine the mesh. Mesh Settings controls are available to assist you in adjusting the mesh density and quality.

In the multi-body analysis, you can apply local Mesh Method object and scope the target bodies to achieve a finer or coarser mesh comparing to other bodies.

"},{"location":"welsim/users/steps/#defining-connections","title":"Defining connections","text":"

In some analyses, you may need to set up the connections such as contact. The available connection features are:

"},{"location":"welsim/users/steps/#defining-study-settings","title":"Defining study settings","text":"

The Study and Study Settings objects are inserted automatically when you started a new FEM project in the step of Creating Analysis Environment. These two objects define the necessary conditions for the solving, such as steps, substeps, end time, convergence tolerance, etc.

You can create multiple steps in the properties of the Study object. As shown in Figure\u00a0below, the property Number of Steps determines the total steps in the analysis. The Current Step property of determines the current step that other properties are defining on.

The spreadsheet for the Study Settings object displays the related properties for all steps.

"},{"location":"welsim/users/steps/#defining-initial-conditions","title":"Defining initial conditions","text":"

Based on the chosen analysis type, you can define the initial conditions to the analysis. The following initial conditions are supported:

"},{"location":"welsim/users/steps/#applying-boundary-conditions","title":"Applying boundary conditions","text":"

You can impose various boundary conditions based on the types of analysis. For instance, the structural analysis allows you to impose pressure, force, displacement, and other boundary conditions. The thermal analysis enable you to impose thermal flux and temperature boundary conditions.

The body conditions are imposed on the volumes instead of surfaces or edges. For example, the standard earth gravity, acceleration, and rotational velocity act on the bodies.

The boundary and body conditions act according to the steps. For the multi-step analysis, the magnitude of those conditions can vary. The Tabular Data and Chart windows show related data and curves to represent the input values along time/steps.

For the transient analysis, the Initial Status property provides options for the user to define the boundary value at the beginning of the simulation. As shown in Figure\u00a0below, you can choose the initial value to be None or Equal to Step 1.

"},{"location":"welsim/users/steps/#solving","title":"Solving","text":"

The WELSIM application contains the integrated solvers. These solvers are essentially executable applications and can be instantiated by the front-end using inter-processing scheme. During the solving process, the front-end program generates the input scripts, mesh data file and feeds these files to the solvers. After calculation, the front-end interface can consume the generated result files and displays the resulting contour on the GUI.

Depended on the analysis type, the following solvers are available in WELSIM:

"},{"location":"welsim/users/steps/#solution-progress","title":"Solution progress","text":"

The overall solution progress can be indicated by the Output window, where you can view the output information from the solvers. If an calculation is completed successfully, you can see the similar message below in the Output window: 

WelSimFemSolver2 Completed !!\n

"},{"location":"welsim/users/steps/#evaluating-results","title":"Evaluating results","text":"

The WELSIM application provides fully integrated result review module, and you can evaluate simulation results with no need of other software tools. Depends on the analysis type, various results are available for you to examine solutions. The Using Results section lists all available results that may be used in the post-processing.

The following lists the methods to add result objects:

The following steps are to evaluate results:

The following result types are available:

See the Using Results section for more details on results.

"},{"location":"welsim/users/steps/#saving-analysis-project","title":"Saving analysis project","text":"

You can save the solution with all settings into an external file, and open this file later or on a different computer that has WELSIM installed. The persisted data include two parts:

Note

The saved database file (*.wsdb) contains the information of objects and their properties. The geometry data is saved as external STEP files. The mesh and result object settings are saved. However, the mesh and result data are not included yet. You need to perform meshing and solving to obtain those data in a resumed project.

"},{"location":"welsim/users/study/","title":"Configuring study settings","text":"

This section describes the Study and Study Settings configuration.

"},{"location":"welsim/users/study/#general-settings","title":"General settings","text":"

When you start a new FEM Project, the Study and Study Settings objects are inserted in the tree automatically. With these objects selected, you can define many solving options in the Properties View window. For example, you can define the properties of Steps, Substeps, Solver, etc.

"},{"location":"welsim/users/study/#step-controls","title":"Step controls","text":"

Step Controls define the analysis steps for both static and transient analysis. These properties in the Study object has such characteristics:

"},{"location":"welsim/users/study/#nonlinear-controls","title":"Nonlinear controls","text":"

For the nonlinear analysis, the properties of the Nonlinear Settings Controls determine the convergence of the solution. Those properties are mainly related to the Newton-Raphson algorithm.

"},{"location":"welsim/users/study/#solver-controls","title":"Solver controls","text":"

Solver Controls determines the attributes of the linear algebra solvers. The following lists the related properties:

"},{"location":"welsim/users/study/#output-controls","title":"Output controls","text":"

The Output Controls determines the output rules of solving and results. The available options are:

"},{"location":"welsim/vm/electromagnetic/","title":"Electromagnetic","text":"

To be added...

"},{"location":"welsim/vm/introduction/","title":"Introduction","text":"

WELSIM Verification Manual presents a collection of test cases that demonstrate a number of the capabilities of the WELSIM analysis environment. The available tests are engineering problems that provide independent verification, usually a closed form equation. Many of them are classical engineering problems.

"},{"location":"welsim/vm/introduction/#introduction","title":"Introduction","text":""},{"location":"welsim/vm/introduction/#index-of-test-cases","title":"Index of test cases","text":"

The following lists all verification cases tested with WELSIM application. Each case entry describes the test case number, element type, analysis type, and solution options.

"},{"location":"welsim/vm/structural/","title":"Structural","text":""},{"location":"welsim/vm/structural/#statically-inteterminate-reaction-force-analysis-vm001","title":"Statically inteterminate reaction force analysis VM001","text":"

An assembly of three cylinder bars is supported at both end surfaces. Forces \\(F_{1}\\) and \\(F_{2}\\) is applied on the middle of the assembly as shown in Figure\u00a0[fig:ch5_vm_001_schematic].

The input data about material, geometry, and loads are given in Table\u00a0[tab:ch5_vm_001_parameters].

Material Properties Geometric Properties Boundary Conditions Young's Modulus E=2e11 h=10 \\(F_{1}\\)=2000 Mass Density \\(\\rho\\)=7850 a=3 \\(F_{2}\\)=1000 Poission's Ratio v=0.3 b=3

The geometries and imposed boundary conditions are shown in Figure\u00a0[fig:ch5_vm_001_bc].

The result comparison is given in Table\u00a0[tab:ch5_vm_001_result].

Results Theory WELSIM Error (%) Z Reaction Force at Top Fixed Support 1800 1810 0.556 Z Reaction Force at Bottom Fixed Support 1200 1202 0.167

This test case project file is located at [vm/VM_WELSIM_001.wsdb].

"},{"location":"welsim/vm/structural/#rectangular-plate-with-circular-hole-subjected-to-tensile-pressure-vm002","title":"Rectangular plate with circular hole subjected to tensile pressure VM002","text":"

A rectangular plate with a circular hole is fixed along one of the end faces. A tensile pressure load is imposed on another end face as shown in Figure\u00a0[fig:ch5_vm_002_schematic].

The input data about material, geometry, and loads are given in Table\u00a0[tab:ch5_vm_002_parameters].

Material Properties Geometric Properties Boundary Conditions Young's Modulus E=2e11 a=15 Pressure P=1e4 Poission's Ratio v=0.3 b=7.5 c=2.5 d=5 thickness=1

The geometries and imposed boundary conditions are shown in Figure\u00a0[fig:ch5_vm_002_bc].

The result comparison is given in Table\u00a0[tab:ch5_vm_002_result].

Results Theory WELSIM Error (%) Maximum Normal X Stress 3.125e4 3.156e4 0.992

This test case project file is located at %Installation Directory%/vm/VM_WELSIM_002.wsdb.

"},{"location":"welsim/vm/thermal/","title":"Thermal","text":""},{"location":"welsim/vm/thermal/#heat-transfer-in-a-composite-wall-vm003","title":"Heat transfer in a composite wall VM003","text":"

An assembly wall consists of fire brick and insulating brick. The temperature and surface convection coefficient are given for both end surfaces. The simulation tries to find the temperature distribution of the assembly. The schematic view of the model is shown in Figure\u00a0[fig:ch5_vm_003_schematic].

The input data about material, geometry, and loads are given in Table\u00a0[tab:ch5_vm_003_parameters].

Material Properties Geometric Properties Boundary Conditions Thermal conductivity of fire brick wall: \\(k_{F}\\) = 1.852e-5 a=14 Convection coefficient \\(h_{F}\\)=2.315e-5 Thermal conductivity of insulating wall: \\(k_{A}\\)=2.315e-6 b=9 Ambient temperature \\(T_{F}\\)=3000 cross-section=1x1 Convection coefficient \\(h_{A}\\)=3.858e-6 Ambient temperature \\(T_{A}\\)=80

The geometries and imposed boundary conditions are shown in Figure\u00a0[fig:ch5_vm_003_bc].

The result comparison is given in Table\u00a0[tab:ch5_vm_003_result].

Results Theory WELSIM Error (%) Minimum Temperature 336 336.724 0.215 Maximum Temperature 2957 2957.216 0.007

Info

This test case file is located at vm/VM_WELSIM_003.wsdb.

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Support - WelSim Documentation
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Support

Thanks so much for choosing WELSIM! At WELSIM, we want all engineers and scientists to excel. We believe that given the right tools and guidance, all engineers can be highly productive. We strive to provide tools that give their users super powers and we’re happy to provide any guidance we can to help you use them most effectively. If you have any questions or need any help of any kind, don’t hesitate to contact us in whatever way is most convenient for you.

WelSim/docs

Support

Thanks so much for choosing WELSIM! At WELSIM, we want all engineers and scientists to excel. We believe that given the right tools and guidance, all engineers can be highly productive. We strive to provide tools that give their users super powers and we’re happy to provide any guidance we can to help you use them most effectively. If you have any questions or need any help of any kind, don’t hesitate to contact us in whatever way is most convenient for you.

We exist to help you be as productive you can be. Let us know how we can help you. Happy simulation!

\ No newline at end of file +Issues and pull requests on our open source projects -->

We exist to help you be as productive you can be. Let us know how we can help you. Happy simulation!

\ No newline at end of file diff --git a/unitconverter/unitconverter/index.html b/unitconverter/unitconverter/index.html index a961c9c..076a228 100755 --- a/unitconverter/unitconverter/index.html +++ b/unitconverter/unitconverter/index.html @@ -1,4 +1,4 @@ - Overview - WelSim Documentation
Skip to content

UnitConverter

UnitConverter is a free unit conversion software program for engineers. This tool allows you to convert a large number of engineering units quickly and accurately.

finite_element_analysis_unitconveter_gui

Specification

Specification Description
Operation system Microsoft Windows 7 to 10; 64-bit
Physical memory At least 4 GB

Supported unit systems :

  • SI: (kg, m, s, K, A, N, V)
  • MKS Standard: (kg, m, s, °C, A, N, V)
  • NMMTON Standard: (tonne, mm, s, °C, A, N, mV)
  • BIN Standard: (lbm, in, s, °F, A, lbf, V)
  • US Engineering: (lb, in, s, R, A, lbf, V)
  • CGS Standard: (g, cm, s, °C, A, dyne, V)
  • NMM Standard: (kg, mm, s, °C, mA, N, mV)
  • UMKS Standard: (kg, µm, s, °C, mA, µN, V)
  • NMMDAT Standard: (decatonne, mm, s, °C, mA, N, mV)
  • BFT Standard: (lbm, ft, s, °F, A, lbf, V)
  • CGS Consistent: (g, m, s, °C, A, dyne, V)
  • NMM Consistent: (tonne, m, s, °C, mA, t⋅mm/s2, mV)
  • UMKS Consistent: (kg, m, s, °C, pA, µN, pV)
  • BIN Consistent: (slinch, in, s, °C, A, slinch⋅in/s2, V)
  • BFT Consistent: (slug, ft, s, °C, A, slug⋅ft/s2, V)
  • CGuS Standard: (g, cm, \(\mu\)s, °C, A, dyne, V)

Supported units

The supported units are listed in the table below.

Category Materials
Base Angle, Current, Length, Mass, Temperature, Time
Common Area, Density, Energy, Frequency, Volume
Mechanical Acceleration, Angular Acceleration, Angular Velocity, Force, Moment of Inertia, Power, Pressure, Torque, Velocity
Thermal Heat Flux Density, Heat Transfer Coefficient, Specific Heat Capacity, Thermal Conductivity, Thermal Expansivity
Electrical Capacitance, Electric Charge, Electrical Conductance, Electrical Conductivity, Inductance, Surface Charge Density, Surface Current Density, Voltage, Volume Charge Density
Magnetic Magnetic field strength, Magnetic flux density
WelSim/docs

UnitConverter

UnitConverter is a free unit conversion software program for engineers. This tool allows you to convert a large number of engineering units quickly and accurately.

finite_element_analysis_unitconveter_gui

Specification

Specification Description
Operation system Microsoft Windows 7 to 10; 64-bit
Physical memory At least 4 GB

Supported unit systems :

  • SI: (kg, m, s, K, A, N, V)
  • MKS Standard: (kg, m, s, °C, A, N, V)
  • NMMTON Standard: (tonne, mm, s, °C, A, N, mV)
  • BIN Standard: (lbm, in, s, °F, A, lbf, V)
  • US Engineering: (lb, in, s, R, A, lbf, V)
  • CGS Standard: (g, cm, s, °C, A, dyne, V)
  • NMM Standard: (kg, mm, s, °C, mA, N, mV)
  • UMKS Standard: (kg, µm, s, °C, mA, µN, V)
  • NMMDAT Standard: (decatonne, mm, s, °C, mA, N, mV)
  • BFT Standard: (lbm, ft, s, °F, A, lbf, V)
  • CGS Consistent: (g, m, s, °C, A, dyne, V)
  • NMM Consistent: (tonne, m, s, °C, mA, t⋅mm/s2, mV)
  • UMKS Consistent: (kg, m, s, °C, pA, µN, pV)
  • BIN Consistent: (slinch, in, s, °C, A, slinch⋅in/s2, V)
  • BFT Consistent: (slug, ft, s, °C, A, slug⋅ft/s2, V)
  • CGuS Standard: (g, cm, \(\mu\)s, °C, A, dyne, V)

Supported units

The supported units are listed in the table below.

Category Materials
Base Angle, Current, Length, Mass, Temperature, Time
Common Area, Density, Energy, Frequency, Volume
Mechanical Acceleration, Angular Acceleration, Angular Velocity, Force, Moment of Inertia, Power, Pressure, Torque, Velocity
Thermal Heat Flux Density, Heat Transfer Coefficient, Specific Heat Capacity, Thermal Conductivity, Thermal Expansivity
Electrical Capacitance, Electric Charge, Electrical Conductance, Electrical Conductivity, Inductance, Surface Charge Density, Surface Current Density, Voltage, Volume Charge Density
Magnetic Magnetic field strength, Magnetic flux density

Download

UnitConverter software is available at our official website.

\ No newline at end of file +* [x] Magnetic flux density -->

Download

UnitConverter software is available at our official website.

\ No newline at end of file diff --git a/welsim/get_started/electromagnetics/electrostatic/index.html b/welsim/get_started/electromagnetics/electrostatic/index.html index cdf7858..ae6d7db 100755 --- a/welsim/get_started/electromagnetics/electrostatic/index.html +++ b/welsim/get_started/electromagnetics/electrostatic/index.html @@ -1 +1 @@ - Electro-static analysis - WelSim Documentation
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Electrostatic analysis

This example shows you how to conduct a 3D electrostatic analysis for a unibody part.

Specifying analysis

In the Properties View of the FEM Project object, you set the Physics Type property to Electromagnetic and Analysis Type to Electrostatic. An Electro-Static analysis is defined as shown in Figure below.

finite_element_analysis_welsim_ex6_analysis_type

Preparing geometry

Next, you can import the geometry file “h_section_unibody.step” by clicking the Import... command from the Toolbar or Geometry Menu. The imported geometry and material property are shown in Figure below.

finite_element_analysis_welsim_ex6_geom_mat

Setting mesh

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 3e-3.

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 34,764 nodes, and 20,657 Tet10 elements generated as shown in Figure below.

finite_element_analysis_welsim_ex6_mesh_data

Imposing conditions

Next, you impose two boundary conditions, a Ground, and Voltage by clicking the corresponding commands from the Toolbar and Electromagnetic Menu. In the Properties View of the Ground object, holding the Ctrl or Shift key and select left bottom and right top surfaces for the Geometry property, as shown in Figure below.

finite_element_analysis_welsim_ex6_bc_ground

In the Properties View of Voltage object, set the Voltage value to 5, and scope surfaces for the Geometry property, as shown in Figure below.

finite_element_analysis_welsim_ex6_bc_voltage

Solving the model

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process. As shown in Figure [fig:ch2_start_ex1_output_solver], this model is solved successfully.

Evaluating results

To evaluate the deformation of the structure, you can add a Voltage object to the tree by clicking the Voltage item from the Toolbar, Electromagnetic Menu. Next, double-clicking the result object or clicking the Evaluate item from the Toolbar or FEM Menu, you display the contour in the Graphics window as shown in Figure below.

finite_element_analysis_welsim_ex6_rst_voltage

Adding an electric field result object is similar. Clicking the Electric Field result from Toolbar or Electromagnetic Menu, you insert a Electric Field result object to the tree. Evaluating the default Total Electric Field Type, you obtain the magnitude of the electric field vector contour on the body in the Graphics window. The Maximum and Minimum values of field data are displayed in the Properties View window as shown in Figure below.

finite_element_analysis_welsim_ex6_rst_voltage

Info

This project file is located at examples/quick_electrostatic_01.wsdb.

\ No newline at end of file + Electro-static analysis - WelSim Documentation
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Electrostatic analysis

This example shows you how to conduct a 3D electrostatic analysis for a unibody part.

Specifying analysis

In the Properties View of the FEM Project object, you set the Physics Type property to Electromagnetic and Analysis Type to Electrostatic. An Electro-Static analysis is defined as shown in Figure below.

finite_element_analysis_welsim_ex6_analysis_type

Preparing geometry

Next, you can import the geometry file “h_section_unibody.step” by clicking the Import... command from the Toolbar or Geometry Menu. The imported geometry and material property are shown in Figure below.

finite_element_analysis_welsim_ex6_geom_mat

Setting mesh

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 3e-3.

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 34,764 nodes, and 20,657 Tet10 elements generated as shown in Figure below.

finite_element_analysis_welsim_ex6_mesh_data

Imposing conditions

Next, you impose two boundary conditions, a Ground, and Voltage by clicking the corresponding commands from the Toolbar and Electromagnetic Menu. In the Properties View of the Ground object, holding the Ctrl or Shift key and select left bottom and right top surfaces for the Geometry property, as shown in Figure below.

finite_element_analysis_welsim_ex6_bc_ground

In the Properties View of Voltage object, set the Voltage value to 5, and scope surfaces for the Geometry property, as shown in Figure below.

finite_element_analysis_welsim_ex6_bc_voltage

Solving the model

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process. As shown in Figure [fig:ch2_start_ex1_output_solver], this model is solved successfully.

Evaluating results

To evaluate the deformation of the structure, you can add a Voltage object to the tree by clicking the Voltage item from the Toolbar, Electromagnetic Menu. Next, double-clicking the result object or clicking the Evaluate item from the Toolbar or FEM Menu, you display the contour in the Graphics window as shown in Figure below.

finite_element_analysis_welsim_ex6_rst_voltage

Adding an electric field result object is similar. Clicking the Electric Field result from Toolbar or Electromagnetic Menu, you insert a Electric Field result object to the tree. Evaluating the default Total Electric Field Type, you obtain the magnitude of the electric field vector contour on the body in the Graphics window. The Maximum and Minimum values of field data are displayed in the Properties View window as shown in Figure below.

finite_element_analysis_welsim_ex6_rst_voltage

Info

This project file is located at examples/quick_electrostatic_01.wsdb.

\ No newline at end of file diff --git a/welsim/get_started/quick_start/index.html b/welsim/get_started/quick_start/index.html index 508be44..5d67a4f 100755 --- a/welsim/get_started/quick_start/index.html +++ b/welsim/get_started/quick_start/index.html @@ -1 +1 @@ - Quick start - WelSim Documentation
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Quick start

This section demonstrates you the primary GUI features and workflow of WELSIM application.

Graphical user interface

Overview

The WELSIM application provides you an ease-of-use graphical interface to customize the finite element analysis settings. The primary components of graphical user interface include:

  • Menus
  • Toolbar
  • Project Explorer (Tree) Window
  • Properties View Window
  • Graphics Window
  • Tabular Data Window
  • Chart Window
  • Output Window

An overview of graphical user interface is shown in Figure below.

finite_element_analysis_welsim_gui_overall.

Menus and toolbar contain primary commands of the application as shown in Figure below. Sections Main Menus and Toolbars of have more details.

finite_element_analysis_welsim_gui_toolbar.

Graphics window

The Graphics window displays the geometries and associated symbols, text, and annotations. In this window, you can pan, rotate, and zoom the 3D geometries using mouse and key. In addition to the geometries, this window may contain annotation, Graphics Toolbar, coordinate system symbol, ruler, logo, etc. A schematic view of the Graphics window is shown in Figure below.

finite_element_analysis_welsim_gui_graphics.

Material definition spreadsheet

The material module provides a spreadsheet panel for you to define and review material properties. An overview of the material property spreadsheet is shown in Figure below.

finite_element_analysis_welsim_gui_material.

Geometry display

The Graphics window displays the 3D geometries, meshed elements, result contours, etc. A 3D geometry and object properties are shown in Figure below.

finite_element_analysis_welsim_gui_gemoetry.

Mesh display

Graphics window displays the mesh as you select the mesh related objects in the tree. The Properties View shows the statistical data of the mesh as shown in Figure below.

finite_element_analysis_welsim_gui_mesh.

Boundary condition display

For the boundary conditions, the Graphics window displays the highlighted entities (faces, edges, vertices), the Property View, Tabular Data, and Chart windows show the boundary values over time. The Properties View window also allows you to scope the geometry entities and set values, as shown in Figure below.

finite_element_analysis_welsim_gui_bc.

Solution display

After solving, the user interface displays the solution and results. The Graphics window displays the result contour and legend. The Properties View shows the Maximum and Minimum values of the result at the given Set Number. The Tabular Data and Chart Windows illustrate the maximum and minimum values over the time as shown in Figure  below.

finite_element_analysis_welsim_gui_result.

Result legend

You can adjust the result contour and legend by right clicking on the legend field and set the parameters in the context menu, as shown in Figure below.

finite_element_analysis_welsim_gui_result_legend.

Workflow

Using WELSIM is straightforward. The following gives you the primary workflow steps in starting a finite element analysis project from scratch:

Create a new project

Clicking New command from Toolbar or File Menu creates a new simulation project. Several default objects are automatically generated in the tree, and the Graphics window is filled with the 3D modeling interface. The following shows the behaviors of creating a new project:

  • A Material Project and a FEM Project are created simultaneously. The Material Project object holds only Material objects, and the FEM Project object contains all modeling objects that allow users to customize a finite element analysis. Only one Material Project is allowed in the tree, while you can add multiple FEM Projects to conduct multiple simulation studies at one interface.

  • An activated project displays the object name in Bold. You can double click the project object to activate a FEM Project.

  • Many commands on Toolbar and Menu become available as a FEM project is created.

  • Each object provides a unique context menu, and you can right-click to display the context menu. For example, you can rename an object via the context menu.

  • Each object provides unique options in Properties View window, which is automatically updated as you select objects.

Defining materials

In addition to the default Structural Steel material, you can add new materials and define the properties. A Material object represents a material database. The following gives the behaviors of material definition.

  • You can create a new material object by clicking Add Material command from Toolbar or Material Menu. The Material Project many holds multiple Material objects.

  • A newly created Material object requires you to specify the properties. Double-clicking or right-clicking on the material object, you open the Edit spreadsheet.

  • Two methods are available for you to add material properties in the Edit spreadsheet. The Library tab provides you pre-defined material data to directly import. The Build tab lists all available properties for you to add properties one by one.

Importing or creating geometries

You can add geometry data by importing a CAD file or creating primitive shapes using the commands from Toolbar or Geometry Menu.

  • The built-in modeler allows you to create primitive shapes such as Box, Cylinder, Plate, and Line.
  • The supported CAD geometry file formats are: STEP, IGES.
  • The ruler in the Graphics window provides you a reference to estimate the size of geometries.
  • The size of the imported geometry can be adjusted by the tuning the Scale property value.

Meshing

You can skip meshing at this moment because the system automatically meshes the domain at solving step if no mesh is generated. However, meshing at this step provides you an insight of the mesh quality and a chance to optimize the mesh. You can click the Mesh commands from the Toolbar or FEM Menu to perform the meshing operations.

  • The mesh module supports Tet10, Tet4, Tri6, and Tri3 elements. The default type is the linear element, and you can change the element order by modifying the Quadratic property in Mesh Settings object.
  • For multiple body geometries, you can add a Mesh Method object to make some bodies have different mesh density to the global mesh density, which is defined by the Mesh Settings object.
  • The Toolbar and FEM Menu provide you mesh tools, such as Clear Generated Mesh, Examine Mesh.
  • The mesh density can be adjusted by tuning the properties of Mesh Settings, such as Maximum Size, Mesh Density.

Analysis settings

You can define the analysis settings in the following order:

  • Set the Physics Type and Analysis Type in the FEM Project object.
  • Determine the Number of Steps, Current Step, and Current End Time properties in Study object.
  • Determine the analysis settings properties in Study Settings object.
  • Determine the solver settings properties in the Answers object.

Imposing initial conditions

For the transient analysis, you can define initial conditions. The available initial conditions are

  • Initial Temperature

Imposing boundary conditions

The boundary and body conditions are essential for the conducted analysis. Depending on the Physics Type and Analysis Type, you can insert various condition objects into the tree via the Toolbar or Menu. The following gives the behaviors of the body and boundary conditions.

  • The body and boundary condition value is Step-based.
  • Multiple boundary and body conditions can be jointly imposed on the geometry.
  • In the condition scoping, you can select multiple entities by pressing Ctrl or Shift key. However, the multiple entities for one property field must be the same type of geometry.
  • Graphics window displays the annotation and highlighted geometry entities if a condition object is valid.
  • Tabular Data and Chart windows can show the condition values over time.

Solve

To solve the customized model, you can click the Compute command from the Toolbar or FEM Menu. The behaviors of solving are

  • You may be required to Save the project before performing a solving process. The system needs to save the input scripts and mesh data for solvers.
  • The Output window displays the solver messages. The promoted message indicates the success or failure of the solving process.
  • You can discontinue the solving process by clicking the Stop Interprocess button in the Output pane.

Displaying results

Depending on the Physics Type and Analysis Type, you can insert various result objects into the tree via the Toolbar or Menu. The following gives the behaviors of the solution and results.

  • To display the resulting contour, you can select the target result object, and click the Evaluate from the Toolbar or FEM Menu, or double click the object.
  • You can adjust the contour format by right clicking on the resulting legend.
  • You can clear result contour by clicking Clear Result, or Clear Calculated Solution commands from the Toolbar or FEM Menu.

Completed

The analysis is completed. You can Save the projects to an external “wsdb” file and close the application.

Note

The *.wsdb file and associated folder are the WELSIM database for project data persistence, you can open this project file later, on another computer, and on different operation systems.

\ No newline at end of file + Quick start - WelSim Documentation
Skip to content

Quick start

This section demonstrates you the primary GUI features and workflow of WELSIM application.

Graphical user interface

Overview

The WELSIM application provides you an ease-of-use graphical interface to customize the finite element analysis settings. The primary components of graphical user interface include:

  • Menus
  • Toolbar
  • Project Explorer (Tree) Window
  • Properties View Window
  • Graphics Window
  • Tabular Data Window
  • Chart Window
  • Output Window

An overview of graphical user interface is shown in Figure below.

finite_element_analysis_welsim_gui_overall.

Menus and toolbar contain primary commands of the application as shown in Figure below. Sections Main Menus and Toolbars of have more details.

finite_element_analysis_welsim_gui_toolbar.

Graphics window

The Graphics window displays the geometries and associated symbols, text, and annotations. In this window, you can pan, rotate, and zoom the 3D geometries using mouse and key. In addition to the geometries, this window may contain annotation, Graphics Toolbar, coordinate system symbol, ruler, logo, etc. A schematic view of the Graphics window is shown in Figure below.

finite_element_analysis_welsim_gui_graphics.

Material definition spreadsheet

The material module provides a spreadsheet panel for you to define and review material properties. An overview of the material property spreadsheet is shown in Figure below.

finite_element_analysis_welsim_gui_material.

Geometry display

The Graphics window displays the 3D geometries, meshed elements, result contours, etc. A 3D geometry and object properties are shown in Figure below.

finite_element_analysis_welsim_gui_gemoetry.

Mesh display

Graphics window displays the mesh as you select the mesh related objects in the tree. The Properties View shows the statistical data of the mesh as shown in Figure below.

finite_element_analysis_welsim_gui_mesh.

Boundary condition display

For the boundary conditions, the Graphics window displays the highlighted entities (faces, edges, vertices), the Property View, Tabular Data, and Chart windows show the boundary values over time. The Properties View window also allows you to scope the geometry entities and set values, as shown in Figure below.

finite_element_analysis_welsim_gui_bc.

Solution display

After solving, the user interface displays the solution and results. The Graphics window displays the result contour and legend. The Properties View shows the Maximum and Minimum values of the result at the given Set Number. The Tabular Data and Chart Windows illustrate the maximum and minimum values over the time as shown in Figure  below.

finite_element_analysis_welsim_gui_result.

Result legend

You can adjust the result contour and legend by right clicking on the legend field and set the parameters in the context menu, as shown in Figure below.

finite_element_analysis_welsim_gui_result_legend.

Workflow

Using WELSIM is straightforward. The following gives you the primary workflow steps in starting a finite element analysis project from scratch:

Create a new project

Clicking New command from Toolbar or File Menu creates a new simulation project. Several default objects are automatically generated in the tree, and the Graphics window is filled with the 3D modeling interface. The following shows the behaviors of creating a new project:

  • A Material Project and a FEM Project are created simultaneously. The Material Project object holds only Material objects, and the FEM Project object contains all modeling objects that allow users to customize a finite element analysis. Only one Material Project is allowed in the tree, while you can add multiple FEM Projects to conduct multiple simulation studies at one interface.

  • An activated project displays the object name in Bold. You can double click the project object to activate a FEM Project.

  • Many commands on Toolbar and Menu become available as a FEM project is created.

  • Each object provides a unique context menu, and you can right-click to display the context menu. For example, you can rename an object via the context menu.

  • Each object provides unique options in Properties View window, which is automatically updated as you select objects.

Defining materials

In addition to the default Structural Steel material, you can add new materials and define the properties. A Material object represents a material database. The following gives the behaviors of material definition.

  • You can create a new material object by clicking Add Material command from Toolbar or Material Menu. The Material Project many holds multiple Material objects.

  • A newly created Material object requires you to specify the properties. Double-clicking or right-clicking on the material object, you open the Edit spreadsheet.

  • Two methods are available for you to add material properties in the Edit spreadsheet. The Library tab provides you pre-defined material data to directly import. The Build tab lists all available properties for you to add properties one by one.

Importing or creating geometries

You can add geometry data by importing a CAD file or creating primitive shapes using the commands from Toolbar or Geometry Menu.

  • The built-in modeler allows you to create primitive shapes such as Box, Cylinder, Plate, and Line.
  • The supported CAD geometry file formats are: STEP, IGES.
  • The ruler in the Graphics window provides you a reference to estimate the size of geometries.
  • The size of the imported geometry can be adjusted by the tuning the Scale property value.

Meshing

You can skip meshing at this moment because the system automatically meshes the domain at solving step if no mesh is generated. However, meshing at this step provides you an insight of the mesh quality and a chance to optimize the mesh. You can click the Mesh commands from the Toolbar or FEM Menu to perform the meshing operations.

  • The mesh module supports Tet10, Tet4, Tri6, and Tri3 elements. The default type is the linear element, and you can change the element order by modifying the Quadratic property in Mesh Settings object.
  • For multiple body geometries, you can add a Mesh Method object to make some bodies have different mesh density to the global mesh density, which is defined by the Mesh Settings object.
  • The Toolbar and FEM Menu provide you mesh tools, such as Clear Generated Mesh, Examine Mesh.
  • The mesh density can be adjusted by tuning the properties of Mesh Settings, such as Maximum Size, Mesh Density.

Analysis settings

You can define the analysis settings in the following order:

  • Set the Physics Type and Analysis Type in the FEM Project object.
  • Determine the Number of Steps, Current Step, and Current End Time properties in Study object.
  • Determine the analysis settings properties in Study Settings object.
  • Determine the solver settings properties in the Answers object.

Imposing initial conditions

For the transient analysis, you can define initial conditions. The available initial conditions are

  • Initial Temperature

Imposing boundary conditions

The boundary and body conditions are essential for the conducted analysis. Depending on the Physics Type and Analysis Type, you can insert various condition objects into the tree via the Toolbar or Menu. The following gives the behaviors of the body and boundary conditions.

  • The body and boundary condition value is Step-based.
  • Multiple boundary and body conditions can be jointly imposed on the geometry.
  • In the condition scoping, you can select multiple entities by pressing Ctrl or Shift key. However, the multiple entities for one property field must be the same type of geometry.
  • Graphics window displays the annotation and highlighted geometry entities if a condition object is valid.
  • Tabular Data and Chart windows can show the condition values over time.

Solve

To solve the customized model, you can click the Compute command from the Toolbar or FEM Menu. The behaviors of solving are

  • You may be required to Save the project before performing a solving process. The system needs to save the input scripts and mesh data for solvers.
  • The Output window displays the solver messages. The promoted message indicates the success or failure of the solving process.
  • You can discontinue the solving process by clicking the Stop Interprocess button in the Output pane.

Displaying results

Depending on the Physics Type and Analysis Type, you can insert various result objects into the tree via the Toolbar or Menu. The following gives the behaviors of the solution and results.

  • To display the resulting contour, you can select the target result object, and click the Evaluate from the Toolbar or FEM Menu, or double click the object.
  • You can adjust the contour format by right clicking on the resulting legend.
  • You can clear result contour by clicking Clear Result, or Clear Calculated Solution commands from the Toolbar or FEM Menu.

Completed

The analysis is completed. You can Save the projects to an external “wsdb” file and close the application.

Note

The *.wsdb file and associated folder are the WELSIM database for project data persistence, you can open this project file later, on another computer, and on different operation systems.

\ No newline at end of file diff --git a/welsim/get_started/structural/structural_modal/index.html b/welsim/get_started/structural/structural_modal/index.html index 77ffb35..c2c98ef 100755 --- a/welsim/get_started/structural/structural_modal/index.html +++ b/welsim/get_started/structural/structural_modal/index.html @@ -1 +1 @@ - Modal analysis - WelSim Documentation
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Structural modal analysis

This example shows you how to conduct a 3D transient structural analysis for an assembly.

Defining materials

In this multi-body analysis, we assign Structural Steel and Aluminum materials to different parts. Since a Structural Steel object is already added as you initialize a FEM Project, you only need to insert an aluminum material object by clicking Add Material from Toolbar or FEM Menu.

To edit the material properties, you can double-click the Material object, or right-click on the Material object and select the Edit command from the context menu. In the material editor, you select the Library tab > General Materials > Aluminum Alloy, then click Import button or double-click the Aluminum Alloy entry. Click the OK to save and exit the material editing.

You can rename this new material object to Aluminum by press F2 key or right-clicking.

Specifying analysis

In the Properties View of the FEM Project object, you set the Analysis Type property to Modal. A Modal Structural analysis is defined as shown in Figure below.

finite_element_analysis_welsim_ex3_analysis_type

Preparing geometry

Next, you can import the geometry file “h_section_multibody.step” and assign the materials to the corresponding parts. Three Part objects in the Geometry group represent three bodies in the Graphics window, respectively. You assign the Aluminum material to the Part2, which is the connection body in the middle, the rest bodies are assigned with Structural Steel material.

Setting mesh

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 3e-3, as shown in Figure below.

finite_element_analysis_welsim_ex3_mesh_settings

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 42,329 nodes, and 25,920 Tet10 elements generated as shown in Figure below.

finite_element_analysis_welsim_ex3_mesh_data

Specifying contacts

Next, you need to define two Contact Pairs to bond the three parts into one uni-body for the analysis. Clicking the Add Contact command from the Toolbar or FEM Menu, you add two Contact Pair objects into the tree. You can rename these two objects to Contact1 and Contact2, respectively. Then you select the surfaces for Master and Target Geometry properties.

Defining analysis settings

In the Properties View of Study Settings object, you can define the analysis details such as Number of Modes. Here, you can use the default settings as shown in Figure below.

finite_element_analysis_welsim_ex3_study_settings

Imposing boundary conditions

In this modal analysis, you impose a Constraint (Fixed Support) boundary condition, which can be processed by clicking the corresponding commands from the Toolbar and Structural Menu. In the Properties View of the Constraint object, select the left bottom surface for the Geometry property.

Solving the model

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process.

Evaluating results

To evaluate the deformation of the structure, you can add a Deformation object to the tree by clicking the Deformation item from the Toolbar, Structural Menu. A result object may provide multiple sub-result types. For example, a Deformation result object allows you to specify one deformation type from the candidates Deformation X, Y, Z, and Total.

After setting the Type property to Deformation Z, double-clicking on the result object displays the resulting contour in the Graphics window as shown in Figure below. You also can click the Evaluate item from the Toolbar or FEM Menu to evaluate the result.

finite_element_analysis_welsim_ex3_rst_disp_total1

Info

This project file is located at examples/quick_structural_modal_solid_01.wsdb.

\ No newline at end of file + Modal analysis - WelSim Documentation
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Structural modal analysis

This example shows you how to conduct a 3D transient structural analysis for an assembly.

Defining materials

In this multi-body analysis, we assign Structural Steel and Aluminum materials to different parts. Since a Structural Steel object is already added as you initialize a FEM Project, you only need to insert an aluminum material object by clicking Add Material from Toolbar or FEM Menu.

To edit the material properties, you can double-click the Material object, or right-click on the Material object and select the Edit command from the context menu. In the material editor, you select the Library tab > General Materials > Aluminum Alloy, then click Import button or double-click the Aluminum Alloy entry. Click the OK to save and exit the material editing.

You can rename this new material object to Aluminum by press F2 key or right-clicking.

Specifying analysis

In the Properties View of the FEM Project object, you set the Analysis Type property to Modal. A Modal Structural analysis is defined as shown in Figure below.

finite_element_analysis_welsim_ex3_analysis_type

Preparing geometry

Next, you can import the geometry file “h_section_multibody.step” and assign the materials to the corresponding parts. Three Part objects in the Geometry group represent three bodies in the Graphics window, respectively. You assign the Aluminum material to the Part2, which is the connection body in the middle, the rest bodies are assigned with Structural Steel material.

Setting mesh

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 3e-3, as shown in Figure below.

finite_element_analysis_welsim_ex3_mesh_settings

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 42,329 nodes, and 25,920 Tet10 elements generated as shown in Figure below.

finite_element_analysis_welsim_ex3_mesh_data

Specifying contacts

Next, you need to define two Contact Pairs to bond the three parts into one uni-body for the analysis. Clicking the Add Contact command from the Toolbar or FEM Menu, you add two Contact Pair objects into the tree. You can rename these two objects to Contact1 and Contact2, respectively. Then you select the surfaces for Master and Target Geometry properties.

Defining analysis settings

In the Properties View of Study Settings object, you can define the analysis details such as Number of Modes. Here, you can use the default settings as shown in Figure below.

finite_element_analysis_welsim_ex3_study_settings

Imposing boundary conditions

In this modal analysis, you impose a Constraint (Fixed Support) boundary condition, which can be processed by clicking the corresponding commands from the Toolbar and Structural Menu. In the Properties View of the Constraint object, select the left bottom surface for the Geometry property.

Solving the model

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process.

Evaluating results

To evaluate the deformation of the structure, you can add a Deformation object to the tree by clicking the Deformation item from the Toolbar, Structural Menu. A result object may provide multiple sub-result types. For example, a Deformation result object allows you to specify one deformation type from the candidates Deformation X, Y, Z, and Total.

After setting the Type property to Deformation Z, double-clicking on the result object displays the resulting contour in the Graphics window as shown in Figure below. You also can click the Evaluate item from the Toolbar or FEM Menu to evaluate the result.

finite_element_analysis_welsim_ex3_rst_disp_total1

Info

This project file is located at examples/quick_structural_modal_solid_01.wsdb.

\ No newline at end of file diff --git a/welsim/get_started/structural/structural_static/index.html b/welsim/get_started/structural/structural_static/index.html index 2ae1ae0..0980d37 100755 --- a/welsim/get_started/structural/structural_static/index.html +++ b/welsim/get_started/structural/structural_static/index.html @@ -1 +1 @@ - Static structural analysis - WelSim Documentation
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Static structural analysis

This example shows you how to conduct a 3D static structural analysis for an assembly.

Defining materials

In this multi-body analysis, we assign Structural Steel and Aluminum materials to different parts. Since a Structural Steel object is already added as you initialize a FEM Project, you only need to insert an aluminum material object by clicking Add Material from Toolbar or FEM Menu.

To edit the material properties, you can double-click the Material object, or right-click on the Material object and select the Edit command from the context menu. In the material editor, you select the Library tab > General Materials > Aluminum Alloy, then click Import button or double-click the Aluminum Alloy entry. The material properties are set as shown in Figure below. Click the OK to save and exit the material editing.

You can rename this new material object to Aluminum by press F2 key or right-clicking.

finite_element_analysis_welsim_ex1_mat_al.

Specifying analysis

Since the Static Structural analysis is the default settings at WELSIM application, you can keep the default settings as shown in Figure below.

finite_element_analysis_welsim_ex1_analysis_type

Preparing geometry

Next, you can import the geometry file “h_section_multibody.step” and assign the materials to the corresponding parts. As shown in Figure below, three Part objects in the Geometry group represent three bodies in the Graphics window, respectively. You assign the Aluminum material to the Part2, which is the connection body in the middle, the rest bodies are assigned with Structural Steel material.

finite_element_analysis_welsim_ex1_geom_mat

Setting mesh

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 5e-3, as shown in Figure below.

finite_element_analysis_welsim_ex1_mesh_settings

Next, you add a Mesh Method object from the Toolbar or FEM Menu. In the property of this object, you select the left body for the Geometry property, and set Maximum Size value to 3e-3, , as shown in Figure below.

finite_element_analysis_welsim_ex1_mesh_method

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 21,117 nodes, and 12,427 Tet10 elements generated as shown in Figure below.

finite_element_analysis_welsim_ex1_mesh_data

Specifying contacts

Next, you need to define two Contact Pairs to bond the three parts into one uni-body for the analysis. Clicking the Add Contact command from the Toolbar or FEM Menu, you add two Contact Pair objects into the tree. You can rename these two objects to Contact1 and Contact2, respectively. Then you select the surfaces for Master and Target Geometry properties as shown in Figures below.

finite_element_analysis_welsim_ex1_contact1 finite_element_analysis_welsim_ex1_contact2

Imposing conditions

Next, you impose two boundary conditions, a Constraint (Fixed Support) and a Pressure by clicking the corresponding commands from the Toolbar and Structural Menu. In the Properties View of the Constraint object, select the left bottom surface for the Geometry property, as shown in Figure below.

finite_element_analysis_welsim_ex1_bc1_fixed

In the Properties View of Pressure object, set the Normal Pressure value to 1e7, and scope the right top surface for the Geometry property, as shown in Figure below.

finite_element_analysis_welsim_ex1_bc2_pressure

Solving the model

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process. As shown in Figure [fig:ch2_start_ex1_output_solver], this model is solved successfully.

finite_element_analysis_welsim_ex1_output_solver

Evaluating results

To evaluate the deformation of the structure, you can add a Deformation object to the tree by clicking the Deformation item from the Toolbar, Structural Menu. A result object may provide multiple sub-result types. For example, a Deformation result object allows you to specify one deformation type from the candidates Deformation X, Y, Z, and Total, as shown in Figure below.

After setting the property Type to Total Deformation, double-clicking on the result object displays the resulting contour in the Graphics window. You can click the Evaluate item from the Toolbar or FEM Menu to evaluate the result.

finite_element_analysis_welsim_ex1_rst_disp_total

Adding a stress result object is similar. Clicking the Stress result from Toolbar or Structural Menu, you insert a stress object to the tree. Evaluating the default von-Mises Stress Type, you obtain the von-Mises stress contour on bodies in the Graphics window. The Maximum and Minimum values of stress data are displayed in the Properties View, Tabular Data, and Chart windows.

finite_element_analysis_welsim_ex1_rst_stress_vm

Info

This project file is located at examples/quick_structural_static_solid_01.wsdb.

\ No newline at end of file + Static structural analysis - WelSim Documentation
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Static structural analysis

This example shows you how to conduct a 3D static structural analysis for an assembly.

Defining materials

In this multi-body analysis, we assign Structural Steel and Aluminum materials to different parts. Since a Structural Steel object is already added as you initialize a FEM Project, you only need to insert an aluminum material object by clicking Add Material from Toolbar or FEM Menu.

To edit the material properties, you can double-click the Material object, or right-click on the Material object and select the Edit command from the context menu. In the material editor, you select the Library tab > General Materials > Aluminum Alloy, then click Import button or double-click the Aluminum Alloy entry. The material properties are set as shown in Figure below. Click the OK to save and exit the material editing.

You can rename this new material object to Aluminum by press F2 key or right-clicking.

finite_element_analysis_welsim_ex1_mat_al.

Specifying analysis

Since the Static Structural analysis is the default settings at WELSIM application, you can keep the default settings as shown in Figure below.

finite_element_analysis_welsim_ex1_analysis_type

Preparing geometry

Next, you can import the geometry file “h_section_multibody.step” and assign the materials to the corresponding parts. As shown in Figure below, three Part objects in the Geometry group represent three bodies in the Graphics window, respectively. You assign the Aluminum material to the Part2, which is the connection body in the middle, the rest bodies are assigned with Structural Steel material.

finite_element_analysis_welsim_ex1_geom_mat

Setting mesh

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 5e-3, as shown in Figure below.

finite_element_analysis_welsim_ex1_mesh_settings

Next, you add a Mesh Method object from the Toolbar or FEM Menu. In the property of this object, you select the left body for the Geometry property, and set Maximum Size value to 3e-3, , as shown in Figure below.

finite_element_analysis_welsim_ex1_mesh_method

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 21,117 nodes, and 12,427 Tet10 elements generated as shown in Figure below.

finite_element_analysis_welsim_ex1_mesh_data

Specifying contacts

Next, you need to define two Contact Pairs to bond the three parts into one uni-body for the analysis. Clicking the Add Contact command from the Toolbar or FEM Menu, you add two Contact Pair objects into the tree. You can rename these two objects to Contact1 and Contact2, respectively. Then you select the surfaces for Master and Target Geometry properties as shown in Figures below.

finite_element_analysis_welsim_ex1_contact1 finite_element_analysis_welsim_ex1_contact2

Imposing conditions

Next, you impose two boundary conditions, a Constraint (Fixed Support) and a Pressure by clicking the corresponding commands from the Toolbar and Structural Menu. In the Properties View of the Constraint object, select the left bottom surface for the Geometry property, as shown in Figure below.

finite_element_analysis_welsim_ex1_bc1_fixed

In the Properties View of Pressure object, set the Normal Pressure value to 1e7, and scope the right top surface for the Geometry property, as shown in Figure below.

finite_element_analysis_welsim_ex1_bc2_pressure

Solving the model

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process. As shown in Figure [fig:ch2_start_ex1_output_solver], this model is solved successfully.

finite_element_analysis_welsim_ex1_output_solver

Evaluating results

To evaluate the deformation of the structure, you can add a Deformation object to the tree by clicking the Deformation item from the Toolbar, Structural Menu. A result object may provide multiple sub-result types. For example, a Deformation result object allows you to specify one deformation type from the candidates Deformation X, Y, Z, and Total, as shown in Figure below.

After setting the property Type to Total Deformation, double-clicking on the result object displays the resulting contour in the Graphics window. You can click the Evaluate item from the Toolbar or FEM Menu to evaluate the result.

finite_element_analysis_welsim_ex1_rst_disp_total

Adding a stress result object is similar. Clicking the Stress result from Toolbar or Structural Menu, you insert a stress object to the tree. Evaluating the default von-Mises Stress Type, you obtain the von-Mises stress contour on bodies in the Graphics window. The Maximum and Minimum values of stress data are displayed in the Properties View, Tabular Data, and Chart windows.

finite_element_analysis_welsim_ex1_rst_stress_vm

Info

This project file is located at examples/quick_structural_static_solid_01.wsdb.

\ No newline at end of file diff --git a/welsim/get_started/structural/structural_transient/index.html b/welsim/get_started/structural/structural_transient/index.html index cd6a4f3..8b13b1c 100755 --- a/welsim/get_started/structural/structural_transient/index.html +++ b/welsim/get_started/structural/structural_transient/index.html @@ -1 +1 @@ - Transient structural analysis - WelSim Documentation
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Transient structural analysis

This example shows you how to conduct a 3D transient structural analysis for an assembly.

Defining materials

In this multi-body analysis, we assign Structural Steel and Aluminum materials to different parts. Since a Structural Steel object is already added as you initialize a FEM Project, you only need to insert an aluminum material object by clicking Add Material from Toolbar or FEM Menu.

To edit the material properties, you can double-click the Material object, or right-click on the Material object and select the Edit command from the context menu. In the material editor, you select the Library tab > General Materials > Aluminum Alloy, then click Import button or double-click the Aluminum Alloy entry. The material properties are set as shown in Figure below. Click the OK to save and exit the material editing.

You can rename this new material object to Aluminum by press F2 key or right-clicking.

Specifying analysis

In the Properties View of the FEM Project object, you set the Analysis Type property to Transient. A Transient Structural analysis is defined as shown in Figure below.

finite_element_analysis_welsim_ex2_analysis_type

Preparing geometry

Next, you can import the geometry file “h_section_multibody.step” and assign the materials to the corresponding parts. As shown in Figure below, three Part objects in the Geometry group represent three bodies in the Graphics window, respectively. You assign the Aluminum material to the Part2, which is the connection body in the middle, the rest bodies are assigned with Structural Steel material.

Setting mesh

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 5e-3, as shown in Figure below.

Next, you add a Mesh Method object from the Toolbar or FEM Menu. In the property of this object, you select the left body for the Geometry property, and set Maximum Size value to 3e-3, as shown in Figure below.

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 21,117 nodes, and 12,427 Tet10 elements generated as shown in Figure below.

Specifying contacts

Next, you need to define two Contact Pairs to bond the three parts into one uni-body for the analysis. Clicking the Add Contact command from the Toolbar or FEM Menu, you add two Contact Pair objects into the tree. You can rename these two objects to Contact1 and Contact2, respectively. Then you select the surfaces for Master and Target Geometry properties as shown in Figures below.

Note

Defining contacts is optional, adding a contact or not is up to your specific model.

Defining analysis settings

In this transient analysis, you define 18 steps and set the End Time for each step, as shown in Figure below.

finite_element_analysis_welsim_ex2_study_prop

Next, you select the Study Settings object in the tree and set the Substeps property to 18, which determines the total number of substeps of the transient analysis. A screen capture of the defined properties is shown in Figure below.

finite_element_analysis_welsim_ex2_study_settings_prop

Imposing conditions

Next, you impose two boundary conditions, a Constraint (Fixed Support) and an Acceleration by clicking the corresponding commands from the Toolbar or Structural Menu. In the Properties View of the Constraint object, select the left bottom surface for the Geometry property, as shown in Figure below.

In the Properties View of Acceleration object, set the Acceleration value for the current step, and repeat this value definition for each Step. After defining the acceleration values for all steps, you scope a surface on Part2 for the Geometry property, as shown in Figure below.

finite_element_analysis_welsim_ex2_bc_acceleration

Solving the model

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process. As shown in Figure below, this model is solved successfully.

Evaluating results

To evaluate the deformation of the structure, you can add a Deformation object to the tree by clicking the Deformation item from the Toolbar, Structural Menu. A result object may provide multiple sub-result types. For example, a Deformation result object allows you to specify one deformation type from the candidates Deformation X, Y, Z, and Total.

After setting the result Type to Deformation Z, double-clicking on the result object displays the resulting contour in the Graphics window as shown in Figure below. You can click the Evaluate item from the Toolbar or FEM Menu to evaluate the result.

finite_element_analysis_welsim_ex2_rst_deformation_z18

Adding a stress result object is similar. Clicking the Stress result from Toolbar or Structural Menu, you insert a stress object to the tree. Evaluating the default von-Mises Stress Type, you obtain the von-Mises stress contour on bodies in the Graphics window as shown in Figure below. The Maximum and Minimum values of stress data are displayed in the Properties View, Tabular Data, and Chart windows.

finite_element_analysis_welsim_ex2_rst_stress_vm18

Info

This project file is located at examples/quick_structural_transient_solid_01.wsdb.

\ No newline at end of file + Transient structural analysis - WelSim Documentation
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Transient structural analysis

This example shows you how to conduct a 3D transient structural analysis for an assembly.

Defining materials

In this multi-body analysis, we assign Structural Steel and Aluminum materials to different parts. Since a Structural Steel object is already added as you initialize a FEM Project, you only need to insert an aluminum material object by clicking Add Material from Toolbar or FEM Menu.

To edit the material properties, you can double-click the Material object, or right-click on the Material object and select the Edit command from the context menu. In the material editor, you select the Library tab > General Materials > Aluminum Alloy, then click Import button or double-click the Aluminum Alloy entry. The material properties are set as shown in Figure below. Click the OK to save and exit the material editing.

You can rename this new material object to Aluminum by press F2 key or right-clicking.

Specifying analysis

In the Properties View of the FEM Project object, you set the Analysis Type property to Transient. A Transient Structural analysis is defined as shown in Figure below.

finite_element_analysis_welsim_ex2_analysis_type

Preparing geometry

Next, you can import the geometry file “h_section_multibody.step” and assign the materials to the corresponding parts. As shown in Figure below, three Part objects in the Geometry group represent three bodies in the Graphics window, respectively. You assign the Aluminum material to the Part2, which is the connection body in the middle, the rest bodies are assigned with Structural Steel material.

Setting mesh

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 5e-3, as shown in Figure below.

Next, you add a Mesh Method object from the Toolbar or FEM Menu. In the property of this object, you select the left body for the Geometry property, and set Maximum Size value to 3e-3, as shown in Figure below.

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 21,117 nodes, and 12,427 Tet10 elements generated as shown in Figure below.

Specifying contacts

Next, you need to define two Contact Pairs to bond the three parts into one uni-body for the analysis. Clicking the Add Contact command from the Toolbar or FEM Menu, you add two Contact Pair objects into the tree. You can rename these two objects to Contact1 and Contact2, respectively. Then you select the surfaces for Master and Target Geometry properties as shown in Figures below.

Note

Defining contacts is optional, adding a contact or not is up to your specific model.

Defining analysis settings

In this transient analysis, you define 18 steps and set the End Time for each step, as shown in Figure below.

finite_element_analysis_welsim_ex2_study_prop

Next, you select the Study Settings object in the tree and set the Substeps property to 18, which determines the total number of substeps of the transient analysis. A screen capture of the defined properties is shown in Figure below.

finite_element_analysis_welsim_ex2_study_settings_prop

Imposing conditions

Next, you impose two boundary conditions, a Constraint (Fixed Support) and an Acceleration by clicking the corresponding commands from the Toolbar or Structural Menu. In the Properties View of the Constraint object, select the left bottom surface for the Geometry property, as shown in Figure below.

In the Properties View of Acceleration object, set the Acceleration value for the current step, and repeat this value definition for each Step. After defining the acceleration values for all steps, you scope a surface on Part2 for the Geometry property, as shown in Figure below.

finite_element_analysis_welsim_ex2_bc_acceleration

Solving the model

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process. As shown in Figure below, this model is solved successfully.

Evaluating results

To evaluate the deformation of the structure, you can add a Deformation object to the tree by clicking the Deformation item from the Toolbar, Structural Menu. A result object may provide multiple sub-result types. For example, a Deformation result object allows you to specify one deformation type from the candidates Deformation X, Y, Z, and Total.

After setting the result Type to Deformation Z, double-clicking on the result object displays the resulting contour in the Graphics window as shown in Figure below. You can click the Evaluate item from the Toolbar or FEM Menu to evaluate the result.

finite_element_analysis_welsim_ex2_rst_deformation_z18

Adding a stress result object is similar. Clicking the Stress result from Toolbar or Structural Menu, you insert a stress object to the tree. Evaluating the default von-Mises Stress Type, you obtain the von-Mises stress contour on bodies in the Graphics window as shown in Figure below. The Maximum and Minimum values of stress data are displayed in the Properties View, Tabular Data, and Chart windows.

finite_element_analysis_welsim_ex2_rst_stress_vm18

Info

This project file is located at examples/quick_structural_transient_solid_01.wsdb.

\ No newline at end of file diff --git a/welsim/get_started/thermal/thermal_ss/index.html b/welsim/get_started/thermal/thermal_ss/index.html index 929fc61..c45ef8e 100755 --- a/welsim/get_started/thermal/thermal_ss/index.html +++ b/welsim/get_started/thermal/thermal_ss/index.html @@ -1 +1 @@ - Steady-state thermal analysis - WelSim Documentation
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Steady-state thermal analysis

This example shows you how to conduct a 3D static thermal analysis for an assembly.

Defining materials

In this multi-body analysis, we assign Structural Steel and Aluminum materials to different parts. Since a Structural Steel object is already added as you initialize a FEM Project, you only need to insert an aluminum material object by clicking Add Material from Toolbar or FEM Menu.

To edit the material properties, you can double-click the Material object, or right-click on the Material object and select the Edit command from the context menu. In the material editor, you select the Library tab > General Materials > Aluminum Alloy, then click Import button or double-click the Aluminum Alloy entry. The material properties are set as shown in Figure below. Click the OK to save and exit the material editing.

You can rename this new material object to Aluminum by press F2 key or right-clicking.

Specifying analysis

In the Properties View of the FEM Project object, you set the Physics Type property to Thermal. A Steady-State Thermal analysis is defined as shown in Figure below.

finite_element_analysis_welsim_ex4_analysis_type

Preparing geometry

Next, you can import the geometry file “h_section_multibody.step” and assign the materials to the corresponding parts. As shown in Figure, three Part objects in the Geometry group represent three bodies in the Graphics window, respectively. You assign the Aluminum material to the Part2, which is the connection body in the middle, the rest bodies are assigned with Structural Steel material.

Setting mesh

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 3e-3.

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 42,329 nodes, and 25,920 Tet10 elements generated.

Specifying contacts

Next, you need to define two Contact Pairs to bond the three parts into one uni-body for the analysis. Clicking the Add Contact command from the Toolbar or FEM Menu, you add two Contact Pair objects into the tree. You can rename these two objects to Contact1 and Contact2, respectively. Then you select the surfaces for Master and Target Geometry properties.

Imposing boundary conditions

Next, you impose four boundary conditions, a Temperature, Heat Flux, Convection, and Radiation by clicking the corresponding commands from the Toolbar or Thermal Menu. In the Properties View of the Temperature object, select a left bottom surface for the Geometry property and set the Temperature value to 0, as shown in Figure below.

finite_element_analysis_welsim_ex4_bc_temp

In the Properties View of Heat Flux object, set the Heat Flux value to 5e3, and scope a surface for the Geometry property, as shown in Figure below.

finite_element_analysis_welsim_ex4_bc_heatflux

In the Properties View of Heat Radiation object, set the Radiation Coefficient value to 1e-6, Ambient Temperature value to 22.3, and scope a surface for the Geometry property, as shown in Figure below.

finite_element_analysis_welsim_ex4_bc_radiation

In the Properties View of Heat Convection object, set the Convection Coefficient value to 1e3 and Ambient Temperature value to 22.3, and scope a surface for the Geometry property, as shown in Figure below.

finite_element_analysis_welsim_ex4_bc_convection

Solving the model

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process. As shown in Figure below, this model is solved successfully.

Evaluating results

To evaluate the deformation of the structure, you can add a Temperature object to the tree by clicking the Temperature item from the Toolbar or Thermal Menu. Next, double-clicking the result object or clicking the Evaluate item from the Toolbar or FEM Menu, you display the result contour in the Graphics window as shown in Figure below.

finite_element_analysis_welsim_ex4_rst_temp

Info

This project file is located at examples/quick_thermal_static_solid_01.wsdb.

\ No newline at end of file + Steady-state thermal analysis - WelSim Documentation
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Steady-state thermal analysis

This example shows you how to conduct a 3D static thermal analysis for an assembly.

Defining materials

In this multi-body analysis, we assign Structural Steel and Aluminum materials to different parts. Since a Structural Steel object is already added as you initialize a FEM Project, you only need to insert an aluminum material object by clicking Add Material from Toolbar or FEM Menu.

To edit the material properties, you can double-click the Material object, or right-click on the Material object and select the Edit command from the context menu. In the material editor, you select the Library tab > General Materials > Aluminum Alloy, then click Import button or double-click the Aluminum Alloy entry. The material properties are set as shown in Figure below. Click the OK to save and exit the material editing.

You can rename this new material object to Aluminum by press F2 key or right-clicking.

Specifying analysis

In the Properties View of the FEM Project object, you set the Physics Type property to Thermal. A Steady-State Thermal analysis is defined as shown in Figure below.

finite_element_analysis_welsim_ex4_analysis_type

Preparing geometry

Next, you can import the geometry file “h_section_multibody.step” and assign the materials to the corresponding parts. As shown in Figure, three Part objects in the Geometry group represent three bodies in the Graphics window, respectively. You assign the Aluminum material to the Part2, which is the connection body in the middle, the rest bodies are assigned with Structural Steel material.

Setting mesh

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 3e-3.

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 42,329 nodes, and 25,920 Tet10 elements generated.

Specifying contacts

Next, you need to define two Contact Pairs to bond the three parts into one uni-body for the analysis. Clicking the Add Contact command from the Toolbar or FEM Menu, you add two Contact Pair objects into the tree. You can rename these two objects to Contact1 and Contact2, respectively. Then you select the surfaces for Master and Target Geometry properties.

Imposing boundary conditions

Next, you impose four boundary conditions, a Temperature, Heat Flux, Convection, and Radiation by clicking the corresponding commands from the Toolbar or Thermal Menu. In the Properties View of the Temperature object, select a left bottom surface for the Geometry property and set the Temperature value to 0, as shown in Figure below.

finite_element_analysis_welsim_ex4_bc_temp

In the Properties View of Heat Flux object, set the Heat Flux value to 5e3, and scope a surface for the Geometry property, as shown in Figure below.

finite_element_analysis_welsim_ex4_bc_heatflux

In the Properties View of Heat Radiation object, set the Radiation Coefficient value to 1e-6, Ambient Temperature value to 22.3, and scope a surface for the Geometry property, as shown in Figure below.

finite_element_analysis_welsim_ex4_bc_radiation

In the Properties View of Heat Convection object, set the Convection Coefficient value to 1e3 and Ambient Temperature value to 22.3, and scope a surface for the Geometry property, as shown in Figure below.

finite_element_analysis_welsim_ex4_bc_convection

Solving the model

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process. As shown in Figure below, this model is solved successfully.

Evaluating results

To evaluate the deformation of the structure, you can add a Temperature object to the tree by clicking the Temperature item from the Toolbar or Thermal Menu. Next, double-clicking the result object or clicking the Evaluate item from the Toolbar or FEM Menu, you display the result contour in the Graphics window as shown in Figure below.

finite_element_analysis_welsim_ex4_rst_temp

Info

This project file is located at examples/quick_thermal_static_solid_01.wsdb.

\ No newline at end of file diff --git a/welsim/get_started/thermal/thermal_transient/index.html b/welsim/get_started/thermal/thermal_transient/index.html index 9f7aa9a..0966913 100755 --- a/welsim/get_started/thermal/thermal_transient/index.html +++ b/welsim/get_started/thermal/thermal_transient/index.html @@ -1 +1 @@ - Transient thermal analysis - WelSim Documentation
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Transient thermal analysis

This example shows you how to conduct a 3D transient thermal analysis for an assembly.

Defining materials

In this multi-body analysis, we assign Structural Steel and Aluminum materials to different parts. Since a Structural Steel object is already added as you initialize a FEM Project, you only need to insert an aluminum material object by clicking Add Material from Toolbar or FEM Menu.

To edit the material properties, you can double-click the Material object, or right-click on the Material object and select the Edit command from the context menu. In the material editor, you select the Library tab > General Materials > Aluminum Alloy, then click Import button or double-click the Aluminum Alloy entry. The material properties are set as shown in Figure below. Click the OK to save and exit the material editing.

You can rename this new material object to Aluminum by press F2 key or right-clicking.

Specifying analysis

In the Properties View of the FEM Project object, you set the Physics Type property to Thermal and Analysis Type property to Transient. A Transient Thermal analysis is defined as shown in Figure below.

finite_element_analysis_welsim_ex5_analysis_type

Preparing geometry

Next, you can import the geometry file “h_section_multibody.step” and assign the materials to the corresponding parts. As shown in Figure, three Part objects in the Geometry group represent three bodies in the Graphics window, respectively. You assign the Aluminum material to the Part2, which is the connection body in the middle, the rest bodies are assigned with Structural Steel material.

Setting mesh

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 3e-3.

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 42,329 nodes, and 25,920 Tet10 elements generated.

Specifying contacts

Next, you need to define two Contact Pairs to bond the three parts into one uni-body for the analysis. Clicking the Add Contact command from the Toolbar or FEM Menu, you add two Contact Pair objects into the tree. You can rename these two objects to Contact1 and Contact2, respectively. Then you select the surfaces for Master and Target Geometry properties as shown in Figures below.

Defining analysis settings

In this transient analysis, you define 1 step and set the Current End Time value to 600, as shown in Figure below.

finite_element_analysis_welsim_ex5_study_prop

In the Properties View of Study Settings object in the tree, you can use the default settings as shown in Figure below.

finite_element_analysis_welsim_ex5_study_settings_prop

Imposing conditions

Next, you can add an Initial Temperature object from the Toolbar or Thermal Menu. The initial temperature value is 300 as shown in Figure below.

finite_element_analysis_welsim_ex5_initial_temp_prop

Next, you impose three boundary conditions, a Temperature, Heat Flux, and a Heat Convection by clicking the corresponding commands from the Toolbar and Thermal Menu. In the Properties View of the Temperature object, you select the bottom surface of Part1 for the Geometry property. Next set the Temperature value to 0, and define Initial Status to Equal to Step 1, as shown in Figure below.

finite_element_analysis_welsim_ex5_temp

In the Properties View of Heat Flux object, set the Heat Flux value to -5000 and Initial Status to Equal to Step 1. Next, you scope a surface on Part1 for the Geometry property, as shown in Figure below.

finite_element_analysis_welsim_ex5_bc_heatflux

In the Properties View of Heat Convection object, set the Convection Coefficient value to 1000, Ambient Temperature value to 22.3, and Initial Status to Equal to Step 1. After defining these property values, you scope a surface on Part2 for the Geometry property, as shown in Figure below.

finite_element_analysis_welsim_ex5_bc_convection

Solving the model

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process. As shown messages in Output window, this model is solved successfully.

Evaluating results

To evaluate the temperature of the model, you can add a Temperature object to the tree by clicking the Temperature item from the Toolbar, Thermal Menu.

After inserting the result object and settings the Set Number to 15, double-clicking on the result object displays the resulting contour in the Graphics window as shown in Figure below. You can click the Evaluate item from the Toolbar or FEM Menu to evaluate the result.

finite_element_analysis_welsim_ex5_rst_temp15

Info

This project file is located at examples/quick_thermal_transient_solid_01.wsdb.

\ No newline at end of file + Transient thermal analysis - WelSim Documentation
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Transient thermal analysis

This example shows you how to conduct a 3D transient thermal analysis for an assembly.

Defining materials

In this multi-body analysis, we assign Structural Steel and Aluminum materials to different parts. Since a Structural Steel object is already added as you initialize a FEM Project, you only need to insert an aluminum material object by clicking Add Material from Toolbar or FEM Menu.

To edit the material properties, you can double-click the Material object, or right-click on the Material object and select the Edit command from the context menu. In the material editor, you select the Library tab > General Materials > Aluminum Alloy, then click Import button or double-click the Aluminum Alloy entry. The material properties are set as shown in Figure below. Click the OK to save and exit the material editing.

You can rename this new material object to Aluminum by press F2 key or right-clicking.

Specifying analysis

In the Properties View of the FEM Project object, you set the Physics Type property to Thermal and Analysis Type property to Transient. A Transient Thermal analysis is defined as shown in Figure below.

finite_element_analysis_welsim_ex5_analysis_type

Preparing geometry

Next, you can import the geometry file “h_section_multibody.step” and assign the materials to the corresponding parts. As shown in Figure, three Part objects in the Geometry group represent three bodies in the Graphics window, respectively. You assign the Aluminum material to the Part2, which is the connection body in the middle, the rest bodies are assigned with Structural Steel material.

Setting mesh

To obtain a fine mesh for the analysis, you set the Mesh Settings properties Quadratic to True, and Maximum Size to 3e-3.

Clicking the Mesh command from the Toolbar or FEM Menu, you can mesh the geometries. There are 42,329 nodes, and 25,920 Tet10 elements generated.

Specifying contacts

Next, you need to define two Contact Pairs to bond the three parts into one uni-body for the analysis. Clicking the Add Contact command from the Toolbar or FEM Menu, you add two Contact Pair objects into the tree. You can rename these two objects to Contact1 and Contact2, respectively. Then you select the surfaces for Master and Target Geometry properties as shown in Figures below.

Defining analysis settings

In this transient analysis, you define 1 step and set the Current End Time value to 600, as shown in Figure below.

finite_element_analysis_welsim_ex5_study_prop

In the Properties View of Study Settings object in the tree, you can use the default settings as shown in Figure below.

finite_element_analysis_welsim_ex5_study_settings_prop

Imposing conditions

Next, you can add an Initial Temperature object from the Toolbar or Thermal Menu. The initial temperature value is 300 as shown in Figure below.

finite_element_analysis_welsim_ex5_initial_temp_prop

Next, you impose three boundary conditions, a Temperature, Heat Flux, and a Heat Convection by clicking the corresponding commands from the Toolbar and Thermal Menu. In the Properties View of the Temperature object, you select the bottom surface of Part1 for the Geometry property. Next set the Temperature value to 0, and define Initial Status to Equal to Step 1, as shown in Figure below.

finite_element_analysis_welsim_ex5_temp

In the Properties View of Heat Flux object, set the Heat Flux value to -5000 and Initial Status to Equal to Step 1. Next, you scope a surface on Part1 for the Geometry property, as shown in Figure below.

finite_element_analysis_welsim_ex5_bc_heatflux

In the Properties View of Heat Convection object, set the Convection Coefficient value to 1000, Ambient Temperature value to 22.3, and Initial Status to Equal to Step 1. After defining these property values, you scope a surface on Part2 for the Geometry property, as shown in Figure below.

finite_element_analysis_welsim_ex5_bc_convection

Solving the model

To solve the model, you can click the Compute command from the Toolbar, FEM Menu, or right-click on the Answers object and select Compute command from context menu. Depending on the complexity of the model, the solving process can be completed in seconds to hours. The Output window displays the solver messages and indicates the status of the solving process. As shown messages in Output window, this model is solved successfully.

Evaluating results

To evaluate the temperature of the model, you can add a Temperature object to the tree by clicking the Temperature item from the Toolbar, Thermal Menu.

After inserting the result object and settings the Set Number to 15, double-clicking on the result object displays the resulting contour in the Graphics window as shown in Figure below. You can click the Evaluate item from the Toolbar or FEM Menu to evaluate the result.

finite_element_analysis_welsim_ex5_rst_temp15

Info

This project file is located at examples/quick_thermal_transient_solid_01.wsdb.

\ No newline at end of file diff --git a/welsim/material/mat_overview/index.html b/welsim/material/mat_overview/index.html index ec96d8a..272bf75 100755 --- a/welsim/material/mat_overview/index.html +++ b/welsim/material/mat_overview/index.html @@ -1,5 +1,5 @@ - Overview - WelSim Documentation
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Overview

Material Module serves as a database for material properties used in analysis projects. The module not only provides a material library but allow you to create a material using the given properties. The properties view of a Material object is the primary user interface designed to let you create, save, and retrieve material models. The well-defined material object can be saved and used in the subsequent projects.

finite_element_analysis_material_suppression

Note

The WELSIM Material module and MatEditor share the same features. For the completed and latest content, you can refer to the manual of MatEditor.

Graphical user interface

The ease-of-use Material Module contains the following graphical user interface components:

  • Toolbox: provdies two options (Library and Build tabs) for you to edit material data.
  • Library outline pane: lists predefined materials for you to quickly add material data.
  • Property outline pane: shows an outline of the contents of the togglable material properties. You can add a property data entry to the material by toggling on the property entry or remove property by toggling off the property entry.
  • Properties view pane: displays all properties that are going to be added to the Material Object. You can tune the property values at this pane.
  • Table pane: allows you to define and review tabular data for material properies.
  • Chart pane: displays the property tabular data in vivid.

Predefined materials

WELSIM also provide predefined materials, which covers most of commonly used materials. Users can choose these materials and apply to the successive finite element analysis.

Category Materials
General Materials Structural Steel, Stainless Steel, Aluminum Alloy, Concrete, Copper Alloy, Gray Cast Iron, Titanium Alloy
Nonlinear Materials Aluminum Alloy NL, Concrete NL, Copper Alloy NL, Stainless Steel NL, Structural Steel NL, Titanium Alloy NL
Hyperelastic Materials Elastomer Mooney-Rivlin, Elastomer Neo-Hookean, Elastomer Ogden, Elastomer Yeoh, Neoprene Rubber
Thermal Materials Brass, Bronze, Copper, Diamond, Ferrite, Nodular Cast Iron, Solder, Teflon, Tungsten, Wood
Electromagnetic Materials SS416, Supermendure
Other Materials Water Liquid, Argon, Ash

Material properties

The supported material properties are listed in the table below.

Category Materials
Basic Density, Isotropic Thermal Expansion, Isotropic Instantaneous Thermal Expansion, Orthotropic Thermal Expansion, Orthotropic Instantaneous Thermal Expansion, Constant Damping Coefficient
Linear Elastic Isotropic Elasticity, Orthotropic Elasticity, Viscoelastic
Hyperelastic Test Data Uniaxial Test Data, Biaxial Test Data, Shear Test Data, Volumetric Test Data, SimpleShear Test Data, Uniaxial Tension Test Data, Uniaxial Compression Test Data
Hyperelastic Arruda-Boyce, Blatz-Ko, Gent, Mooney-Rivlin 2, Mooney-Rivlin 3, Mooney-Rivlin 5, Mooney-Rivlin 9, Neo-Hookean, Ogden 1st Order, Ogden 2nd Order, Ogden 3rd Order, Polynomial 1st Order, Polynomial 2nd Order, Polynomial 3rd Order, Yeoh 1st Order, Yeoh 2nd Order, Yeoh 3rd Order
Plasticity Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening, Anand Viscoplasticity
Creep Strain Hardening, Time Hardening, Generalized Exponential, Generalized Graham, Generalized Blackburn, Modified Time Hardening, Modified Strain Hardening, Generalized Garofalo, Exponential Form, Norton, Combined Time Hardening, Rational Polynomial, Generalized Time Hardening
Visco-elastic Prony Shear Relaxation, Prony Volumetric Relaxation
Other Mechanical Strain Life Parameters, Compressive Ultimate Strength, Compressive Yield Strength, LaRc0304 Constants, Orthotropic Strain Limits, Orthotropic Stress Limits, Puck Constants, Tensile Ultimate Strength, Tensile Yield Strength, Tsai-Wu Constants, Shape Memory Effect, Drucker-Prager Strength Piecewise, Drucker-Prager Strength Linear, Ideal Gas EOS, Crushable Foam, Nonlinear Elastic Model Damage, Plakin Special Hardening, Tensile Pressure Failure, Crack Softening Failure
Thermal Enthalpy, Isotropic Thermal Conductivity, Orthotropic Thermal Conductivity, Specific Heat
Electromagnetics B-H Curve, Isotropic Relative Permeability, Orthotropic Relative Permeability, Isotropic Resistivity, Orthotropic Resistivity

Working with material data

Exporting

You can export the complete material data to an external XML file. The following format is supported for export:

  • XML in WELSIM Material (MatML 3.1) schema.
  • JSON in WELSIM Material schema.
  • OpenRadioss input script
WelSim/docs

Overview

Material Module serves as a database for material properties used in analysis projects. The module not only provides a material library but allow you to create a material using the given properties. The properties view of a Material object is the primary user interface designed to let you create, save, and retrieve material models. The well-defined material object can be saved and used in the subsequent projects.

finite_element_analysis_material_suppression

Note

The WELSIM Material module and MatEditor share the same features. For the completed and latest content, you can refer to the manual of MatEditor.

Graphical user interface

The ease-of-use Material Module contains the following graphical user interface components:

  • Toolbox: provdies two options (Library and Build tabs) for you to edit material data.
  • Library outline pane: lists predefined materials for you to quickly add material data.
  • Property outline pane: shows an outline of the contents of the togglable material properties. You can add a property data entry to the material by toggling on the property entry or remove property by toggling off the property entry.
  • Properties view pane: displays all properties that are going to be added to the Material Object. You can tune the property values at this pane.
  • Table pane: allows you to define and review tabular data for material properies.
  • Chart pane: displays the property tabular data in vivid.

Predefined materials

WELSIM also provide predefined materials, which covers most of commonly used materials. Users can choose these materials and apply to the successive finite element analysis.

Category Materials
General Materials Structural Steel, Stainless Steel, Aluminum Alloy, Concrete, Copper Alloy, Gray Cast Iron, Titanium Alloy
Nonlinear Materials Aluminum Alloy NL, Concrete NL, Copper Alloy NL, Stainless Steel NL, Structural Steel NL, Titanium Alloy NL
Hyperelastic Materials Elastomer Mooney-Rivlin, Elastomer Neo-Hookean, Elastomer Ogden, Elastomer Yeoh, Neoprene Rubber
Thermal Materials Brass, Bronze, Copper, Diamond, Ferrite, Nodular Cast Iron, Solder, Teflon, Tungsten, Wood
Electromagnetic Materials SS416, Supermendure
Other Materials Water Liquid, Argon, Ash

Material properties

The supported material properties are listed in the table below.

Category Materials
Basic Density, Isotropic Thermal Expansion, Isotropic Instantaneous Thermal Expansion, Orthotropic Thermal Expansion, Orthotropic Instantaneous Thermal Expansion, Constant Damping Coefficient
Linear Elastic Isotropic Elasticity, Orthotropic Elasticity, Viscoelastic
Hyperelastic Test Data Uniaxial Test Data, Biaxial Test Data, Shear Test Data, Volumetric Test Data, SimpleShear Test Data, Uniaxial Tension Test Data, Uniaxial Compression Test Data
Hyperelastic Arruda-Boyce, Blatz-Ko, Gent, Mooney-Rivlin 2, Mooney-Rivlin 3, Mooney-Rivlin 5, Mooney-Rivlin 9, Neo-Hookean, Ogden 1st Order, Ogden 2nd Order, Ogden 3rd Order, Polynomial 1st Order, Polynomial 2nd Order, Polynomial 3rd Order, Yeoh 1st Order, Yeoh 2nd Order, Yeoh 3rd Order
Plasticity Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Bilinear Kinematic Hardening, Multilinear Kinematic Hardening, Anand Viscoplasticity
Creep Strain Hardening, Time Hardening, Generalized Exponential, Generalized Graham, Generalized Blackburn, Modified Time Hardening, Modified Strain Hardening, Generalized Garofalo, Exponential Form, Norton, Combined Time Hardening, Rational Polynomial, Generalized Time Hardening
Visco-elastic Prony Shear Relaxation, Prony Volumetric Relaxation
Other Mechanical Strain Life Parameters, Compressive Ultimate Strength, Compressive Yield Strength, LaRc0304 Constants, Orthotropic Strain Limits, Orthotropic Stress Limits, Puck Constants, Tensile Ultimate Strength, Tensile Yield Strength, Tsai-Wu Constants, Shape Memory Effect, Drucker-Prager Strength Piecewise, Drucker-Prager Strength Linear, Ideal Gas EOS, Crushable Foam, Nonlinear Elastic Model Damage, Plakin Special Hardening, Tensile Pressure Failure, Crack Softening Failure
Thermal Enthalpy, Isotropic Thermal Conductivity, Orthotropic Thermal Conductivity, Specific Heat
Electromagnetics B-H Curve, Isotropic Relative Permeability, Orthotropic Relative Permeability, Isotropic Resistivity, Orthotropic Resistivity

Working with material data

Exporting

You can export the complete material data to an external XML file. The following format is supported for export:

  • XML in WELSIM Material (MatML 3.1) schema.
  • JSON in WELSIM Material schema.
  • OpenRadioss input script
\ No newline at end of file +* Right-click the **Material Project** and select the **Export Materials** item from the context menu. -->
\ No newline at end of file diff --git a/welsim/mesh/mesh_usage/index.html b/welsim/mesh/mesh_usage/index.html index e988c41..5869581 100755 --- a/welsim/mesh/mesh_usage/index.html +++ b/welsim/mesh/mesh_usage/index.html @@ -1 +1 @@ - Usage in WELSIM - WelSim Documentation
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Usage in WELSIM

Basic meshing process

The following steps provide the fundamental workflow for using the Meshing module as part of a finite element analysis in WELSIM.

  1. Create a finite element project and set the appropriate project type in the Properties of FEM Project object, such as Static Structural.

  2. Define appropriate material data for your analysis. The system provide a Structural Steel material, and you can create a new material object. Double-click, or Right click the material object. The Material Editing workspace appears, where you can add or edit material data as necessary.

  3. Import geometry to your system or build new geometry. Assign the material to the geometry.

  4. Click on the Mesh object in the Tree to access Meshing application functionality and apply mesh controls.

  5. Define loads and boundary conditions. Set up your analysis using that application's tools and features.

  6. You can solve your analysis by clicking solve button.

  7. Review your analysis results.

Note

You should save your data periodically (File>Save Project). The data will be saved as a .wsdb file and associated folder.

\ No newline at end of file + Usage in WELSIM - WelSim Documentation
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Usage in WELSIM

Basic meshing process

The following steps provide the fundamental workflow for using the Meshing module as part of a finite element analysis in WELSIM.

  1. Create a finite element project and set the appropriate project type in the Properties of FEM Project object, such as Static Structural.

  2. Define appropriate material data for your analysis. The system provide a Structural Steel material, and you can create a new material object. Double-click, or Right click the material object. The Material Editing workspace appears, where you can add or edit material data as necessary.

  3. Import geometry to your system or build new geometry. Assign the material to the geometry.

  4. Click on the Mesh object in the Tree to access Meshing application functionality and apply mesh controls.

  5. Define loads and boundary conditions. Set up your analysis using that application's tools and features.

  6. You can solve your analysis by clicking solve button.

  7. Review your analysis results.

Note

You should save your data periodically (File>Save Project). The data will be saved as a .wsdb file and associated folder.

\ No newline at end of file diff --git a/welsim/mesh/meshing/index.html b/welsim/mesh/meshing/index.html index 500fb18..8f4c31b 100755 --- a/welsim/mesh/meshing/index.html +++ b/welsim/mesh/meshing/index.html @@ -1,4 +1,4 @@ - Meshing Overview - WelSim Documentation
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Meshing Overview

Philosophy

The goal of meshing in WELSIM is to provide easy-to-use and stable meshing utilities that will simplify the mesh generation process.

Physics-based meshing

The WELSIM mesh generation is set based on the physics and engineering preferences. Particularly, the mesh system targets on the mechanical, thermal and electromagnetics physics.

Meshing application interface

The intuitive Meshing applicaiton interface, shown in the figure below, faciliates your use of all meshing controls and settings.

The funcational elements of the interface are described in the following table.

Window Component Description
Main Menu This menu includes all basic menus such as File and Mesh.
Standard Toolbar This toolbar contains commonly used application commands.
Graphics Toolbar This toolbar contains commands that control pointer mode or cause an action in the graphics browser.
Tree Outline Outline view of the project. Always visible. Location in the outline sets the context for other controls. Provides access to object's context menus. Allows renaming of objects. Establishes what details display in the Details View.
Property Details View The Details View corresponds to the Outline selection. Displays a details window on the lower left panel (by default) which contains details about each object in the Outline.
Geometry Window (also sometimes called the Graphics window) Displays and manipulates the visual representation of the object selected in the Outline. This window may display: <\br>
3D Geometry<\br>
2D/3D Graph<\br>
Spreadsheet<\br>
HTML Pages<\br>
Scale ruler<\br>
Triad control<\br>
Legend<\br>
WelSim/docs

Meshing Overview

Philosophy

The goal of meshing in WELSIM is to provide easy-to-use and stable meshing utilities that will simplify the mesh generation process.

Physics-based meshing

The WELSIM mesh generation is set based on the physics and engineering preferences. Particularly, the mesh system targets on the mechanical, thermal and electromagnetics physics.

Meshing application interface

The intuitive Meshing applicaiton interface, shown in the figure below, faciliates your use of all meshing controls and settings.

The funcational elements of the interface are described in the following table.

Window Component Description
Main Menu This menu includes all basic menus such as File and Mesh.
Standard Toolbar This toolbar contains commonly used application commands.
Graphics Toolbar This toolbar contains commands that control pointer mode or cause an action in the graphics browser.
Tree Outline Outline view of the project. Always visible. Location in the outline sets the context for other controls. Provides access to object's context menus. Allows renaming of objects. Establishes what details display in the Details View.
Property Details View The Details View corresponds to the Outline selection. Displays a details window on the lower left panel (by default) which contains details about each object in the Outline.
Geometry Window (also sometimes called the Graphics window) Displays and manipulates the visual representation of the object selected in the Outline. This window may display: <\br>
3D Geometry<\br>
2D/3D Graph<\br>
Spreadsheet<\br>
HTML Pages<\br>
Scale ruler<\br>
Triad control<\br>
Legend<\br>
\ No newline at end of file +## Tutorials -->
\ No newline at end of file diff --git a/welsim/release_notes/index.html b/welsim/release_notes/index.html index 4b624a3..0452c72 100755 --- a/welsim/release_notes/index.html +++ b/welsim/release_notes/index.html @@ -1 +1 @@ - Release notes - WelSim Documentation
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WELSIM release notes

This release notes are specific to WELSIM 2024R1 and arranged by the version and features.

Upgrading

To upgrade WELSIM to the latest version, download the installer from our official website .

​

Since version 2.1, WelSim provides a version checker in the application, users can click Help -> Check for Updates on the menu and know if a new version is available.

finite_element_analysis_welsim_check_updates


To inspect the currently installed version, open the About dialog in WELSIM application.

finite_element_analysis_welsim_about

Changelog

2024R1 (2.8) Jan. at 2024

  • Import GDSII files and display in the project tree and 3D graphics window.
  • Allow users to choose the layer of selection in 3D geometry picking.
  • Enable ruler to show the micro and nano meter markers to better support micro shapes.
  • Add new 3D EM features: Eigenmode, Transient, and Driven analyses.
  • Include EM solver Palace, and all dependencies, MFEM, GSLib, libCEED, libXSMM, ARPACK-NG, etc. Built Palace on Windows operation system. Set the Palace as the default EM solver. Remove FemSolver1.
  • MatEditor
    • Add a new unit system: Metric (kg, mm, ns, A, N, V).
    • Add new material properties: Material Axes.
    • Add new materials: Sapphire.
  • Upgrade Linux version version to Ubuntu 22.04 LTS, upgrade compiler to GCC11.
  • Upgrade HYPRE from 2.25 to 2.30.
  • Enhancement and improvement.

2023R3 (2.7) Sept. at 2023

  • Support open-source CFD package Su2 pre-processing:
    • Configure file and Su2 format mesh file.
    • Solver options: EULER, NAVIER_STOKES, RANS, INC_EULER, INC_NAVIER_STOKES, INC_RANS.
    • Time-dependent and steady-state analyses.
    • Free-stream field.
    • Fluid Model: STANDARD_AIR, IDEAL_GAS, VW_GAS, PR_GAS, CONSTANT_DENSITY, INC_IDEAL_GAS, INC_IDEAL_GAS_POLY, FLUID_MIXTURE, SU2_NONEQ, MUTATIONPP.
    • Turbulence models: Spalart-Allmaras (SA), Shear Stress Transport (SST).
    • Markers and Boundary Conditions: Euler (Slip) Wall, Symmetry, Heatflux, Isothermal Wall, Far field, Inlet, Supersonic Inlet, Outlet, etc.
    • Convective Schemes: JST, ROE, AUSM, HLLC, CUSP, MSW, FDS.
    • Limiter Options: SLOPE_LIMITER_FLOW, SLOPE_LIMITER_TURB, BARTH_JESPERSEN, VENKATAKRISHNAN, VENKATAKRISHNAN_WANG, SHARP_EDGES, WALL_DISTANCE, VAN_ALBADA_EDGE.
    • Restart and Visualization Files: RESTART, MESH, CSV, PARAVIEW_MULTIBLOCK, PARAVIEW, SURFACE_CSV, SURFACE_PARAVIEW.
    • Customizing the Screen and History Output: TIME_ITER, OUTER_ITER, INNER_ITER, CUR_TIME, TIME_STEP, WALL_TIME.
  • Pre- and post-processing for OpenRadioss
    • Support multi-step analysis
    • Support output frequency for the engine file.
    • Expose the thickness results option in the animation files.
    • Expose the FLD results option in the animation files.
  • Add the Adaptive Mesh Region condition.
  • Support pressure boundary condition for shell structure.
  • Support RMB context menu for the result color legend bar. The context menu allows user to:
    • Select the type of bar.
    • Toggle the display of date and time, logarithmic scale, deformation scale factor, scientific notation, and semi-transparency.
    • Set the number of digits, number of labels, and color spectrum.
  • Support RMB context menu for the 3D graphics window.
  • Support Isometric view for the dropdown AxisWidget.
  • Expose Ffmpeg executable file path in the Preferences.
  • Expose regression recorder and tester to the end users.
  • Open source all regression test cases.
  • MatEditor:
    • Add JWL material property and Test143.
    • Add Shear Test Data - Viscoelastic, Bulk Test Data - Viscoelastic, and Uniaxial Plastic Strain Test Data material properties.
  • CurveFitter:
    • Add an Output window to display more information to users.
    • Add the Johnson-Cook, Swift, Voce, and Swift-Voce functions in the Nonlinear section.
  • Introduce glog 0.6. Upgrade MFEM from 4.5 to 4.5.2.
  • Enhancement and optimization

2023R2 (2.6) April at 2023

  • Generate solver scripts and associated mesh files for Palace. Support boundary conditions: PEC, PMC, Absorbing, Conductivity, Impedance, LumpedPort, WavePort, SurfaceCurrent, Ground, ZeroCharge. Support material properties: Permeability, Permittivity, LossTan, Conductivity. Support solver settings: Electrostatic, Magnetostatic, Eigenmode, Driven, Transient, Linear. Support mesh formats: Gmsh, MFEM, VTK, Vtu, Nastran.
  • Export mesh files in Gmsh and Nastran formats.
  • Support rigid body condition for the OpenRadioss solver.
  • Support spring boundary condition for the structural analysis.
  • Check geometries before meshing implementation.
  • Add the ”Open Recent“ feature to the File menu.
  • Directory persistence for tabular data import and export.
  • Introduce nlohmann/json third-party library.
  • Upgrade MFEM to 4.5 from 4.4, Hypre to 2.25 from 2.12, and FrontISTR to 5.5 from 5.3.
  • Enhancement and optimization.

2023R1 (2.5) Jan. at 2023

  • Support OpenRadioss pre-processing.
    • Export OpenRadioss solver scripts including starter and engine files.
    • Supported blocks with keywords: MAT, NODE, GRNOD/NODE, BCS, PART, SHELL, BRICK, PROP/SOLID, PROP/SHELL, FUNCT, GRAV, INTER/TYPE7, SURF/SEG, RBODY, TH/PART, TH/INTER, INIVEL.
  • Support OpenRadioss post-processing.
    • Load T01 file.
    • Load A001 files.
    • Display result contours: displacement, velocity, acceleration, stresses, and strains.
    • Generate dynamic analysis result videos.
  • Support explicit structural dynamics using OpenRadioss solver.
  • Support explicit structural dynamics using OpenRadioss solver.
  • Support Contact Search for multi-body analysis.
  • Support Exploded View for multi-body analysis.
  • Optimize the meshing modules and improve the meshing user experience.
  • Refactor the chart module.
  • Support data persistence of mesh and results.
  • Upgrade Windows C++ compiler to Visual Studio 2022, SDK to 10.0.19041
  • Upgrade 3rd party libraries:
    • Qt to 5.15.2
    • OpenCascade to 7.5.3
    • Boost to 1.80, replace nowide with Boost/nowide
  • Start to use the external version name based on the calendar year, such as 2023R1.
  • Enhancements and optimizations.

2.4 Dec. at 2022

  • Export MFEM mesh file.
  • Export time-dependent results in Paraview Data format (*.pvd)
  • Export FrontISTR, MFEM, and SU2 input scripts.
  • UnitConverter:
    • Add new units: Energy Density By Area, Energy Density By Volume, Dynamic Viscosity, Kinematic Viscosity, Specific Heat Density By Volume, Specific Volume, Heat Capacity, Stiffness.
    • Add new unit system: g-cm-um.
  • CurveFitter:
    • Support multi-thread parallel computing (OpenMP), add 1st-6th Schulz-Flory functions。
    • Expose solver options to GUI.
  • MatEditor:
    • Add new material: Air.
    • Add new fluid properties: Dynamic Viscosity, Kinematic Viscosity, Lemalar Prandtl Number, Turbulent Prandtl Number.
    • Add new Equation of State properties: EOS Compaction, EOS Gruneisen, EOS Ideal Gas, EOS Ideal Gas VT, EOS Linear, EOS LSZK, EOS Murnaghan, EOS NASG, EOS Noble Abel, EOS Osborne, EOS Polynomial EOS Puff, EOS Sesame, EOS Stiff Gas, EOS Tillotson.
    • Add new plasticity properties: Johnson Cook Strength, Zerilli Armstrong Strength, Hill, Rate-Dependent Multilinear Hardening, Orthotropic Hill, Cowper-Symonds, Zhao, Steinberg-Guinan, Gurson, Barlat3, Yoshida-Uemori, Johnson-Holmquist, Hensel-Spittel, Swift-Voce, and Vegter.
    • Add new Failure Criteria: Glass, Bi-Quadratic, Cockcroft, Connect, Extended Mohr-Coulomb, Energy, Fabric, Forming Limit Diagram, Hashin, Hosford-Coulomb, Johnson-Cook, Ladeveze delamination, Mullins Effect, NXT, Orthotropic Bi-Quadratic, Orthotropic Strain, Puck, Tuler-Butcher, Tensile Strain, Wierzbicki, Wilkins.
    • Add viscoelastic properties: Boltzman, Maxwell-Kelvin-Voigt, Maxwell-Kelvin.
    • Support tooltips for the materials and properties.
    • Support collapse and expand on the selected material properties.
    • Support deletion of the selected material properties.
    • Support Save/Resume.
    • Support writing OpenRadioss material scripts;
  • Upgrade MFEM to 4.4.
  • Upgrade MKL and Fortran Compiler to Intel oneAPI 2022.02.
  • Linux version: new release since v1.9; Upgrade Qt to 5.15.2, MKL to Intel oneAPI 2022.01.
  • Enhancements and optimizations.

2.3 July at 2022

  • Improve meshing performance; Reduce the size of the temporary mesh data files.
  • Add 2D circular shape geometry creation.
  • Add a Refine Geometry feature.
  • Add new HPC options in the Preference settings.
  • Support new units: Momentum.
  • Upgrade structural solver to 5.3.
  • Upgrade the 3D rendering module to 5.0.3.
  • Upgrade third-party libraries: HDF to 1.12.2, CGNS to 4.3.0, ITK to 5.2.1.
  • Enhancements and optimizations.

2.2 May at 2022

  • Add screen capture feature.
  • Support video export feature for the spinning view.
  • Add a result VCR controller to the Graph window.
  • Support result animation review and video export.
  • Enhancements and optimizations.

2.1 Dec. at 2021

  • Add Sphere, and Torus build-in shape creation.
  • Support Clip Planes for the section view in post-processing.
  • Add vector (Glyph3D arrows) electric field and vector electric flux density results for electrostatic analysis.
  • Add Point Charge, Spherical Charge Density, and Polarization source conditions for electrostatic analysis.
  • Add Cylindrical Magnet, Ring Current source conditions for magnetostatic analysis.
  • Add image-saving feature for the Chart window.
  • Launch independent beam cross-section application - BeamSection.
  • CurveFitter: support R-squared (R2) calculation, enhance solver.
  • Upgrade Eigen to 3.3.9.

2.0 January at 2021

  • All new 3D graphics module supports 4K display, auto spin/swing, stereo views, etc.
  • New "Pre-Selection", "Show Vertices", "Wireframe", "Show Mesh", "Stop Meshing/Solving" commands on Menu and Toolbar.
  • A new dimension ruler supports both metric and U.S. customary units.
  • A new bounding box feature for all presented objects in the 3D scene.
  • Optimized meshing module with better performance and usability.
  • Optimized mesh and result 3D rendering.
  • Added a new Selection View to the GUI main window.
  • Upgrade QT framework to 5.12.9, OCCT to 7.4, VTK to 8.2, MUMPS to 5.3.5, PETSc to 3.14.2, etc.

1.9.1 July at 2020

  • Support curve fitting features for the Core Loss Model and test data.
  • Support curve fitting for the hyperelastic material models and test data.
  • Launch general-purpose curve fitting application - CurveFitter.

1.9 November, 2019

  • Support units.
  • Support nonlinear thermal analysis.
  • All new table and graph windows.
  • All new About dialogs with capability of displaying software and hardware information.
  • Launch the engineering material data tool - MatEditor.
  • Launch the engineering unit converter - UnitConverter.
  • Launch online documentation at docs.welsim.com and replaced the PDF documents.
  • Result legend supports user-defined min/max values.
  • Upgrade C++ compiler to vs2017, QT framework to 5.12.2, HDF5 to 1.8.21, Boost to 1.69, OCCT to 7.3, etc.
  • Enhancements and optimizations.

1.8 December, 2018

  • Input/Output: Add Nastran and Abaqus input scripts generation; Read generated result files.
  • GUI: Add system preferences database and associated user interface; Enhance Output/Message window, promote more detailed messages.
  • Geometry: New STL geometry object. Import STL files; Add geometry checking feature.
  • Mesh: mesh STL geometry. export mesh data to file.
  • Analysis: Support Vertex scoping for the boundary conditions. Add body heat flux condition for thermal analysis.
  • Upgrade Microsoft MPI to 10.0. General enhancements.

1.7 July, 2018

  • Add structural shell analysis, including the associated fixed rotation boundary condition, rotation result, reaction moment probe.
  • Add structural body conditions: body force, acceleration, earth gravity, rotational velocity.
  • Add mesh method object to support distinct mesh density for bodies.
  • Add geometry selection controller on graphics toolbar, support body, face, edge, and vertex selections.
  • Add plane shape creation feature.
  • Add official user manual.
  • General enhancements.

1.6 April, 2018

  • Add data persistence module to support project save/resume feature.
  • Add user-defined and reaction force probe results.
  • Add velocity and acceleration boundary conditions and results for transient structural analysis.
  • Add geometry export feature.
  • General enhancements.

1.5 February, 2018

  • Launch Linux 64-bit version that supports Ubuntu 16.04 LTS and Fedora 27.
  • Add status engine for the project tree objects, small icon represents the current state of the object.
  • General enhancements.

1.4 November, 2017

  • Add 3D static and transient lamellar flow analysis (Deprecated).
  • General enhancements.

1.3 September, 2017

  • Add 3D electrostatic analysis with supported boundary conditions: ground, symmetry, voltage, zero charges, surface charge density, electric displacement.
  • Add 3D magnetostatic analysis with supported boundary conditions: insulting, magnetic flux density.
  • General enhancements.

1.2 August, 2017

  • Add 3D steady-state and transient thermal analysis with associated boundary conditions.
  • General enhancements.

1.1 July, 2017

  • Add chart, tabular data, and output window to GUI.
  • Add multi-body and contact features to structural analysis.
  • Add nonlinear material analysis features with the capabilities of solving hyperelastic, elastoplastic, viscoelastic, and creep materials.
  • Add 3D static, transient, and modal structural analyses.
  • General enhancements.

1.0 March 2017

  • Launch all-in-one simulation framework including a graphical user interface, meshers, and solvers.
  • Add 3D linear elastic structural analysis.
  • Add Automatic mesh generator for Tet4 and Tet10 elements.
  • Add geometry creation and CAD model import features.
  • Add graphics, tree, and property windows to the GUI.
\ No newline at end of file + Release notes - WelSim Documentation
Skip to content

WELSIM release notes

This release notes are specific to WELSIM 2024R1 and arranged by the version and features.

Upgrading

To upgrade WELSIM to the latest version, download the installer from our official website .

​

Since version 2.1, WelSim provides a version checker in the application, users can click Help -> Check for Updates on the menu and know if a new version is available.

finite_element_analysis_welsim_check_updates


To inspect the currently installed version, open the About dialog in WELSIM application.

finite_element_analysis_welsim_about

Changelog

2024R1 (2.8) Jan. at 2024

  • Import GDSII files and display in the project tree and 3D graphics window.
  • Allow users to choose the layer of selection in 3D geometry picking.
  • Enable ruler to show the micro and nano meter markers to better support micro shapes.
  • Add new 3D EM features: Eigenmode, Transient, and Driven analyses.
  • Include EM solver Palace, and all dependencies, MFEM, GSLib, libCEED, libXSMM, ARPACK-NG, etc. Built Palace on Windows operation system. Set the Palace as the default EM solver. Remove FemSolver1.
  • MatEditor
    • Add a new unit system: Metric (kg, mm, ns, A, N, V).
    • Add new material properties: Material Axes.
    • Add new materials: Sapphire.
  • Upgrade Linux version version to Ubuntu 22.04 LTS, upgrade compiler to GCC11.
  • Upgrade HYPRE from 2.25 to 2.30.
  • Enhancement and improvement.

2023R3 (2.7) Sept. at 2023

  • Support open-source CFD package Su2 pre-processing:
    • Configure file and Su2 format mesh file.
    • Solver options: EULER, NAVIER_STOKES, RANS, INC_EULER, INC_NAVIER_STOKES, INC_RANS.
    • Time-dependent and steady-state analyses.
    • Free-stream field.
    • Fluid Model: STANDARD_AIR, IDEAL_GAS, VW_GAS, PR_GAS, CONSTANT_DENSITY, INC_IDEAL_GAS, INC_IDEAL_GAS_POLY, FLUID_MIXTURE, SU2_NONEQ, MUTATIONPP.
    • Turbulence models: Spalart-Allmaras (SA), Shear Stress Transport (SST).
    • Markers and Boundary Conditions: Euler (Slip) Wall, Symmetry, Heatflux, Isothermal Wall, Far field, Inlet, Supersonic Inlet, Outlet, etc.
    • Convective Schemes: JST, ROE, AUSM, HLLC, CUSP, MSW, FDS.
    • Limiter Options: SLOPE_LIMITER_FLOW, SLOPE_LIMITER_TURB, BARTH_JESPERSEN, VENKATAKRISHNAN, VENKATAKRISHNAN_WANG, SHARP_EDGES, WALL_DISTANCE, VAN_ALBADA_EDGE.
    • Restart and Visualization Files: RESTART, MESH, CSV, PARAVIEW_MULTIBLOCK, PARAVIEW, SURFACE_CSV, SURFACE_PARAVIEW.
    • Customizing the Screen and History Output: TIME_ITER, OUTER_ITER, INNER_ITER, CUR_TIME, TIME_STEP, WALL_TIME.
  • Pre- and post-processing for OpenRadioss
    • Support multi-step analysis
    • Support output frequency for the engine file.
    • Expose the thickness results option in the animation files.
    • Expose the FLD results option in the animation files.
  • Add the Adaptive Mesh Region condition.
  • Support pressure boundary condition for shell structure.
  • Support RMB context menu for the result color legend bar. The context menu allows user to:
    • Select the type of bar.
    • Toggle the display of date and time, logarithmic scale, deformation scale factor, scientific notation, and semi-transparency.
    • Set the number of digits, number of labels, and color spectrum.
  • Support RMB context menu for the 3D graphics window.
  • Support Isometric view for the dropdown AxisWidget.
  • Expose Ffmpeg executable file path in the Preferences.
  • Expose regression recorder and tester to the end users.
  • Open source all regression test cases.
  • MatEditor:
    • Add JWL material property and Test143.
    • Add Shear Test Data - Viscoelastic, Bulk Test Data - Viscoelastic, and Uniaxial Plastic Strain Test Data material properties.
  • CurveFitter:
    • Add an Output window to display more information to users.
    • Add the Johnson-Cook, Swift, Voce, and Swift-Voce functions in the Nonlinear section.
  • Introduce glog 0.6. Upgrade MFEM from 4.5 to 4.5.2.
  • Enhancement and optimization

2023R2 (2.6) April at 2023

  • Generate solver scripts and associated mesh files for Palace. Support boundary conditions: PEC, PMC, Absorbing, Conductivity, Impedance, LumpedPort, WavePort, SurfaceCurrent, Ground, ZeroCharge. Support material properties: Permeability, Permittivity, LossTan, Conductivity. Support solver settings: Electrostatic, Magnetostatic, Eigenmode, Driven, Transient, Linear. Support mesh formats: Gmsh, MFEM, VTK, Vtu, Nastran.
  • Export mesh files in Gmsh and Nastran formats.
  • Support rigid body condition for the OpenRadioss solver.
  • Support spring boundary condition for the structural analysis.
  • Check geometries before meshing implementation.
  • Add the ”Open Recent“ feature to the File menu.
  • Directory persistence for tabular data import and export.
  • Introduce nlohmann/json third-party library.
  • Upgrade MFEM to 4.5 from 4.4, Hypre to 2.25 from 2.12, and FrontISTR to 5.5 from 5.3.
  • Enhancement and optimization.

2023R1 (2.5) Jan. at 2023

  • Support OpenRadioss pre-processing.
    • Export OpenRadioss solver scripts including starter and engine files.
    • Supported blocks with keywords: MAT, NODE, GRNOD/NODE, BCS, PART, SHELL, BRICK, PROP/SOLID, PROP/SHELL, FUNCT, GRAV, INTER/TYPE7, SURF/SEG, RBODY, TH/PART, TH/INTER, INIVEL.
  • Support OpenRadioss post-processing.
    • Load T01 file.
    • Load A001 files.
    • Display result contours: displacement, velocity, acceleration, stresses, and strains.
    • Generate dynamic analysis result videos.
  • Support explicit structural dynamics using OpenRadioss solver.
  • Support explicit structural dynamics using OpenRadioss solver.
  • Support Contact Search for multi-body analysis.
  • Support Exploded View for multi-body analysis.
  • Optimize the meshing modules and improve the meshing user experience.
  • Refactor the chart module.
  • Support data persistence of mesh and results.
  • Upgrade Windows C++ compiler to Visual Studio 2022, SDK to 10.0.19041
  • Upgrade 3rd party libraries:
    • Qt to 5.15.2
    • OpenCascade to 7.5.3
    • Boost to 1.80, replace nowide with Boost/nowide
  • Start to use the external version name based on the calendar year, such as 2023R1.
  • Enhancements and optimizations.

2.4 Dec. at 2022

  • Export MFEM mesh file.
  • Export time-dependent results in Paraview Data format (*.pvd)
  • Export FrontISTR, MFEM, and SU2 input scripts.
  • UnitConverter:
    • Add new units: Energy Density By Area, Energy Density By Volume, Dynamic Viscosity, Kinematic Viscosity, Specific Heat Density By Volume, Specific Volume, Heat Capacity, Stiffness.
    • Add new unit system: g-cm-um.
  • CurveFitter:
    • Support multi-thread parallel computing (OpenMP), add 1st-6th Schulz-Flory functions。
    • Expose solver options to GUI.
  • MatEditor:
    • Add new material: Air.
    • Add new fluid properties: Dynamic Viscosity, Kinematic Viscosity, Lemalar Prandtl Number, Turbulent Prandtl Number.
    • Add new Equation of State properties: EOS Compaction, EOS Gruneisen, EOS Ideal Gas, EOS Ideal Gas VT, EOS Linear, EOS LSZK, EOS Murnaghan, EOS NASG, EOS Noble Abel, EOS Osborne, EOS Polynomial EOS Puff, EOS Sesame, EOS Stiff Gas, EOS Tillotson.
    • Add new plasticity properties: Johnson Cook Strength, Zerilli Armstrong Strength, Hill, Rate-Dependent Multilinear Hardening, Orthotropic Hill, Cowper-Symonds, Zhao, Steinberg-Guinan, Gurson, Barlat3, Yoshida-Uemori, Johnson-Holmquist, Hensel-Spittel, Swift-Voce, and Vegter.
    • Add new Failure Criteria: Glass, Bi-Quadratic, Cockcroft, Connect, Extended Mohr-Coulomb, Energy, Fabric, Forming Limit Diagram, Hashin, Hosford-Coulomb, Johnson-Cook, Ladeveze delamination, Mullins Effect, NXT, Orthotropic Bi-Quadratic, Orthotropic Strain, Puck, Tuler-Butcher, Tensile Strain, Wierzbicki, Wilkins.
    • Add viscoelastic properties: Boltzman, Maxwell-Kelvin-Voigt, Maxwell-Kelvin.
    • Support tooltips for the materials and properties.
    • Support collapse and expand on the selected material properties.
    • Support deletion of the selected material properties.
    • Support Save/Resume.
    • Support writing OpenRadioss material scripts;
  • Upgrade MFEM to 4.4.
  • Upgrade MKL and Fortran Compiler to Intel oneAPI 2022.02.
  • Linux version: new release since v1.9; Upgrade Qt to 5.15.2, MKL to Intel oneAPI 2022.01.
  • Enhancements and optimizations.

2.3 July at 2022

  • Improve meshing performance; Reduce the size of the temporary mesh data files.
  • Add 2D circular shape geometry creation.
  • Add a Refine Geometry feature.
  • Add new HPC options in the Preference settings.
  • Support new units: Momentum.
  • Upgrade structural solver to 5.3.
  • Upgrade the 3D rendering module to 5.0.3.
  • Upgrade third-party libraries: HDF to 1.12.2, CGNS to 4.3.0, ITK to 5.2.1.
  • Enhancements and optimizations.

2.2 May at 2022

  • Add screen capture feature.
  • Support video export feature for the spinning view.
  • Add a result VCR controller to the Graph window.
  • Support result animation review and video export.
  • Enhancements and optimizations.

2.1 Dec. at 2021

  • Add Sphere, and Torus build-in shape creation.
  • Support Clip Planes for the section view in post-processing.
  • Add vector (Glyph3D arrows) electric field and vector electric flux density results for electrostatic analysis.
  • Add Point Charge, Spherical Charge Density, and Polarization source conditions for electrostatic analysis.
  • Add Cylindrical Magnet, Ring Current source conditions for magnetostatic analysis.
  • Add image-saving feature for the Chart window.
  • Launch independent beam cross-section application - BeamSection.
  • CurveFitter: support R-squared (R2) calculation, enhance solver.
  • Upgrade Eigen to 3.3.9.

2.0 January at 2021

  • All new 3D graphics module supports 4K display, auto spin/swing, stereo views, etc.
  • New "Pre-Selection", "Show Vertices", "Wireframe", "Show Mesh", "Stop Meshing/Solving" commands on Menu and Toolbar.
  • A new dimension ruler supports both metric and U.S. customary units.
  • A new bounding box feature for all presented objects in the 3D scene.
  • Optimized meshing module with better performance and usability.
  • Optimized mesh and result 3D rendering.
  • Added a new Selection View to the GUI main window.
  • Upgrade QT framework to 5.12.9, OCCT to 7.4, VTK to 8.2, MUMPS to 5.3.5, PETSc to 3.14.2, etc.

1.9.1 July at 2020

  • Support curve fitting features for the Core Loss Model and test data.
  • Support curve fitting for the hyperelastic material models and test data.
  • Launch general-purpose curve fitting application - CurveFitter.

1.9 November, 2019

  • Support units.
  • Support nonlinear thermal analysis.
  • All new table and graph windows.
  • All new About dialogs with capability of displaying software and hardware information.
  • Launch the engineering material data tool - MatEditor.
  • Launch the engineering unit converter - UnitConverter.
  • Launch online documentation at docs.welsim.com and replaced the PDF documents.
  • Result legend supports user-defined min/max values.
  • Upgrade C++ compiler to vs2017, QT framework to 5.12.2, HDF5 to 1.8.21, Boost to 1.69, OCCT to 7.3, etc.
  • Enhancements and optimizations.

1.8 December, 2018

  • Input/Output: Add Nastran and Abaqus input scripts generation; Read generated result files.
  • GUI: Add system preferences database and associated user interface; Enhance Output/Message window, promote more detailed messages.
  • Geometry: New STL geometry object. Import STL files; Add geometry checking feature.
  • Mesh: mesh STL geometry. export mesh data to file.
  • Analysis: Support Vertex scoping for the boundary conditions. Add body heat flux condition for thermal analysis.
  • Upgrade Microsoft MPI to 10.0. General enhancements.

1.7 July, 2018

  • Add structural shell analysis, including the associated fixed rotation boundary condition, rotation result, reaction moment probe.
  • Add structural body conditions: body force, acceleration, earth gravity, rotational velocity.
  • Add mesh method object to support distinct mesh density for bodies.
  • Add geometry selection controller on graphics toolbar, support body, face, edge, and vertex selections.
  • Add plane shape creation feature.
  • Add official user manual.
  • General enhancements.

1.6 April, 2018

  • Add data persistence module to support project save/resume feature.
  • Add user-defined and reaction force probe results.
  • Add velocity and acceleration boundary conditions and results for transient structural analysis.
  • Add geometry export feature.
  • General enhancements.

1.5 February, 2018

  • Launch Linux 64-bit version that supports Ubuntu 16.04 LTS and Fedora 27.
  • Add status engine for the project tree objects, small icon represents the current state of the object.
  • General enhancements.

1.4 November, 2017

  • Add 3D static and transient lamellar flow analysis (Deprecated).
  • General enhancements.

1.3 September, 2017

  • Add 3D electrostatic analysis with supported boundary conditions: ground, symmetry, voltage, zero charges, surface charge density, electric displacement.
  • Add 3D magnetostatic analysis with supported boundary conditions: insulting, magnetic flux density.
  • General enhancements.

1.2 August, 2017

  • Add 3D steady-state and transient thermal analysis with associated boundary conditions.
  • General enhancements.

1.1 July, 2017

  • Add chart, tabular data, and output window to GUI.
  • Add multi-body and contact features to structural analysis.
  • Add nonlinear material analysis features with the capabilities of solving hyperelastic, elastoplastic, viscoelastic, and creep materials.
  • Add 3D static, transient, and modal structural analyses.
  • General enhancements.

1.0 March 2017

  • Launch all-in-one simulation framework including a graphical user interface, meshers, and solvers.
  • Add 3D linear elastic structural analysis.
  • Add Automatic mesh generator for Tet4 and Tet10 elements.
  • Add geometry creation and CAD model import features.
  • Add graphics, tree, and property windows to the GUI.
\ No newline at end of file diff --git a/welsim/theory/contact/index.html b/welsim/theory/contact/index.html index 1e6ff85..8ff2d3d 100755 --- a/welsim/theory/contact/index.html +++ b/welsim/theory/contact/index.html @@ -1 +1 @@ - Structures with contact - WelSim Documentation
Skip to content

Structures with contact

As contact occurs among multiple bodies, the contact force \(\mathbf{t}_{c}\) is transmitted via the contact surface. The principle equation of the virtual work can be rewritten as follows

\[ \begin{align} \label{eq:ch5_contact_gov1} \intop_{^{t'}V}\thinspace^{t'}\sigma\colon\delta^{t'}\mathbf{A}_{(L)}d^{t'}v=\intop_{^{t'}S_{t}}\thinspace^{t'}\mathbf{t}\cdot\delta\mathbf{u}d^{t'}s+\intop_{V}\thinspace^{t'}\mathbf{b}\cdot\delta\mathbf{u}d^{t'}v+\intop_{^{t'}S\text{c}}\thinspace^{t'}\mathbf{t}_{c}[\delta\mathbf{u}^{(1)}-\delta\mathbf{u}^{(2)}] \end{align} \]

where notation \(s_{c}\) represents the contact area, \(\mathbf{u}^{(1)}\) and \(\mathbf{u}^{(2)}\) denotes the displacement of the contact object 1 and 2, respectively.

In the contact analysis, the surfaces involve contact are paired. One of these surfaces is called the master surface, and another type of surface is target surface. We also assume

  • The target nodes do not penetrate the master surface
  • When contact occurs, the target nodes become the contact position, the master surface and the target surface mutually transmit the contact force and the frictional force through the points of contact.

The governing equations with contact term can be reduced to the finite element formation

\[ \intop_{^{t'}S_{c}}\thinspace^{t'}\mathbf{t}_{c}[\delta\mathbf{u}^{(1)}-\delta\mathbf{u}^{(2)}]\approx\delta\mathbf{UK}_{C}\triangle\mathbf{U}+\delta\mathbf{UF}_{C} \]

where \(\mathbf{K}_{c}\) and \(\mathbf{F}_{c}\) are contact rigid matrix, and the contact forces, respectively.

Remember that we introduced total Lagrange and update Lagrange methods, those formulation can be extended with the consideration of contact factors. The total Lagrange and updated Lagrange formulation with contact terms are given below

\[ \delta\mathbf{U}^{T}(_{0}^{t}\mathbf{K}_{L}+_{0}^{t}\mathbf{K}_{NL}+\mathbf{K}_{c})\triangle\mathbf{U}=\delta\mathbf{U}^{T}\thinspace_{0}^{t'}\mathbf{F}-\delta\mathbf{U}^{T}\thinspace_{0}^{t}\mathbf{Q}+\delta\mathbf{U}^{T}\mathbf{F}_{c} \]
\[ \delta\mathbf{U}^{T}(_{t}^{t}\mathbf{K}_{L}+_{t}^{t}\mathbf{K}_{NL}+\mathbf{K}_{c})\triangle\mathbf{U}=\delta\mathbf{U}^{T}\thinspace_{t}^{t'}\mathbf{F}-\delta\mathbf{U}^{T}\thinspace_{t}^{t}\mathbf{Q}+\delta\mathbf{U}^{T}\mathbf{F}_{c} \]
\ No newline at end of file + Structures with contact - WelSim Documentation
Skip to content

Structures with contact

As contact occurs among multiple bodies, the contact force \(\mathbf{t}_{c}\) is transmitted via the contact surface. The principle equation of the virtual work can be rewritten as follows

\[ \begin{align} \label{eq:ch5_contact_gov1} \intop_{^{t'}V}\thinspace^{t'}\sigma\colon\delta^{t'}\mathbf{A}_{(L)}d^{t'}v=\intop_{^{t'}S_{t}}\thinspace^{t'}\mathbf{t}\cdot\delta\mathbf{u}d^{t'}s+\intop_{V}\thinspace^{t'}\mathbf{b}\cdot\delta\mathbf{u}d^{t'}v+\intop_{^{t'}S\text{c}}\thinspace^{t'}\mathbf{t}_{c}[\delta\mathbf{u}^{(1)}-\delta\mathbf{u}^{(2)}] \end{align} \]

where notation \(s_{c}\) represents the contact area, \(\mathbf{u}^{(1)}\) and \(\mathbf{u}^{(2)}\) denotes the displacement of the contact object 1 and 2, respectively.

In the contact analysis, the surfaces involve contact are paired. One of these surfaces is called the master surface, and another type of surface is target surface. We also assume

  • The target nodes do not penetrate the master surface
  • When contact occurs, the target nodes become the contact position, the master surface and the target surface mutually transmit the contact force and the frictional force through the points of contact.

The governing equations with contact term can be reduced to the finite element formation

\[ \intop_{^{t'}S_{c}}\thinspace^{t'}\mathbf{t}_{c}[\delta\mathbf{u}^{(1)}-\delta\mathbf{u}^{(2)}]\approx\delta\mathbf{UK}_{C}\triangle\mathbf{U}+\delta\mathbf{UF}_{C} \]

where \(\mathbf{K}_{c}\) and \(\mathbf{F}_{c}\) are contact rigid matrix, and the contact forces, respectively.

Remember that we introduced total Lagrange and update Lagrange methods, those formulation can be extended with the consideration of contact factors. The total Lagrange and updated Lagrange formulation with contact terms are given below

\[ \delta\mathbf{U}^{T}(_{0}^{t}\mathbf{K}_{L}+_{0}^{t}\mathbf{K}_{NL}+\mathbf{K}_{c})\triangle\mathbf{U}=\delta\mathbf{U}^{T}\thinspace_{0}^{t'}\mathbf{F}-\delta\mathbf{U}^{T}\thinspace_{0}^{t}\mathbf{Q}+\delta\mathbf{U}^{T}\mathbf{F}_{c} \]
\[ \delta\mathbf{U}^{T}(_{t}^{t}\mathbf{K}_{L}+_{t}^{t}\mathbf{K}_{NL}+\mathbf{K}_{c})\triangle\mathbf{U}=\delta\mathbf{U}^{T}\thinspace_{t}^{t'}\mathbf{F}-\delta\mathbf{U}^{T}\thinspace_{t}^{t}\mathbf{Q}+\delta\mathbf{U}^{T}\mathbf{F}_{c} \]
\ No newline at end of file diff --git a/welsim/theory/electromagnetic/index.html b/welsim/theory/electromagnetic/index.html index e113f7a..73b8728 100755 --- a/welsim/theory/electromagnetic/index.html +++ b/welsim/theory/electromagnetic/index.html @@ -1,8 +1,8 @@ - Electromagnetic analysis - WelSim Documentation
Skip to content

Electromagnetic analysis

This section discuss the electromagnetic theories that are applied in the WELSIM application.

Electromagnetic field fundamentals

The electromagnetic fields are governed by the well-known Maxwell's equations \(\eqref{eq:ch4_theory_maxwell1}\)-\(\eqref{eq:ch4_theory_maxwell4}\)12.

\[ \begin{align} \label{eq:ch4_theory_maxwell1} \nabla\times\mathbf{H}=\mathbf{J}+\dfrac{\partial\mathbf{D}}{\partial t}=\mathbf{J}_{S}+\mathbf{J}_{e}+\mathbf{J}_{V}+\dfrac{\partial\mathbf{D}}{\partial t} \end{align} \]
\[ \begin{align} \label{eq:ch4_theory_maxwell2} \nabla\times\mathbf{E}=-\dfrac{\partial\mathbf{B}}{\partial t} \end{align} \]
\[ \begin{align} \label{eq:ch4_theory_maxwell3} \nabla\cdot\mathbf{B}=0 \end{align} \]
\[ \begin{align} \label{eq:ch4_theory_maxwell4} \nabla\cdot\mathbf{D}=\rho \end{align} \]

where \(\mathbf{H}\) is the magnetic field intensity vector, \(\mathbf{J}\) is total current density vector, \(\mathbf{J}_{s}\) is the applied source current density vector, \(\mathbf{J}_{e}\) is the induced eddy current density vector, and \(\mathbf{J}_{VS}\) is the velocity current density vector, \(\mathbf{D}\) is the electric flux density vector (this term is also called electric displacement), \(\mathbf{E}\) is the electric field intensity vector, \(\mathbf{B}\) is the magnetic flux density vector, and \(\rho\) is the electric charge density.

The above field governing equations contian the constitutive relations:

\[ \mathbf{D}=\epsilon\mathbf{E}+\mathbf{P} \]

and

\[ \mathbf{B}=\mu\mathbf{H} \]

where \(\mathbf{P}\) is the polarization density, and \(\mathbf{M}\) is t he magnetization. In many materials the polarization density can be approximated as a scalar multiple of the electric field. \(\mu\) is the magnetic permeability matrix. For example, if the magnetic permeability is a function of temperature,

\[ \mu=\mu_{0}\left[\begin{array}{ccc} \mu_{rx} & 0 & 0\\ 0 & \mu_{ry} & 0\\ 0 & 0 & \mu_{rz} \end{array}\right] \]

For the permanent magnets, the constitutive relation of magnetic field becomes

\[ \mathbf{B}=\mu\mathbf{H}+\mu_{0}\mathbf{M}_{0} \]

where \(\mathbf{M}_{0}\) is the remanet intrinsic magnetization vector.

Similarly, the consitutive relations for the related electric fields are:

\[ \mathbf{J}=\sigma[\mathbf{E}+\mathbf{v}\times\mathbf{B}] \]
\[ \sigma=\left[\begin{array}{ccc} \sigma_{xx} & 0 & 0\\ 0 & \sigma_{yy} & 0\\ 0 & 0 & \sigma_{zz} \end{array}\right] \]
\[ \epsilon=\left[\begin{array}{ccc} \epsilon_{xx} & 0 & 0\\ 0 & \epsilon_{yy} & 0\\ 0 & 0 & \epsilon_{zz} \end{array}\right] \]

where \(\sigma\) is the electrical conductivity matrix, \(\epsilon\) is the permittivity matrix, and \(v\) is the velocity vector.

Electrostatics

The WELSIM application introduces electric scalar potential to solve the electrostatic problems. When the time-derivetive of magnetic flux density is neglected from the full Maxwell's equations. The governing equations are reduced to

\[ \begin{align} \label{eq:ch4_theory_govern_eqn_electrostatic} \nabla\times\mathbf{H}=\mathbf{J}+\dfrac{\partial\mathbf{D}}{\partial t} \end{align} \]
\[ \nabla\times\mathbf{E}=\mathbf{0} \]
\[ \nabla\cdot\mathbf{B}=0 \]
\[ \nabla\cdot\mathbf{D}=\rho \]

Since the electric field \(\mathbf{E}\) is irrotational and can be expressed as the function of electric scalar potential

\[ \mathbf{E}=-\nabla \varphi \]

where \(\varphi\) is the electric scalar potential and has units of Volts in the SI system. Inserting this definition into the Gauss's Law gives:

\[ -\nabla \cdot \epsilon\nabla\varphi = \rho - \nabla \cdot \mathbf{P} \]

which is Poisson's equation for the electric potential , where we have assumed a linear constitutive relation between \(\mathbf{D}\) and \(\mathbf{E}\) of the form \(\mathbf{D}=\epsilon\mathbf{E}+\mathbf{P}\).

Boundary Conditions

For an electric material interface, the continuious conditions for \(\mathbf{E}\), \(\mathbf{D}\), and \(\mathbf{J}\) are

\[ E_{t1}-E_{t2}=0 \]
\[ J_{1n}+\dfrac{\partial D_{1n}}{\partial t}=J_{2n}+\dfrac{\partial D_{2n}}{\partial t} \]
\[ D_{1n}-D_{2n}=\rho_{s} \]

where \(E_{t}\) is the tangential components of \(\mathbf{E}\), \(J_{n}\) is the normal components of \(\mathbf{J}\), \(D_{n}\) is the normal components of \(\mathbf{D}\), and \(\rho_{s}\) is the surface charge density.

Since the solutons to the governing equation are non-unique, we must impose a Dirichlet boundary condition at least at one node in the domain to get the physical solution. The Dirichlet condition could be a fixed piecewise voltage value on certain nodes. In addition, the normal derivative boundary condition \(\hat{n}\cdot\mathbf{D}\) such as surface charge density can be imposed on the boundary.

Matrix Forms

The electric scalar potential algorithm is applied in the WELSIM application for solving electrostatic problems. The governing equations are reduced to the following:

\[ -\nabla\cdot\left(\epsilon\nabla V\right)=\rho \]

The matrix equation for an electrostatic analysis is derived from Equation \(\eqref{eq:ch4_theory_govern_eqn_electrostatic}\):

\[ \left[K^{VS}\right]\left\{ V_{e}\right\} =\left\{ L_{e}\right\} \]

where

\[ \left[K^{VS}\right]=\intop_{V}\left(\nabla\left\{ N\right\} ^{T}\right)^{T}\epsilon\left(\nabla\left\{ N\right\} ^{T}\right)dV \]
\[ \left\{ L_{e}\right\} =\left\{ L_{e}^{n}\right\} +\left\{ L_{e}^{c}\right\} +\left\{ L_{e}^{SC}\right\} \]
\[ \left\{ L_{e}^{c}\right\} =\int_{V}\rho\left\{ N\right\} ^{T}dV \]
\[ \left\{ L_{e}^{sc}\right\} =\int_{V}\rho_{s}\left\{ N\right\} ^{T}dV \]

Vector magnetic potential

The WELSIM application applies the vector magnetic potential method for the magentostatic analysis. Considering the neglected electric displacement currents, the full Maxwell's equations can be reduced to

\[ \nabla\times\mathbf{H}=\mathbf{J} \]
\[ \nabla\times\mathbf{E}=-\dfrac{\partial\mathbf{B}}{\partial t} \]
\[ \nabla\cdot\mathbf{B}=0 \]

A numerical solution can be achieved by introducing potentials to the governing equations. The proposed magnetic vector potential \(\mathbf{A}\) and electric scalar potential \(V\) have the following characteristics:

\[ \mathbf{B}=\nabla\times\mathbf{A} \]
\[ \mathbf{E}=-\dfrac{\partial\mathbf{A}}{\partial t}-\nabla V \]

In addition, the Coulomb gauge condition is introduced to ensure the uniqueness of the vector potential, as shown in the following equations.

\[ \nabla\times\mathbf{v}\nabla\times\mathbf{A}-\nabla v_{e}\nabla\cdot\mathbf{A}+\sigma\left\{ \dfrac{\partial\mathbf{A}}{\partial t}\right\} +\sigma\nabla V-\mathbf{v}\times\sigma\nabla\times\mathbf{A}=\mathbf{0} \]
\[ \nabla\cdot\left(\sigma\left\{ \dfrac{\partial\mathbf{A}}{\partial t}\right\} -\sigma\nabla V+\mathbf{v}\times\sigma\nabla\times\mathbf{A}\right)=\mathbf{0} \]
\[ \nabla\times\mathbf{v}\nabla\times\mathbf{A}-\nabla v_{e}\nabla\cdot\mathbf{A}=\mathbf{J}_s+\nabla\times\dfrac{1}{\mathbf{v}_{0}}\mathbf{v}\mathbf{M}_{0} \]

where matrix invarient \(v_{e}\) is \(v_{e}=\frac{1}{3}\mathrm{tr}(v)=\frac{1}{3}(v_{11}+v_{22}+v_{33})\).

Edge-element magnetic vector potential

Due to the limitation of node-based vector magnetic potential algorithm2, WELSIM application uses the edge-based finite element for the magnetic vector potential algorithm.

The governing equation for the edge finite element method is given below.

\[ \nabla\times\mathbf{v}\nabla\times\mathbf{A}+\sigma\left\{ \dfrac{\partial\mathbf{A}}{\partial t}+\nabla V\right\} +\epsilon\left(\left\{ \dfrac{\partial^{2}\mathbf{A}}{\partial t^{2}}\right\} +\nabla\left\{ \dfrac{\partial V}{\partial t}\right\} \right)=\mathbf{0} \]
\[ \nabla\cdot\left(\sigma\left(\left\{ \dfrac{\partial\mathbf{A}}{\partial t}\right\} +\nabla V\right)+\epsilon\left(\left\{ \dfrac{\partial^{2}\mathbf{A}}{\partial t^{2}}\right\} +\nabla\left\{ \dfrac{\partial V}{\partial t}\right\} \right)\right)=\mathbf{0} \]
\[ \nabla\times\mathbf{v}\nabla\times\mathbf{A}=\mathbf{J}_{s}+\nabla\times\dfrac{1}{\mathbf{v}_{0}}\mathbf{v}\mathbf{M}_{0} \]

The uniqueness of these equations is ensured by the tree gauging procedure, which sets the edge-flux degrees of freedom related to the spanning tree of the finite element mesh to zero.

WelSim/docs

Electromagnetic analysis

This section discuss the electromagnetic theories that are applied in the WELSIM application.

Electromagnetic field fundamentals

The electromagnetic fields are governed by the well-known Maxwell's equations \(\eqref{eq:ch4_theory_maxwell1}\)-\(\eqref{eq:ch4_theory_maxwell4}\)12.

\[ \begin{align} \label{eq:ch4_theory_maxwell1} \nabla\times\mathbf{H}=\mathbf{J}+\dfrac{\partial\mathbf{D}}{\partial t}=\mathbf{J}_{S}+\mathbf{J}_{e}+\mathbf{J}_{V}+\dfrac{\partial\mathbf{D}}{\partial t} \end{align} \]
\[ \begin{align} \label{eq:ch4_theory_maxwell2} \nabla\times\mathbf{E}=-\dfrac{\partial\mathbf{B}}{\partial t} \end{align} \]
\[ \begin{align} \label{eq:ch4_theory_maxwell3} \nabla\cdot\mathbf{B}=0 \end{align} \]
\[ \begin{align} \label{eq:ch4_theory_maxwell4} \nabla\cdot\mathbf{D}=\rho \end{align} \]

where \(\mathbf{H}\) is the magnetic field intensity vector, \(\mathbf{J}\) is total current density vector, \(\mathbf{J}_{s}\) is the applied source current density vector, \(\mathbf{J}_{e}\) is the induced eddy current density vector, and \(\mathbf{J}_{VS}\) is the velocity current density vector, \(\mathbf{D}\) is the electric flux density vector (this term is also called electric displacement), \(\mathbf{E}\) is the electric field intensity vector, \(\mathbf{B}\) is the magnetic flux density vector, and \(\rho\) is the electric charge density.

The above field governing equations contian the constitutive relations:

\[ \mathbf{D}=\epsilon\mathbf{E}+\mathbf{P} \]

and

\[ \mathbf{B}=\mu\mathbf{H} \]

where \(\mathbf{P}\) is the polarization density, and \(\mathbf{M}\) is t he magnetization. In many materials the polarization density can be approximated as a scalar multiple of the electric field. \(\mu\) is the magnetic permeability matrix. For example, if the magnetic permeability is a function of temperature,

\[ \mu=\mu_{0}\left[\begin{array}{ccc} \mu_{rx} & 0 & 0\\ 0 & \mu_{ry} & 0\\ 0 & 0 & \mu_{rz} \end{array}\right] \]

For the permanent magnets, the constitutive relation of magnetic field becomes

\[ \mathbf{B}=\mu\mathbf{H}+\mu_{0}\mathbf{M}_{0} \]

where \(\mathbf{M}_{0}\) is the remanet intrinsic magnetization vector.

Similarly, the consitutive relations for the related electric fields are:

\[ \mathbf{J}=\sigma[\mathbf{E}+\mathbf{v}\times\mathbf{B}] \]
\[ \sigma=\left[\begin{array}{ccc} \sigma_{xx} & 0 & 0\\ 0 & \sigma_{yy} & 0\\ 0 & 0 & \sigma_{zz} \end{array}\right] \]
\[ \epsilon=\left[\begin{array}{ccc} \epsilon_{xx} & 0 & 0\\ 0 & \epsilon_{yy} & 0\\ 0 & 0 & \epsilon_{zz} \end{array}\right] \]

where \(\sigma\) is the electrical conductivity matrix, \(\epsilon\) is the permittivity matrix, and \(v\) is the velocity vector.

Electrostatics

The WELSIM application introduces electric scalar potential to solve the electrostatic problems. When the time-derivetive of magnetic flux density is neglected from the full Maxwell's equations. The governing equations are reduced to

\[ \begin{align} \label{eq:ch4_theory_govern_eqn_electrostatic} \nabla\times\mathbf{H}=\mathbf{J}+\dfrac{\partial\mathbf{D}}{\partial t} \end{align} \]
\[ \nabla\times\mathbf{E}=\mathbf{0} \]
\[ \nabla\cdot\mathbf{B}=0 \]
\[ \nabla\cdot\mathbf{D}=\rho \]

Since the electric field \(\mathbf{E}\) is irrotational and can be expressed as the function of electric scalar potential

\[ \mathbf{E}=-\nabla \varphi \]

where \(\varphi\) is the electric scalar potential and has units of Volts in the SI system. Inserting this definition into the Gauss's Law gives:

\[ -\nabla \cdot \epsilon\nabla\varphi = \rho - \nabla \cdot \mathbf{P} \]

which is Poisson's equation for the electric potential , where we have assumed a linear constitutive relation between \(\mathbf{D}\) and \(\mathbf{E}\) of the form \(\mathbf{D}=\epsilon\mathbf{E}+\mathbf{P}\).

Boundary Conditions

For an electric material interface, the continuious conditions for \(\mathbf{E}\), \(\mathbf{D}\), and \(\mathbf{J}\) are

\[ E_{t1}-E_{t2}=0 \]
\[ J_{1n}+\dfrac{\partial D_{1n}}{\partial t}=J_{2n}+\dfrac{\partial D_{2n}}{\partial t} \]
\[ D_{1n}-D_{2n}=\rho_{s} \]

where \(E_{t}\) is the tangential components of \(\mathbf{E}\), \(J_{n}\) is the normal components of \(\mathbf{J}\), \(D_{n}\) is the normal components of \(\mathbf{D}\), and \(\rho_{s}\) is the surface charge density.

Since the solutons to the governing equation are non-unique, we must impose a Dirichlet boundary condition at least at one node in the domain to get the physical solution. The Dirichlet condition could be a fixed piecewise voltage value on certain nodes. In addition, the normal derivative boundary condition \(\hat{n}\cdot\mathbf{D}\) such as surface charge density can be imposed on the boundary.

Matrix Forms

The electric scalar potential algorithm is applied in the WELSIM application for solving electrostatic problems. The governing equations are reduced to the following:

\[ -\nabla\cdot\left(\epsilon\nabla V\right)=\rho \]

The matrix equation for an electrostatic analysis is derived from Equation \(\eqref{eq:ch4_theory_govern_eqn_electrostatic}\):

\[ \left[K^{VS}\right]\left\{ V_{e}\right\} =\left\{ L_{e}\right\} \]

where

\[ \left[K^{VS}\right]=\intop_{V}\left(\nabla\left\{ N\right\} ^{T}\right)^{T}\epsilon\left(\nabla\left\{ N\right\} ^{T}\right)dV \]
\[ \left\{ L_{e}\right\} =\left\{ L_{e}^{n}\right\} +\left\{ L_{e}^{c}\right\} +\left\{ L_{e}^{SC}\right\} \]
\[ \left\{ L_{e}^{c}\right\} =\int_{V}\rho\left\{ N\right\} ^{T}dV \]
\[ \left\{ L_{e}^{sc}\right\} =\int_{V}\rho_{s}\left\{ N\right\} ^{T}dV \]

Vector magnetic potential

The WELSIM application applies the vector magnetic potential method for the magentostatic analysis. Considering the neglected electric displacement currents, the full Maxwell's equations can be reduced to

\[ \nabla\times\mathbf{H}=\mathbf{J} \]
\[ \nabla\times\mathbf{E}=-\dfrac{\partial\mathbf{B}}{\partial t} \]
\[ \nabla\cdot\mathbf{B}=0 \]

A numerical solution can be achieved by introducing potentials to the governing equations. The proposed magnetic vector potential \(\mathbf{A}\) and electric scalar potential \(V\) have the following characteristics:

\[ \mathbf{B}=\nabla\times\mathbf{A} \]
\[ \mathbf{E}=-\dfrac{\partial\mathbf{A}}{\partial t}-\nabla V \]

In addition, the Coulomb gauge condition is introduced to ensure the uniqueness of the vector potential, as shown in the following equations.

\[ \nabla\times\mathbf{v}\nabla\times\mathbf{A}-\nabla v_{e}\nabla\cdot\mathbf{A}+\sigma\left\{ \dfrac{\partial\mathbf{A}}{\partial t}\right\} +\sigma\nabla V-\mathbf{v}\times\sigma\nabla\times\mathbf{A}=\mathbf{0} \]
\[ \nabla\cdot\left(\sigma\left\{ \dfrac{\partial\mathbf{A}}{\partial t}\right\} -\sigma\nabla V+\mathbf{v}\times\sigma\nabla\times\mathbf{A}\right)=\mathbf{0} \]
\[ \nabla\times\mathbf{v}\nabla\times\mathbf{A}-\nabla v_{e}\nabla\cdot\mathbf{A}=\mathbf{J}_s+\nabla\times\dfrac{1}{\mathbf{v}_{0}}\mathbf{v}\mathbf{M}_{0} \]

where matrix invarient \(v_{e}\) is \(v_{e}=\frac{1}{3}\mathrm{tr}(v)=\frac{1}{3}(v_{11}+v_{22}+v_{33})\).

Edge-element magnetic vector potential

Due to the limitation of node-based vector magnetic potential algorithm2, WELSIM application uses the edge-based finite element for the magnetic vector potential algorithm.

The governing equation for the edge finite element method is given below.

\[ \nabla\times\mathbf{v}\nabla\times\mathbf{A}+\sigma\left\{ \dfrac{\partial\mathbf{A}}{\partial t}+\nabla V\right\} +\epsilon\left(\left\{ \dfrac{\partial^{2}\mathbf{A}}{\partial t^{2}}\right\} +\nabla\left\{ \dfrac{\partial V}{\partial t}\right\} \right)=\mathbf{0} \]
\[ \nabla\cdot\left(\sigma\left(\left\{ \dfrac{\partial\mathbf{A}}{\partial t}\right\} +\nabla V\right)+\epsilon\left(\left\{ \dfrac{\partial^{2}\mathbf{A}}{\partial t^{2}}\right\} +\nabla\left\{ \dfrac{\partial V}{\partial t}\right\} \right)\right)=\mathbf{0} \]
\[ \nabla\times\mathbf{v}\nabla\times\mathbf{A}=\mathbf{J}_{s}+\nabla\times\dfrac{1}{\mathbf{v}_{0}}\mathbf{v}\mathbf{M}_{0} \]

The uniqueness of these equations is ensured by the tree gauging procedure, which sets the edge-flux degrees of freedom related to the spanning tree of the finite element mesh to zero.

  1. John D. Jackson, Classical Electrodynamics, 3rd edition, Wiley. ↩

  2. Jian-Ming Jin, The Finite Element Method in Electromagnetics, 2nd edition, Wiley-IEEE Press. ↩↩

\ No newline at end of file +## Hall Effect -->

  1. John D. Jackson, Classical Electrodynamics, 3rd edition, Wiley. ↩

  2. Jian-Ming Jin, The Finite Element Method in Electromagnetics, 2nd edition, Wiley-IEEE Press. ↩↩

\ No newline at end of file diff --git a/welsim/theory/elements/index.html b/welsim/theory/elements/index.html index c5286b4..476dcb3 100755 --- a/welsim/theory/elements/index.html +++ b/welsim/theory/elements/index.html @@ -1 +1 @@ - Element library - WelSim Documentation
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Element library

The WELSIM application supports several types of finite elements. This section discuss the details of element that is used in the program.

Element type Finite element type Description
Plane element (Shell) Tri3 Three node triangular element
Plane element (Shell) Tri6 Six node triangular element(quadratic)
Solid element Tet4 Four node tetrahedral element
Solid element Tet10 Ten node tetrahedral element(quadratic)

The element groups shown in Table [tab:ch4_theory_elem_types] can be used for engineering analysis. The schematic views and the surface definition of those elements are given in Figures [fig:ch4_theory_elem_views], [fig:ch4_theory_elem_triangles], and [fig:ch4_theory_elem_tet].

finite_element_analysis_welsim_theory_element_tet

finite_element_analysis_welsim_theory_element_orientation1

Surface No. Linear Quadratic
1 1-2-3 [front] 1-6-2-4-3-5 [front]
2 3-2-1 [back] 3-4-2-6-1-5 [back]

finite_element_analysis_welsim_theory_element_orientation2

Surface No. Linear Quadratic
1 1-2-3 1-7-2-5-3-6
2 1-2-4 1-7-2-9-4-8
3 2-3-4 2-5-3-10-4-9
4 3-1-4 3-6-1-10-4-8
\ No newline at end of file + Element library - WelSim Documentation
Skip to content

Element library

The WELSIM application supports several types of finite elements. This section discuss the details of element that is used in the program.

Element type Finite element type Description
Plane element (Shell) Tri3 Three node triangular element
Plane element (Shell) Tri6 Six node triangular element(quadratic)
Solid element Tet4 Four node tetrahedral element
Solid element Tet10 Ten node tetrahedral element(quadratic)

The element groups shown in Table [tab:ch4_theory_elem_types] can be used for engineering analysis. The schematic views and the surface definition of those elements are given in Figures [fig:ch4_theory_elem_views], [fig:ch4_theory_elem_triangles], and [fig:ch4_theory_elem_tet].

finite_element_analysis_welsim_theory_element_tet

finite_element_analysis_welsim_theory_element_orientation1

Surface No. Linear Quadratic
1 1-2-3 [front] 1-6-2-4-3-5 [front]
2 3-2-1 [back] 3-4-2-6-1-5 [back]

finite_element_analysis_welsim_theory_element_orientation2

Surface No. Linear Quadratic
1 1-2-3 1-7-2-5-3-6
2 1-2-4 1-7-2-9-4-8
3 2-3-4 2-5-3-10-4-9
4 3-1-4 3-6-1-10-4-8
\ No newline at end of file diff --git a/welsim/theory/geometricnl/index.html b/welsim/theory/geometricnl/index.html index 6d079c4..f898db8 100755 --- a/welsim/theory/geometricnl/index.html +++ b/welsim/theory/geometricnl/index.html @@ -1 +1 @@ - Structures with geometric nonlinearity - WelSim Documentation
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Structures with geometric nonlinearity

In the analysis of finite deformation problems, the principle equation of virtual work becomes a nonlinear equation regarding the displacement-strain relation. To solve the nonlinear equation, an iterative algorithm is generally applied. When implementing an incremental analysis for a finite deformation problem, whether to refer to the initial status as a reference layout, or refer to the starting point of the increments can be selected. The former is called the total Lagrange method, and the latter is called the updated Lagrange method. Both the total Lagrange and updated Lagrange methods are available in the program. This section discusses the various geometrically nonlinear options available, including the large strain.

Decomposition of increments of virtual work equation

Given the solid deformation at time t is known, the status at time t'=t+\triangle t is unknown. The equilibrium equation, dynamic boundary condition, and external boundary condition can be expressed as

\[ \begin{align} \label{eq:ch5_nonlinear_gov1} \nabla_{t'\mathbf{x}}\cdot^{t'}\sigma+^{t'}\mathbf{b}=0\quad\text{in}V \end{align} \]
\[ ^{t'}\sigma\cdot^{t'}\mathbf{n}=^{t'}\mathbf{t}\quad\mathrm{on}\thinspace^{t'}S \]
\[ ^{t'}\mathbf{u}=^{t'}\bar{\mathbf{u}} \]

where \(^{t'}\sigma\), \(^{t'}\mathbf{b}\), \(^{t'}\mathbf{n}\), \(^{t'}\mathbf{t}\), \(^{t'}\mathbf{u}\) are the Cauchy stress, body force, outward normal vector of the object's surface, fixed surface force, and fixed displacement in each time t'.

Principle of virtual work

The principle of virtual work to the equation \(\eqref{eq:ch5_nonlinear_gov1}\) is

\[ \begin{align} \label{eq:ch5_nonlinear_gov2} \int_{^{t'}V}^{t'}\sigma:\delta^{t'}\mathbf{A}_{(L)}d^{t'}v=\int_{^{t'}S_{t}}^{t'}\mathbf{t}\cdot\delta\mathbf{u}d^{t'}s+\int_{V}^{t'}\mathbf{b}\cdot\delta\mathbf{u}d^{t'}v \end{align} \]

where \(^{t'}\mathbf{A}_{(L)}\) is the linear portion of the Almansi strain tensor and can be calculated by

\[ ^{t'}\mathbf{A}_{(L)}=\dfrac{1}{2}\{\dfrac{\partial^{t'}\mathbf{u}}{\partial^{t'}\mathbf{x}}+(\dfrac{\partial^{t'}\mathbf{u}}{\partial^{t'}\mathbf{x}})^{T}\} \]

The equation \(\eqref{eq:ch5_nonlinear_gov2}\) needs to be solved referring to layout V at time 0, or layout \(^{t}v\) at time t. The following sections will introduce these two algorithms: total Lagrange method and updated Lagrange method, respectively.

Formulation of total lagrange algorithm

The principle equation of the virtual work at time t' assuming the initial layout of time 0 is the reference domain, which is shown below.

\[ \begin{align} \label{eq:ch5_nonlinear_total_lag_gov1} \intop_{V}\thinspace_{0}^{t'}\mathbf{S}:\delta_{0}^{t'}\mathbf{E}dV=^{t'}\delta\mathbf{R} \end{align} \]
\[ \begin{align} \label{eq:ch5_nonlinear_total_lag_gov2} ^{t'}\delta\mathbf{R}=\intop_{S_{t}}\thinspace_{0}^{t'}\mathbf{t}\cdot\delta dS+\intop_{V}\thinspace_{0}^{t'}\mathbf{b}\cdot\delta\mathbf{u}dV \end{align} \]

where \(_{0}^{t'}\mathbf{S}\) and \(_{0}^{t'}\mathbf{E}\) are the 2nd order Piola-Kirchhoff stress tensor and the Green-Lagrange strain tensor at time t', respectively. The initial domain at time 0 is called the reference domain. The body force \(_{0}^{t'}\mathbf{b}\) and nominal surface force vector \(_{0}^{t'}\mathbf{t}\) are

\[ _{0}^{t'}\mathbf{t}=\dfrac{d^{t'}s}{dS}\thinspace^{t'}\mathbf{t} \]
\[ _{0}^{t'}\mathbf{b}=\dfrac{d^{t'}v}{dV}\thinspace^{t'}\mathbf{b} \]

The Green-Lagrange strain tensor at time t is defined by

\[ _{0}^{t}\mathbf{E}=\dfrac{1}{2}\{\dfrac{\partial^{t}\mathbf{u}}{\partial\mathbf{X}}+(\dfrac{\partial^{t}\mathbf{u}}{\partial\mathbf{X}})^{T}+(\dfrac{\partial^{t}\mathbf{u}}{\partial\mathbf{X}})^{T}\cdot\dfrac{\partial^{t}\mathbf{u}}{\partial\mathbf{X}}\} \]

Then the displacement \(^{t'}\mathbf{u}\) and 2nd order Piola-Kirchhoff stress \(_{0}^{t'}\mathbf{S}\) at time t' are

\[ \begin{align} \label{eq:ch5_nonlinear_total_lag_gov3} ^{t'}\mathbf{u}=^{t}\mathbf{u}+\triangle\mathbf{u} \end{align} \]
\[ \begin{align} \label{eq:ch5_nonlinear_total_lag_gov4} _{0}^{t'}\mathbf{S}=_{0}^{t}\mathbf{S}+\triangle\mathbf{S} \end{align} \]

Similarly, the incremental Green-Lagrange strain can be defined as

\[ \begin{align} \label{eq:ch5_nonlinear_total_lag_gov5} ^{t'}\mathbf{E}=^{t}\mathbf{E}+\triangle\mathbf{E} \end{align} \]
\[ \begin{align} \label{eq:ch5_nonlinear_total_lag_gov6} \triangle\mathbf{E}=\triangle\mathbf{E}_{L}+\triangle\mathbf{E}_{NL} \end{align} \]

where

\[ \triangle\mathbf{E}_{L}=\dfrac{1}{2}\{\dfrac{\partial\triangle\mathbf{u}}{\partial\mathbf{X}}+(\dfrac{\partial\triangle\mathbf{u}}{\partial\mathbf{X}})^{T}+(\dfrac{\partial\triangle\mathbf{u}}{\partial\mathbf{X}})^{T}\cdot\dfrac{\partial^{t}\mathbf{u}}{\partial\mathbf{X}}+(\dfrac{\partial^{t}\mathbf{u}}{\partial\mathbf{X}})^{T}\cdot\dfrac{\partial\triangle\mathbf{u}}{\partial\mathbf{X}}\} \]
\[ \triangle\mathbf{E}_{NL}=\dfrac{1}{2}(\dfrac{\partial\triangle\mathbf{u}}{\partial\mathbf{X}})^{T}\cdot\dfrac{\partial\triangle\mathbf{u}}{\partial\mathbf{X}} \]

Substituting equations \(\eqref{eq:ch5_nonlinear_total_lag_gov3}\), \(\eqref{eq:ch5_nonlinear_total_lag_gov4}\), \(\eqref{eq:ch5_nonlinear_total_lag_gov5}\), and \(\eqref{eq:ch5_nonlinear_total_lag_gov6}\) into governing equations \(\eqref{eq:ch5_nonlinear_total_lag_gov1}\) and \(\eqref{eq:ch5_nonlinear_total_lag_gov2}\), we have

\[ \intop_{v}\triangle\mathbf{S}:(\delta\triangle\mathbf{E}_{L}+\delta\triangle\mathbf{E}_{NL})dV+\intop_{V}\thinspace_{0}^{t}\mathbf{S}\colon\delta\triangle\mathbf{E}_{NL}dV=^{t'}\delta\mathbf{R}-\intop_{V}\thinspace_{0}^{t}\mathbf{S}:\delta\triangle\mathbf{E}_{L}dV \]

where \(\triangle\mathbf{S}\) is assumed to be

\[ \triangle\mathbf{S}=_{0}^{t}\mathbf{C}\colon\triangle\mathbf{E}_{L} \]

then we have

\[ \begin{align} \label{eq:ch5_nonlinear_total_lag_gov7} \intop_{v}(\mathbf{C}\colon\triangle\mathbf{E}):\delta\triangle\mathbf{E}_{L}dV+\intop_{V}\thinspace_{0}^{t}\mathbf{S}\colon\delta\triangle\mathbf{E}_{NL}dV=^{t'}\delta\mathbf{R}-\intop_{V}\thinspace_{0}^{t}\mathbf{S}:\delta\triangle\mathbf{E}_{L}dV \end{align} \]

Equation \(\eqref{eq:ch5_nonlinear_total_lag_gov7}\) can be discreted to finite element formulation

\[ \delta\mathbf{U}^{T}(_{0}^{t}\mathbf{K}_{L}+{}_{0}^{t}\mathbf{K}_{NL})\triangle\mathbf{U}=\delta\mathbf{U}^{T}\thinspace_{0}^{t'}\mathbf{F}-\delta\mathbf{\mathbf{U}}^{T}\thinspace_{0}^{t'}\mathbf{Q} \]

where \(_{0}^{t}\mathbf{K}_{L}\), \(_{0}^{t}\mathbf{K}_{NL}\), \(_{0}^{t'}\mathbf{F}\), \(_{0}^{t}\mathbf{Q}\) are the initial material stiffness matrix, initial geometric stiffness (stress) matrix, external force vector, and internal force vector, respectively. The recursive algorithm to calculate the deformation status at time t' from time t is given:

Step 1: i = 0

\[ \quad\quad_{0}^{t'}\mathbf{K}^{(0)}=_{0}^{t}\mathbf{K}_{L}+_{0}^{t}\mathbf{K}_{NL} \]
\[ \quad\quad_{0}^{t'}\mathbf{Q}^{(0)}=_{0}^{t}\mathbf{Q} \]
\[ \quad\quad^{t'}\mathbf{U}^{(0)}=^{t}\mathbf{U} \]

Step 2:

\[ \quad\quad_{0}^{t'}\mathbf{K}^{(i)}\triangle\mathbf{U}^{(i)}=_{0}^{t'}\mathbf{F}-_{0}^{t'}\mathbf{Q}^{(i-1)} \]

Step 3:

\[ \quad\quad^{t'}\mathbf{U}^{(i)}=^{t'}\mathbf{U}^{(i-1)}+\triangle\mathbf{U}^{(i)} \]

Formulation of updated lagrange algorithm

In addition to the total Lagrange algorithm, the updated Lagrange algorithm is also widely applied in the nonlinear structural model computation. The principle virtual work equation at time t' uses the current domain at time t as reference domain.

\[ \begin{align} \label{eq:ch5_nonlinear_updated_lag_gov1} \intop_{V}\thinspace_{t}^{t'}\mathbf{S}:\delta_{t}^{t'}\mathbf{E}dV=^{t'}\delta\mathbf{R} \end{align} \]
\[ \begin{align} \label{eq:ch5_nonlinear_updated_lag_gov2} ^{t'}\delta\mathbf{R}=\intop_{S_{t}}\thinspace_{t}^{t'}\mathbf{t}\cdot\delta dS+\intop_{V}\thinspace_{t}^{t'}\mathbf{b}\cdot\delta\mathbf{u}dV \end{align} \]

where

\[ _{t}^{t'}\mathbf{t}=\dfrac{d^{t'}s}{d^{t}s}\thinspace^{t'}\mathbf{t} \]
\[ _{t}^{t'}\mathbf{b}=\dfrac{d^{t'}v}{d^{t}v}\thinspace^{t'}\mathbf{b} \]

The tensors \(_{t}^{t'}\mathbf{S}\), \(_{t}^{t'}\mathbf{E}\) and vectors \(_{t}^{t'}\mathbf{t}\), \(_{t}^{t'}\mathbf{b}\) are using the current time domain t as the reference domain. Therefore, the Green-Lagrange strain does not contain the initial displacement (the displacement at the time t) \(^{t}\mathbf{u}\);

\[ \begin{align} \label{eq:ch5_nonlinear_updated_lag_gov3} _{t}^{t'}\mathbf{E}=\triangle_{t}\mathbf{E}_{L}+\triangle_{t}\mathbf{E}_{NL} \end{align} \]

where

\[ \begin{align} \label{eq:ch5_nonlinear_updated_lag_gov4} \triangle_{t}\mathbf{E}_{L}=\dfrac{1}{2}\{\dfrac{\partial\triangle\mathbf{u}}{\partial^{t}x}+(\dfrac{\partial\triangle\mathbf{u}}{\partial^{t}x})^{T}\} \end{align} \]
\[ \begin{align} \label{eq:ch5_nonlinear_updated_lag_gov5} \triangle_{t}\mathbf{E}_{NL}=\dfrac{1}{2}(\dfrac{\partial\triangle\mathbf{u}}{\partial^{t}x})^{T}\cdot\dfrac{\partial\triangle\mathbf{u}}{\partial^{t}x} \end{align} \]

Similarly,

\[ _{t}^{t'}\mathbf{S}=_{t}^{t}\mathbf{S}+\triangle_{t}\mathbf{S} \]

Substituting equations \(\eqref{eq:ch5_nonlinear_updated_lag_gov3}\) and \(\eqref{eq:ch5_nonlinear_updated_lag_gov2}\) into governing equations \(\eqref{eq:ch5_nonlinear_updated_lag_gov1}\), we have

\[ \intop_{^{t}v}\triangle_{t}\mathbf{S}:(\delta\triangle_{t}\mathbf{E}_{L}+\delta\triangle_{t}\mathbf{E}_{NL})d^{t}v+\intop_{V}\thinspace_{t}^{t}\mathbf{S}\colon\delta\triangle_{t}\mathbf{E}_{NL}d^{t}v=^{t'}\delta\mathbf{R}-\intop_{^{t}v}\thinspace_{t}^{t}\mathbf{S}:\delta\triangle_{t}\mathbf{E}_{L}d^{t}v \]

where \(\triangle_{t}\mathbf{S}\) is assumed to be

\[ \triangle_{t}\mathbf{S}=_{t}^{t}\mathbf{C}\colon\triangle_{t}\mathbf{E}_{L} \]

then we have

\[ \begin{align} \label{eq:ch5_nonlinear_updated_lag_gov7} \intop_{v}(\mathbf{C}\colon\triangle t\mathbf{E}_{L}):\delta\triangle_{t}\mathbf{E}_{L}dV+\intop_{V}\thinspace_{t}^{t}\mathbf{S}\colon\delta\triangle_{t}\mathbf{E}_{NL}dV=^{t'}\delta\mathbf{R}-\intop_{V}\thinspace_{t}^{t}\mathbf{S}:\delta\triangle_{t}\mathbf{E}_{L}dV \end{align} \]

Equation \(\eqref{eq:ch5_nonlinear_updated_lag_gov7}\) can be discreted to finite element formulation

\[ \delta\mathbf{U}^{T}(_{t}^{t}\mathbf{K}_{L}+{}_{t}^{t}\mathbf{K}_{NL})\triangle\mathbf{U}=\delta\mathbf{U}^{T}\thinspace_{t}^{t'}\mathbf{F}-\delta\mathbf{\mathbf{U}}^{T}\thinspace_{t}^{t'}\mathbf{Q} \]

where \(_{t}^{t}\mathbf{K}_{L}\), \(_{t}^{t}\mathbf{K}_{NL}\), \(_{t}^{t'}\mathbf{F}\), \(_{t}^{t}\mathbf{Q}\) are the initial material stiffness matrix, initial geometric stiffness (stress) matrix, external force vector, and internal force vector, respectively. The recursive algorithm to calculate the deformation status at time t' from time t is given:

Step 1: i = 0

\[ \quad\quad_{t}^{t'}\mathbf{K}^{(i)}=_{t}^{t}\mathbf{K}_{L}+_{t}^{t}\mathbf{K}_{NL} \]
\[ \quad\quad_{t}^{t'}\mathbf{Q}^{(i)}=_{t}^{t}\mathbf{Q} \]
\[ \quad\quad^{t'}\mathbf{U}^{(i)}=^{t}\mathbf{U} \]

Step 2:

\[ \quad\quad_{0}^{t'}\mathbf{K}^{(i)}\triangle\mathbf{U}^{(i)}=_{0}^{t'}\mathbf{F}-_{0}^{t'}\mathbf{Q}^{(i-1)} \]

Step 3:

\[ \quad\quad^{t'}\mathbf{U}^{(i)}=^{t'}\mathbf{U}^{(i-1)}+\triangle\mathbf{U}^{(i)} \]
\ No newline at end of file + Structures with geometric nonlinearity - WelSim Documentation
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Structures with geometric nonlinearity

In the analysis of finite deformation problems, the principle equation of virtual work becomes a nonlinear equation regarding the displacement-strain relation. To solve the nonlinear equation, an iterative algorithm is generally applied. When implementing an incremental analysis for a finite deformation problem, whether to refer to the initial status as a reference layout, or refer to the starting point of the increments can be selected. The former is called the total Lagrange method, and the latter is called the updated Lagrange method. Both the total Lagrange and updated Lagrange methods are available in the program. This section discusses the various geometrically nonlinear options available, including the large strain.

Decomposition of increments of virtual work equation

Given the solid deformation at time t is known, the status at time t'=t+\triangle t is unknown. The equilibrium equation, dynamic boundary condition, and external boundary condition can be expressed as

\[ \begin{align} \label{eq:ch5_nonlinear_gov1} \nabla_{t'\mathbf{x}}\cdot^{t'}\sigma+^{t'}\mathbf{b}=0\quad\text{in}V \end{align} \]
\[ ^{t'}\sigma\cdot^{t'}\mathbf{n}=^{t'}\mathbf{t}\quad\mathrm{on}\thinspace^{t'}S \]
\[ ^{t'}\mathbf{u}=^{t'}\bar{\mathbf{u}} \]

where \(^{t'}\sigma\), \(^{t'}\mathbf{b}\), \(^{t'}\mathbf{n}\), \(^{t'}\mathbf{t}\), \(^{t'}\mathbf{u}\) are the Cauchy stress, body force, outward normal vector of the object's surface, fixed surface force, and fixed displacement in each time t'.

Principle of virtual work

The principle of virtual work to the equation \(\eqref{eq:ch5_nonlinear_gov1}\) is

\[ \begin{align} \label{eq:ch5_nonlinear_gov2} \int_{^{t'}V}^{t'}\sigma:\delta^{t'}\mathbf{A}_{(L)}d^{t'}v=\int_{^{t'}S_{t}}^{t'}\mathbf{t}\cdot\delta\mathbf{u}d^{t'}s+\int_{V}^{t'}\mathbf{b}\cdot\delta\mathbf{u}d^{t'}v \end{align} \]

where \(^{t'}\mathbf{A}_{(L)}\) is the linear portion of the Almansi strain tensor and can be calculated by

\[ ^{t'}\mathbf{A}_{(L)}=\dfrac{1}{2}\{\dfrac{\partial^{t'}\mathbf{u}}{\partial^{t'}\mathbf{x}}+(\dfrac{\partial^{t'}\mathbf{u}}{\partial^{t'}\mathbf{x}})^{T}\} \]

The equation \(\eqref{eq:ch5_nonlinear_gov2}\) needs to be solved referring to layout V at time 0, or layout \(^{t}v\) at time t. The following sections will introduce these two algorithms: total Lagrange method and updated Lagrange method, respectively.

Formulation of total lagrange algorithm

The principle equation of the virtual work at time t' assuming the initial layout of time 0 is the reference domain, which is shown below.

\[ \begin{align} \label{eq:ch5_nonlinear_total_lag_gov1} \intop_{V}\thinspace_{0}^{t'}\mathbf{S}:\delta_{0}^{t'}\mathbf{E}dV=^{t'}\delta\mathbf{R} \end{align} \]
\[ \begin{align} \label{eq:ch5_nonlinear_total_lag_gov2} ^{t'}\delta\mathbf{R}=\intop_{S_{t}}\thinspace_{0}^{t'}\mathbf{t}\cdot\delta dS+\intop_{V}\thinspace_{0}^{t'}\mathbf{b}\cdot\delta\mathbf{u}dV \end{align} \]

where \(_{0}^{t'}\mathbf{S}\) and \(_{0}^{t'}\mathbf{E}\) are the 2nd order Piola-Kirchhoff stress tensor and the Green-Lagrange strain tensor at time t', respectively. The initial domain at time 0 is called the reference domain. The body force \(_{0}^{t'}\mathbf{b}\) and nominal surface force vector \(_{0}^{t'}\mathbf{t}\) are

\[ _{0}^{t'}\mathbf{t}=\dfrac{d^{t'}s}{dS}\thinspace^{t'}\mathbf{t} \]
\[ _{0}^{t'}\mathbf{b}=\dfrac{d^{t'}v}{dV}\thinspace^{t'}\mathbf{b} \]

The Green-Lagrange strain tensor at time t is defined by

\[ _{0}^{t}\mathbf{E}=\dfrac{1}{2}\{\dfrac{\partial^{t}\mathbf{u}}{\partial\mathbf{X}}+(\dfrac{\partial^{t}\mathbf{u}}{\partial\mathbf{X}})^{T}+(\dfrac{\partial^{t}\mathbf{u}}{\partial\mathbf{X}})^{T}\cdot\dfrac{\partial^{t}\mathbf{u}}{\partial\mathbf{X}}\} \]

Then the displacement \(^{t'}\mathbf{u}\) and 2nd order Piola-Kirchhoff stress \(_{0}^{t'}\mathbf{S}\) at time t' are

\[ \begin{align} \label{eq:ch5_nonlinear_total_lag_gov3} ^{t'}\mathbf{u}=^{t}\mathbf{u}+\triangle\mathbf{u} \end{align} \]
\[ \begin{align} \label{eq:ch5_nonlinear_total_lag_gov4} _{0}^{t'}\mathbf{S}=_{0}^{t}\mathbf{S}+\triangle\mathbf{S} \end{align} \]

Similarly, the incremental Green-Lagrange strain can be defined as

\[ \begin{align} \label{eq:ch5_nonlinear_total_lag_gov5} ^{t'}\mathbf{E}=^{t}\mathbf{E}+\triangle\mathbf{E} \end{align} \]
\[ \begin{align} \label{eq:ch5_nonlinear_total_lag_gov6} \triangle\mathbf{E}=\triangle\mathbf{E}_{L}+\triangle\mathbf{E}_{NL} \end{align} \]

where

\[ \triangle\mathbf{E}_{L}=\dfrac{1}{2}\{\dfrac{\partial\triangle\mathbf{u}}{\partial\mathbf{X}}+(\dfrac{\partial\triangle\mathbf{u}}{\partial\mathbf{X}})^{T}+(\dfrac{\partial\triangle\mathbf{u}}{\partial\mathbf{X}})^{T}\cdot\dfrac{\partial^{t}\mathbf{u}}{\partial\mathbf{X}}+(\dfrac{\partial^{t}\mathbf{u}}{\partial\mathbf{X}})^{T}\cdot\dfrac{\partial\triangle\mathbf{u}}{\partial\mathbf{X}}\} \]
\[ \triangle\mathbf{E}_{NL}=\dfrac{1}{2}(\dfrac{\partial\triangle\mathbf{u}}{\partial\mathbf{X}})^{T}\cdot\dfrac{\partial\triangle\mathbf{u}}{\partial\mathbf{X}} \]

Substituting equations \(\eqref{eq:ch5_nonlinear_total_lag_gov3}\), \(\eqref{eq:ch5_nonlinear_total_lag_gov4}\), \(\eqref{eq:ch5_nonlinear_total_lag_gov5}\), and \(\eqref{eq:ch5_nonlinear_total_lag_gov6}\) into governing equations \(\eqref{eq:ch5_nonlinear_total_lag_gov1}\) and \(\eqref{eq:ch5_nonlinear_total_lag_gov2}\), we have

\[ \intop_{v}\triangle\mathbf{S}:(\delta\triangle\mathbf{E}_{L}+\delta\triangle\mathbf{E}_{NL})dV+\intop_{V}\thinspace_{0}^{t}\mathbf{S}\colon\delta\triangle\mathbf{E}_{NL}dV=^{t'}\delta\mathbf{R}-\intop_{V}\thinspace_{0}^{t}\mathbf{S}:\delta\triangle\mathbf{E}_{L}dV \]

where \(\triangle\mathbf{S}\) is assumed to be

\[ \triangle\mathbf{S}=_{0}^{t}\mathbf{C}\colon\triangle\mathbf{E}_{L} \]

then we have

\[ \begin{align} \label{eq:ch5_nonlinear_total_lag_gov7} \intop_{v}(\mathbf{C}\colon\triangle\mathbf{E}):\delta\triangle\mathbf{E}_{L}dV+\intop_{V}\thinspace_{0}^{t}\mathbf{S}\colon\delta\triangle\mathbf{E}_{NL}dV=^{t'}\delta\mathbf{R}-\intop_{V}\thinspace_{0}^{t}\mathbf{S}:\delta\triangle\mathbf{E}_{L}dV \end{align} \]

Equation \(\eqref{eq:ch5_nonlinear_total_lag_gov7}\) can be discreted to finite element formulation

\[ \delta\mathbf{U}^{T}(_{0}^{t}\mathbf{K}_{L}+{}_{0}^{t}\mathbf{K}_{NL})\triangle\mathbf{U}=\delta\mathbf{U}^{T}\thinspace_{0}^{t'}\mathbf{F}-\delta\mathbf{\mathbf{U}}^{T}\thinspace_{0}^{t'}\mathbf{Q} \]

where \(_{0}^{t}\mathbf{K}_{L}\), \(_{0}^{t}\mathbf{K}_{NL}\), \(_{0}^{t'}\mathbf{F}\), \(_{0}^{t}\mathbf{Q}\) are the initial material stiffness matrix, initial geometric stiffness (stress) matrix, external force vector, and internal force vector, respectively. The recursive algorithm to calculate the deformation status at time t' from time t is given:

Step 1: i = 0

\[ \quad\quad_{0}^{t'}\mathbf{K}^{(0)}=_{0}^{t}\mathbf{K}_{L}+_{0}^{t}\mathbf{K}_{NL} \]
\[ \quad\quad_{0}^{t'}\mathbf{Q}^{(0)}=_{0}^{t}\mathbf{Q} \]
\[ \quad\quad^{t'}\mathbf{U}^{(0)}=^{t}\mathbf{U} \]

Step 2:

\[ \quad\quad_{0}^{t'}\mathbf{K}^{(i)}\triangle\mathbf{U}^{(i)}=_{0}^{t'}\mathbf{F}-_{0}^{t'}\mathbf{Q}^{(i-1)} \]

Step 3:

\[ \quad\quad^{t'}\mathbf{U}^{(i)}=^{t'}\mathbf{U}^{(i-1)}+\triangle\mathbf{U}^{(i)} \]

Formulation of updated lagrange algorithm

In addition to the total Lagrange algorithm, the updated Lagrange algorithm is also widely applied in the nonlinear structural model computation. The principle virtual work equation at time t' uses the current domain at time t as reference domain.

\[ \begin{align} \label{eq:ch5_nonlinear_updated_lag_gov1} \intop_{V}\thinspace_{t}^{t'}\mathbf{S}:\delta_{t}^{t'}\mathbf{E}dV=^{t'}\delta\mathbf{R} \end{align} \]
\[ \begin{align} \label{eq:ch5_nonlinear_updated_lag_gov2} ^{t'}\delta\mathbf{R}=\intop_{S_{t}}\thinspace_{t}^{t'}\mathbf{t}\cdot\delta dS+\intop_{V}\thinspace_{t}^{t'}\mathbf{b}\cdot\delta\mathbf{u}dV \end{align} \]

where

\[ _{t}^{t'}\mathbf{t}=\dfrac{d^{t'}s}{d^{t}s}\thinspace^{t'}\mathbf{t} \]
\[ _{t}^{t'}\mathbf{b}=\dfrac{d^{t'}v}{d^{t}v}\thinspace^{t'}\mathbf{b} \]

The tensors \(_{t}^{t'}\mathbf{S}\), \(_{t}^{t'}\mathbf{E}\) and vectors \(_{t}^{t'}\mathbf{t}\), \(_{t}^{t'}\mathbf{b}\) are using the current time domain t as the reference domain. Therefore, the Green-Lagrange strain does not contain the initial displacement (the displacement at the time t) \(^{t}\mathbf{u}\);

\[ \begin{align} \label{eq:ch5_nonlinear_updated_lag_gov3} _{t}^{t'}\mathbf{E}=\triangle_{t}\mathbf{E}_{L}+\triangle_{t}\mathbf{E}_{NL} \end{align} \]

where

\[ \begin{align} \label{eq:ch5_nonlinear_updated_lag_gov4} \triangle_{t}\mathbf{E}_{L}=\dfrac{1}{2}\{\dfrac{\partial\triangle\mathbf{u}}{\partial^{t}x}+(\dfrac{\partial\triangle\mathbf{u}}{\partial^{t}x})^{T}\} \end{align} \]
\[ \begin{align} \label{eq:ch5_nonlinear_updated_lag_gov5} \triangle_{t}\mathbf{E}_{NL}=\dfrac{1}{2}(\dfrac{\partial\triangle\mathbf{u}}{\partial^{t}x})^{T}\cdot\dfrac{\partial\triangle\mathbf{u}}{\partial^{t}x} \end{align} \]

Similarly,

\[ _{t}^{t'}\mathbf{S}=_{t}^{t}\mathbf{S}+\triangle_{t}\mathbf{S} \]

Substituting equations \(\eqref{eq:ch5_nonlinear_updated_lag_gov3}\) and \(\eqref{eq:ch5_nonlinear_updated_lag_gov2}\) into governing equations \(\eqref{eq:ch5_nonlinear_updated_lag_gov1}\), we have

\[ \intop_{^{t}v}\triangle_{t}\mathbf{S}:(\delta\triangle_{t}\mathbf{E}_{L}+\delta\triangle_{t}\mathbf{E}_{NL})d^{t}v+\intop_{V}\thinspace_{t}^{t}\mathbf{S}\colon\delta\triangle_{t}\mathbf{E}_{NL}d^{t}v=^{t'}\delta\mathbf{R}-\intop_{^{t}v}\thinspace_{t}^{t}\mathbf{S}:\delta\triangle_{t}\mathbf{E}_{L}d^{t}v \]

where \(\triangle_{t}\mathbf{S}\) is assumed to be

\[ \triangle_{t}\mathbf{S}=_{t}^{t}\mathbf{C}\colon\triangle_{t}\mathbf{E}_{L} \]

then we have

\[ \begin{align} \label{eq:ch5_nonlinear_updated_lag_gov7} \intop_{v}(\mathbf{C}\colon\triangle t\mathbf{E}_{L}):\delta\triangle_{t}\mathbf{E}_{L}dV+\intop_{V}\thinspace_{t}^{t}\mathbf{S}\colon\delta\triangle_{t}\mathbf{E}_{NL}dV=^{t'}\delta\mathbf{R}-\intop_{V}\thinspace_{t}^{t}\mathbf{S}:\delta\triangle_{t}\mathbf{E}_{L}dV \end{align} \]

Equation \(\eqref{eq:ch5_nonlinear_updated_lag_gov7}\) can be discreted to finite element formulation

\[ \delta\mathbf{U}^{T}(_{t}^{t}\mathbf{K}_{L}+{}_{t}^{t}\mathbf{K}_{NL})\triangle\mathbf{U}=\delta\mathbf{U}^{T}\thinspace_{t}^{t'}\mathbf{F}-\delta\mathbf{\mathbf{U}}^{T}\thinspace_{t}^{t'}\mathbf{Q} \]

where \(_{t}^{t}\mathbf{K}_{L}\), \(_{t}^{t}\mathbf{K}_{NL}\), \(_{t}^{t'}\mathbf{F}\), \(_{t}^{t}\mathbf{Q}\) are the initial material stiffness matrix, initial geometric stiffness (stress) matrix, external force vector, and internal force vector, respectively. The recursive algorithm to calculate the deformation status at time t' from time t is given:

Step 1: i = 0

\[ \quad\quad_{t}^{t'}\mathbf{K}^{(i)}=_{t}^{t}\mathbf{K}_{L}+_{t}^{t}\mathbf{K}_{NL} \]
\[ \quad\quad_{t}^{t'}\mathbf{Q}^{(i)}=_{t}^{t}\mathbf{Q} \]
\[ \quad\quad^{t'}\mathbf{U}^{(i)}=^{t}\mathbf{U} \]

Step 2:

\[ \quad\quad_{0}^{t'}\mathbf{K}^{(i)}\triangle\mathbf{U}^{(i)}=_{0}^{t'}\mathbf{F}-_{0}^{t'}\mathbf{Q}^{(i-1)} \]

Step 3:

\[ \quad\quad^{t'}\mathbf{U}^{(i)}=^{t'}\mathbf{U}^{(i-1)}+\triangle\mathbf{U}^{(i)} \]
\ No newline at end of file diff --git a/welsim/theory/introduction/index.html b/welsim/theory/introduction/index.html index 7238d58..53e9e7a 100755 --- a/welsim/theory/introduction/index.html +++ b/welsim/theory/introduction/index.html @@ -1 +1 @@ - Introduction - WelSim Documentation
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Introduction

This theory reference presents theoretical descriptions of all algorithms, as well as many procedures and elements used in these products. It is useful to any of our users who need to understand how the software program calculates the output based on the inputs.

\ No newline at end of file + Introduction - WelSim Documentation
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Introduction

This theory reference presents theoretical descriptions of all algorithms, as well as many procedures and elements used in these products. It is useful to any of our users who need to understand how the software program calculates the output based on the inputs.

\ No newline at end of file diff --git a/welsim/theory/materialnl/index.html b/welsim/theory/materialnl/index.html index 6258ecd..8a85b74 100755 --- a/welsim/theory/materialnl/index.html +++ b/welsim/theory/materialnl/index.html @@ -1 +1 @@ - Structures with material nonlinearities - WelSim Documentation
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Structures with material nonlinearities

Material nonlinearities occur because of the nonlinear relationship between stress and strain; that is, the stress is a nonlinear function of the strain. The relationship is also path-dependent (except for the case of nonlinear elasticity and hyperelasticity), so that the stress depends on the strain history as well as the strain itself.

The program can account for many material nonlinearities, as follows:

  1. Rate-independent plasticity is characterized by the irreversible instantaneous straining that occurs in a material.

  2. Rate-dependent plasticity allows the plastic-strains to develop over a time interval. It is also termed viscoplasticity.

  3. Creep is also an irreversible straining that occurs in a material and is rate-dependent so that the strains develop over time. The time frame for creep is usually much larger than that for rate-dependent plasticity.

  4. Nonlinear elasticity allows a nonlinear stress-strain relationship to be specified. All straining is reversible.

  5. Hyperelasticity is defined by a strain-energy density potential that characterizes elastomeric and foam-type materials. All straining is reversible.

  6. Viscoelasticity is a rate-dependent material characterization that includes a viscous contribution to the elastic straining.

When the material applicable for analysis is an elastoplastic material, the updated Lagrange method is applied, and the total Lagrange method is applied for hyperelastic material. Moreover, the Newton-Raphson method is applied to the repetitive analysis method.

Strain definitions

For the case of nonlinear materials, the definition of elastic strain given in Equation \(\eqref{eq:ch4_theory_stress_strain_relation}\) expands to

\[ \begin{align} \label{eq:ch4_guide_strain_full} \{\epsilon\}=\{\epsilon^{el}\}+\{\epsilon^{th}\}+\{e^{pl}\}+\{\epsilon^{cr}\}+\{\epsilon^{sw}\} \end{align} \]

where \(\epsilon\) is the total strain vector, \(\epsilon^{el}\) is elastic strain vector, \(\epsilon^{th}\) is the thermal strain vector, \(\epsilon^{pl}\) is the plastic strain vector, \(\epsilon^{cr}\) is the creep strain vector, and \(\epsilon^{sw}\) is the swelling strain vector.

Hyperelasticity

The elastic potential energy in hyperelastic material can be obtained from the initial state with no stress activation. Therefore, we have the main invariable terms of the right Cauchy-Green deformation tensor C(\(I_{1}\), \(I_{2}\), \(I_{3}\)), or the main invariable of the deformation tensor excluding the volume changes (\(\bar{I}_{1}\), \(\bar{I}_{2}\), \(\bar{I}_{3}\)). The potential can be expressed as \(\mathbf{W}=\mathbf{W}(I_{1},I_{2},I_{3})\), or \(\mathbf{W}=\mathbf{W}(\bar{I}_{1},\bar{I}_{2},\bar{I}_{3})\).

The nonlinear constitutive relation of hyperelastic material is defined by the relation between the second order Piola-Kirchhoff stress and the Green-Lagrange strain, the total Lagrange method is more efficient in solving such models.

When the elastic potential energy \(W\) of the hyperelasticity is known, the second Piola-Kirchhoff stress and strain-stress relationship can be calculated as follows

\[ S=2\dfrac{\partial W}{\partial C} \]
\[ C=4\dfrac{\partial^{2}W}{\partial C\partial C} \]

Arruda-Boyce model

The form of the strain-energy potential for Arruda-Boyce model is

\[ \begin{array}{ccc} W & = & [\dfrac{1}{2}(\bar{I}_{1}-3)+\dfrac{1}{20\lambda_{m}^{2}}(\bar{I_{1}^{2}}-9)+\dfrac{11}{1050\lambda_{m}^{4}}(\bar{I_{1}^{3}}-27)\\ & + & \dfrac{19}{7000\lambda_{m}^{6}}(\bar{I_{1}^{4}}-81)+\dfrac{519}{673750\lambda_{m}^{8}}(\bar{I_{1}^{5}}-243)]+\dfrac{1}{D_1}(\dfrac{J^{2}-1}{2}-\mathrm{ln}J) \end{array} \]

where \(\lambda_{m}\) is limiting network stretch, and \(D_1\) is the material incompressibility parameter.

The initial shear modulus is

\[ \mu=\dfrac{\mu_{0}}{1+\dfrac{3}{5\lambda_{m}^{2}}+\dfrac{99}{175\lambda_{m}^{4}}+\dfrac{513}{875\lambda_{m}^{6}}+\dfrac{42039}{67375\lambda_{m}^{8}}} \]

The initial bulk modulus is

\[ K=\dfrac{2}{D_1} \]

As the parameter \(\lambda_L\) goes to infinity, the model is equivalent to neo-Hookean form.

Blatz-Ko foam model

The form of strain-energy potential for the Blatz-Ko model is:

\[ W=\frac{\mu}{2}\left(\frac{I_{2}}{I_{3}}+2\sqrt{I_{3}}-5\right) \]

where \(\mu\) is initla shear modulus of material. The initial bulk modulus is defined as :

\[ K = \frac{5}{3}\mu \]

Extended tube model

The elastic strain-energy potential for the extended tube model is:

\[ \begin{array}{ccc} W & = & \frac{G_{c}}{2}\left[\frac{\left(1-\delta^{2}\right)\left(\bar{I}_{1}-3\right)}{1-\delta^{2}\left(\bar{I}_{1}-3\right)}+\mathrm{ln}\left(1-\delta^{2}\left(\bar{I}_{1}-3\right)\right)\right]\\ & + & \frac{2G_{e}}{\beta^{2}}\sum_{i=1}^{3}\left(\bar{\lambda}_{i}^{-\beta}-1\right)+\frac{1}{D_1}\left(J-1\right)^{2} \end{array} \]

where the initial shear modulus is \(G\)=\(G_c\) + \(G_e\), and \(G_e\) is constraint contribution to modulus, \(G_c\) is crosslinked contribution to modulus, \(\delta\) is extensibility parameter, \(\beta\) is empirical parameter (0\(\leq \beta \leq\)1), and \(D_1\) is material incompressibility parameter.

Extended tube model is equivalent ot a two-term Ogden model with the following parameters:

\[ \begin{array}{cccc} \alpha_1 = 2 &, & \alpha_2=-\beta\\ \mu_1=G_c &, & \mu_2=-\dfrac{2}{\beta}G_e, & \delta=0 \end{array} \]

Gent model

The form of the strian-energy potential for the Gent model is:

\[ W=-\frac{\mu J_{m}}{2}\mathrm{ln}\left(1-\frac{\bar{I}_{1}-3}{J_{m}}\right)+\frac{1}{D_1}\left(\frac{J^{2}-1}{2}-\mathrm{ln}J\right) \]

where \(\mu\) is initial shear modulus of material, \(J_m\) is limiting value of \(\bar{I}_1-3\), \(D_1\) is material incompressibility parameter.

The initial bulk modulus is

\[ K=\dfrac{2}{D_1} \]

When the parameter \(J_m\) goes to infinity, the Gent model is equivalent to neo-Hookean form.

Mooney-Rivlin model

This model includes two-, three-, five-, and nine-terma Mooney-Rivlin models. The form of the strain-energy potential for a two-parameter Mooney-Rivlin model is

\[ W=C_{10}\left(\bar{I}_{1}-3\right)+C_{01}\left(\bar{I}_{2}-3\right)+\frac{1}{D_1}\left(J-1\right)^{2} \]

where \(C_{10}\), \(C_{01}\), and \(D_{1}\) are the material constants.

The form of strain-energy potential for a three-parameter Mooney-Rivlin model is

\[ W=C_{10}\left(\bar{I}_{1}-3\right)+C_{01}\left(\bar{I}_{2}-3\right)+C_{11}\left(\bar{I}_{1}-3\right)\left(\bar{I}_{2}-3\right)+\frac{1}{D_1}\left(J-1\right)^{2} \]

where \(C_{10}\), \(C_{01}\), \(C_{11}\), and \(D_1\) are material ocnstants.

The form of strain-energy potential for a five-parameter Mooney-Rivlin model is

\[ \begin{array}{ccc} W & = & C_{10}\left(\bar{I}_{1}-3\right)+C_{01}\left(\bar{I}_{2}-3\right)+C_{20}\left(\bar{I}_{1}-3\right)^{2}\\ & + & C_{11}\left(\bar{I}_{1}-3\right)\left(\bar{I}_{2}-3\right)+C_{02}\left(\bar{I}_{2}-3\right)^{2}+\frac{1}{D_1}\left(J-1\right)^{2} \end{array} \]

where \(C_{10}\), \(C_{01}\), \(C_{20}\), \(C_{11}\), \(C_{02}\), and \(D_1\) are material ocnstants.

The form of strain-energy potential for a nine-parameter Mooney-Rivlin model is

\[ \begin{array}{ccc} W & = & C_{10}\left(\bar{I}_{1}-3\right)+C_{01}\left(\bar{I}_{2}-3\right)+C_{20}\left(\bar{I}_{1}-3\right)^{2}\\ & + & C_{11}\left(\bar{I}_{1}-3\right)\left(\bar{I}_{2}-3\right)+C_{02}\left(\bar{I}_{2}-3\right)^{2}+C_{30}\left(\bar{I}_{1}-3\right)^{3}\\ & + & C_{21}\left(\bar{I}_{1}-3\right)^{2}\left(\bar{I}_{2}-3\right)+C_{12}\left(\bar{I}_{1}-3\right)\left(\bar{I}_{2}-3\right)^{2}+C_{03}\left(\bar{I}_{2}-3\right)^{3}+\frac{1}{D_1}\left(J-1\right)^{2} \end{array} \]

where \(C_{10}\), \(C_{01}\), \(C_{20}\), \(C_{11}\), \(C_{02}\), \(C_{30}\), \(C_{21}\), \(C_{12}\), \(C_{03}\), and \(D_1\) are material ocnstants.

The initial shear modulus is given by:

\[ \mu=2(C_{10}+C_{01}) \]

The initial bulk modulus is

\[ K=\dfrac{2}{D_1} \]

Neo-Hookean model

The Neo-Hookean model is a well-known hyperelastic model with an expanded linear rule (Hooke rule) having isotropy so that it can respond to finite deformation problems. The elastic potential is as follows.

\[ W=\frac{\mu}{2}(\bar{I}_{1}-3)+\dfrac{1}{D_{1}}(J-1)^{2} \]

where \(\mu\) is initial shear modulus of materials, \(D_{1}\) is the material constant.

The initial bulk modulus is given by:

\[ K=\dfrac{2}{D_1} \]

Ogden compressible foam model

The strain-energy potential of the Ogden compressible foam model is based on the principal stretches of left Cauchy strain tensor, which has the form:

\[ W=\sum_{i=1}^{N}\frac{\mu_{i}}{\alpha_{i}}\left(J^{\alpha_{i}/3}\left(\bar{\lambda}_{1}^{\alpha_{i}}+\bar{\lambda}_{2}^{\alpha_{i}}+\bar{\lambda}_{3}^{\alpha_{i}}\right)-3\right)+\sum_{i=1}^{N}\frac{\mu_{i}}{\alpha_{i}\beta_{i}}\left(J^{-\alpha_{i}\beta_{i}}-1\right) \]

where N determines the order of the polynomial, \(\mu_i\), \(\alpha_i\) are material constants, \(D_k\) is incompressiblity parameter. The reduced principal strench is defined by:

\[ \bar{\lambda}_{p}=J^{-\frac{1}{3}}\lambda_p,\; J=(\lambda_{1}\lambda_{2}\lambda_{3})^{\frac{1}{2}} \]

The initial shear modulus is given by:

\[ \mu=\dfrac{\sum_{i=1}^{N}\mu_{i}\alpha_{i}}{2} \]

The initial bulk modulus K is defined by

\[ K = \sum_{i=1}^{N}\mu_{i}\alpha_{i}\left(\dfrac{1}{3}+\beta_{i}\right) \]

When parameters N=1, \(\alpha_1\)=-2, \(\mu_1\)=-\(\mu\), and \(\beta\)=0.5, the Ogden compressible model is converted to the Blatz-Ko model.

Ogden model

The strain-energy potential of the Ogden compressible foam model is based on the principal stretches of left Cauchy strain tensor, which has the form:

\[ W=\sum_{i=1}^{N}\frac{\mu_{i}}{\alpha_{i}}\left(\bar{\lambda}_{1}^{\alpha_{i}}+\bar{\lambda}_{2}^{\alpha_{i}}+\bar{\lambda}_{3}^{\alpha_{i}}-3\right)+\sum_{k=1}^{N}\frac{1}{D_{k}}\left(J-1\right)^{2k} \]

where N determines the order of the polynomial, \(\mu_i\), \(\alpha_i\) are material constants, \(D_k\) is incompressiblity parameter. The reduced principal strench is defined by:

\[ \bar{\lambda}_{p}=J^{-\frac{1}{3}}\lambda_p,\; J=(\lambda_{1}\lambda_{2}\lambda_{3})^{\frac{1}{2}} \]

The initial shear modulus is given by:

\[ \mu=\dfrac{\sum_{i=1}^{N}\mu_{i}\alpha_{i}}{2} \]

The initial bulk modulus K is defined by

\[ K = \dfrac{2}{D_1} \]

When parameters N=1, \(\alpha_1\)=2, the Ogden model is converted to the neo-Hookean model. When parameters N=2, \(\alpha_1\)=2 and \(\alpha_2\)=-2, the Ogden model is converted to the 2-parameter Mooney-Rivlin model.

Polynomial form

The polynomial form of strain-energy potential is:

\[ W=\sum_{i+j=1}^{N}c_{ij}\left(\bar{I}_{1}-3\right)^{i}\left(\bar{I_{2}}-3\right)^{j}+\sum_{k=1}^{N}\frac{1}{D_{k}}\left(J-1\right)^{2k} \]

where \(N\) determines the order of polynomial, \(c_{ij}\), \(D_k\) are material constants.

The initial shear modulus is given by:

\[ \mu=2\left(C_{10}+C_{01}\right) \]

The initial bulk modulus K is defined by

\[ K = \dfrac{2}{D_1} \]

The Polynomial model is converted to following models with specific paramters:

Parameters of Polynomial model Equivalent model
N=1, \(C_{01}\)=0 neo-Hookean
N=1 2-parameter Mooney-Rivlin
N=2 5-parameter Mooney-Rivlin
N=3 9-parameter Mooney-Rivlin

Yeoh model

The Yeoh model is also called the reduced polynomial form. The strain-energy potential is

\[ W=\sum_{i=1}^{N}c_{i0}\left(\bar{I}_{1}-3\right)^{i}+\sum_{k=1}^{N}\frac{1}{D_{k}}\left(J-1\right)^{2k} \]

where N denotes the order of polynomial, \(C_{i0}\) and \(D_k\) are material constants. When N=1, Yeoh becomes neo-Hookean model.

The initial shear modulus is defined:

\[ \mu=2c_{10} \]

The initial bulk modulus is:

\[ K=\frac{2}{D_1} \]

Rate-independent plasticity

The elastoplasticity based on the flow rule is applied in this program. The constitutive relation between Jaumman rate and the deformation rate tensor of the Kirchhoff stress is numerically solved using the updated Lagrange method.

Elastoplastic constitutive equation

The yield criteria of an elasto-plastic solid can be written into math formulas. The initial yield criteria are

\[ F(\sigma,\sigma_{y0})=0 \]

The Consecutive yield criteria are

\[ F(\sigma,\sigma_{y}(e^{-p}))=0 \]

where \(F\) is the yield function, \(\sigma_{y0}\) is initial yield stress, \(\sigma_{y}\) is consecutive yield stress, \(\sigma\) is stress tensor, \(\mathbf{e}\) is the infinitesimal strain tensor, \(\mathbf{e}^{p}\) is the plastic strain tensor, \(\bar{\mathbf{e}}^{p}\) is equivalent plastic strain.

The yield stress-equivalent plastic strain relationship is assumed to conform to the stress-plastic strain relation in a single axis state. The stress-plastic strain relation about one single axis state is:

\[ \sigma=H(e^{p}) \]
\[ \dfrac{d\sigma}{de^{p}}=H' \]

where \(H'\) is the strain hardening factor. The equivalent stress-equivalent plastic strain relation is :

\[ \bar{\sigma}=H(\bar{e}^{p}) \]
\[ \dot{\bar{\sigma}}=H'\dot{\bar{e^{p}}} \]

The consecutive yield function is generally a function of temperature and plastic strain work. In this program, this function is assumed to be related to the equivalent plastic strain \bar{e}^{p}. Since condition F=0 holds during the plastic deformation, we have

\[ \begin{align} \label{eq:ch5_plastic_gov1} \dot{F}=\dfrac{\partial F}{\partial\sigma}\colon\dot{\sigma}+\dfrac{\partial F}{\partial\mathbf{e}^{p}}\colon\dot{\mathbf{e}}^{p}=0 \end{align} \]

where \(\dot{F}\) is the time derivative function of \(F\).

In this case, we assume the existence of the plastic potential \(\Theta\), the plastic strain rate is

\[ \dot{\mathbf{e}}^{p}=\dot{\lambda}\dfrac{\partial\Theta}{\partial\sigma} \]

where \(\dot{\lambda}\) is the factor. Moreover, assuming the plastic potential \(\Theta\) is equivalent to yield function \(F\), the associated flow rule is assumed as

\[ \dot{\mathbf{e}}^{p}=\dot{\lambda}\dfrac{\partial F}{\partial\sigma} \]

which is substituted with equation \(\eqref{eq:ch5_plastic_gov1}\), we have

\[ \dot{\lambda}=\dfrac{\mathbf{a}^{T}\colon\mathbf{d}_{D}}{A+\mathbf{a}^{T}\colon\mathbf{D}\colon\mathbf{a}}\mathbf{\dot{\mathbf{e}}} \]

where \(\mathbf{D}\) is the elastic matrix, and

\[ \mathbf{a}^{T}=\dfrac{\partial F}{\partial\sigma}\quad\mathbf{d}_{D}=\mathbf{D}\mathbf{a}^{T}\quad A=-\dfrac{1}{\dot{\lambda}}\dfrac{\partial F}{\partial\mathbf{\mathbf{e}}^{p}}\colon\dot{\mathbf{e}}^{p} \]

The stress-strain relation for elastoplasicity can be rewritten to

\[ \begin{align} \label{eq:ch5_plastic_yield_func1} \dot{\sigma}=\{\mathbf{D}-\dfrac{\mathbf{d}_{D}\otimes\mathbf{d}_{D}^{T}}{A+\mathbf{d}_{D}^{T}\mathbf{a}}\}\colon\dot{\mathbf{e}} \end{align} \]

Here we give the explicit form of several yield functions that are applied in the program.

Von-Mises yield function

\[ F=\sqrt{3\mathbf{J}_{2}}-\sigma_{y} = 0 \]

Mohr-Coulomb yield function

\[ F=\sigma_{1}-\sigma_{3}+(\sigma_{1}+\sigma_{3})\mathrm{sin}\phi-2c\mathrm{cos}\phi = 0 \]

Drucker-Prager yield function

\[ F=\sqrt{\mathbf{J}_{2}}-\alpha\sigma\colon\mathbf{I}-\sigma_{y}=0 \]

where material constant \(\alpha\) and \(\sigma_{y}\) are calculated from the viscosity and friction angle of the material as shown below

\[ \alpha=\dfrac{2\mathrm{sin}\phi}{3+\mathrm{sin}\phi},\quad\sigma_{y}=\dfrac{6c\mathrm{cos}\phi}{3+\mathrm{sin}\phi} \]

Viscoelasticity

A material is viscoelastic if the material has both elastic (recoverable) and viscous (nonrecoverable) parts. Upon loads, the elastic deformation is instantaneous while the viscous part occurs over time. A viscoelastic model can depicts the deformation behavior of glass or glass-like materials and simulate heating and cooling processing of such materials.

Constitutive Equations

A generalized Maxwell model is applied for viscoelasticity in this program. The constitutive equation becomes a function of deviatoric strain \(\mathbf{e}\) and deviatoric viscosity strain \(\mathbf{q}\),

\[ \sigma(t)=K\thinspace tr(\epsilon\mathbf{I})+2G(\mu_{0}\mathbf{e}+\mu\mathbf{q}) \]

where

\[ \mu\mathbf{q}=\sum_{m=1}^{M}\mu_{m}\mathbf{q}^{(m)};\quad\sum_{m=0}^{M}\mu_{m}=1 \]

moveover, the deviatoric viscosity strain \(\mathbf{q}\) can be calculated by

\[ \dot{\mathbf{q}}\thinspace^{(m)}+\dfrac{1}{\tau_{m}}\mathbf{q}^{(m)}=\dot{\mathbf{e}} \]

where \(\tau_{m}\) is the relaxation time. The shear and volumetric relaxation coefficient \(G\) is represented by the following Prony series:

\[ G(t)=G[\mu_{0}^{G}+\sum_{i=1}^{M}\mu_{i}^{G}e^{-(t/\tau_{i}^{G})}] \]
\[ K(t)=K[\mu_{0}^{K}+\sum_{i=1}^{M}\mu_{i}^{K} e^{-\frac{t}{\tau_{i}^{K}}}] \]

where \(\tau_{i}^{G}\) and \(\tau_{i}^{K}\) are relaxation times for each Prony component, \(G_i\) and \(K_i\) are shear and volumetric moduli, respectively.

Themorheological Simplicity

Viscous material depends strongly on temperature. For instance, A glass-like material turninto viscous fluids at high temperatures and behave like a solid material at low temperatures. The thermorheological simplicity is proposed to assumes that material response to a load at a high temperature over a short duration is identical to that at lower temperature but over a longer duration. Essentially, the relaxation times in Prony components oby the scaling law:

\[ \tau_{i}^{G}(T) = \dfrac{\tau_{i}^{G}(T_r)}{A(T,T_r)} ,\qquad \tau_{i}^{K}(T) = \dfrac{\tau_{i}^{K}(T_r)}{A(T,T_r)} \]

where \(A(T,T_r)\) is called the shift function.

Shift Functions

WELSIM offers the following forms of the shift function:

  • Williams-Landel-Ferry Shift Function

Williams-Landel-Ferry Shift Function

The Williams-Landel-Ferry (WLF) shift function is defined by

\[ log_{10}(A) = \dfrac{C1(T-T_r)}{C2+T-T_r} \]

where T is temperature, \(T_r\) is reference temperature, \(C_1\) and \(C_2\) are the WLF constants.

Rate-dependent plasticity (including creep and viscoplasticity)

The creep is a deformation phenomenon that the displacement depends on the time even under constant stress condition. The viscoelasticity can be viewed as linear creep. Several nonlinear creep are described in this section. In the mathematical theory, we define creep strain \(\epsilon^{c}\) and creep strain rate \(\dot{\epsilon}^{c}\)

\[ \begin{align} \label{eq:ch5_creep_gov1} \dot{\epsilon}^{c}=\dfrac{\partial\epsilon^{c}}{\partial t}=\beta(\sigma,\epsilon^{c}) \end{align} \]

In this case, if the instantaneous strain is assumed as the elasticity strain \(\epsilon^{e}\), the total strain can be expressed as the summary of elastic and creep strains

\[ \epsilon=\epsilon^{e}+\epsilon^{c} \]

where the elastic strain can be calculated by

\[ \epsilon^{e}=\mathbf{c}^{e-1}\colon\sigma \]

When the creep occurs in the deformation, the stress becomes

\[ \sigma_{n+1}=\mathbf{c}\colon(\epsilon_{n+1}-\epsilon_{n+1}^{c}) \]
\[ \epsilon_{n+1}^{c}=\epsilon_{n}^{c}+\triangle t\beta_{n+\theta} \]

where \(\beta_{n+\theta}\) becomes

\[ \beta_{n+\theta}=(1+\theta)\beta_{n}+\theta\beta_{n+1} \]

The incremental creep strain \(\triangle\epsilon^{c}\) can be simplified to a nonlinear equation

\[ \mathbf{R}_{n+1}=\epsilon_{n+1}-\mathbf{c}^{-1}\colon\sigma_{n+1}-\epsilon_{n}^{c}-\triangle t\beta_{n+\theta}=0 \]

The Newton-Raphson method is applied to solve the nonlinear conditions. The iterative scheme in the finite element framework is

\[ \begin{align} \label{eq:ch5_creep_gov2} \mathbf{R}_{n+1}^{(k+1)}=0=\mathbf{R}_{n+1}^{(k)}-(\mathbf{c}^{-1}+\triangle t\mathbf{c}_{n+1}^{c})d\sigma_{n+1}^{(k)} \end{align} \]

which yields

\[ \begin{align} \label{eq:ch5_creep_gov3} \mathbf{c}_{n+1}^{c}=\dfrac{\partial\beta}{\partial\sigma}\mid_{n+\theta}=\theta\dfrac{\partial\beta}{\partial\sigma}\mid_{n+1} \end{align} \]

The above equations \(\eqref{eq:ch5_creep_gov2}\) and \(\eqref{eq:ch5_creep_gov3}\) are used in the iterative scheme. As the residual \(\mathbf{R}\) gets close to zero, the stress \(\sigma_{n+1}\) and tangent tensile modulus are

\[ \mathbf{c}_{n+1}^{*}=[\mathbf{c}^{-1}+\triangle t\mathbf{c}_{n+1}^{c}]^{-1} \]

To solve the equation \(\eqref{eq:ch5_creep_gov1}\), the following Norton model is applied in the program. The equivalent clip strain \(\dot{\epsilon}^{cr}\) is defined to be the function of Mises stress \(q\) and time \(t\).

\[ \dot{\epsilon}^{cr}=Aq^{n}t^{m} \]

where \(A\), \(m\), \(n\) are the material coefficients.

Creep

Creep is the inelastic, irreversible deformation of structures during time. It is a life limiting factor and depends on stress, strain, temperature and time. This dependency can be modeled as followed:

\[ \dot{\epsilon}^{cr}=f(\sigma,\epsilon,T,t) \]

Creep can occur in all crystalline materials, such as metal or glass, has various impacts on the behavior of the material.

Three types of creep

Creep can be divided in three different stages: primary creep, secondary creep and irradiation induced creep.

Primary creep (0<m<1) starts rapidly with an infinite creep rate at the initialization. Here is m the time index. It occurs after a certain amount of time and slows down constantly. It occurs in the first hour after applying the load and is essential in calculating the relaxation over time.

Secondary creep (m=1) follows right after the primary creep stage. The strain rate is now constant over a long period of time.

The strain rate in the irradiation induced creep stage is growing rapidly until failure. This happens in a short period of time and is not of great interest. Therefore only primary and secondary creep are modeled in WelSim.

Creep models

WELSIM supports implicit creep models including Strain Hardening, Time Hardening, Generalized Exponentia, Generalized Graham, Generalized Blackburn, Modified Time Hardening, Modified Strain Hardening, Generalized Garofalo, Exponential form, Norton, Combined Time Hardening, Rational polynomial, and Generalized Time Hardening. The details of these models are given in the table below.

Creep Model
(index)		 Name Equations Parameters Type
1 Strain Hardening \(\dot{\epsilon}_{cr}=C_{1}\sigma^{C_2}\epsilon_{cr}^{C_3}e^{-C_4/T}\) \(C_1>0\) Primary
2 Time Hardening \(\dot{\epsilon}_{cr}=C_{1}\sigma^{C_2}t^{C_3}e^{-C_4/T}\) \(C_1>0\) Primary
3 Generalized Exponential \(\dot{\epsilon}_{cr}=C_{1}\sigma^{C_2}re^{-rt}\), \(r=C_{5}\sigma^{C_3}e^{-C4/T}\) \(C_1>0\)
\(C_5>0\)		 Primary
4 Generalized Graham \(\dot{\epsilon}_{cr}=C_{1}\sigma^{C_2}\left( t^{C_3} + C_{4}t^{C_5} + C_{6}t^{C_7} \right) e^{-C_8/T}\) \(C_1>0\) Primary
5 Generalized Blackburn \(\dot{\epsilon}_{cr} = f\left(1-e^{-rt}\right)+gt\)
\(f=C_{1}e^{C_2\sigma}\), \(r=C_3\left(\sigma/C_4\right)^{C_5}\), \(g=C_{6}e^{C_{7}\sigma}\)		 \(C_1>0\)
\(C_3>0\)
\(C_6>0\)		 Primary
6 Modified Time Hardening \(\dot{\epsilon}_{cr}=\dfrac{C_{1}}{C_3+1}\sigma^{C_2}t^{C_3+1}e^{-C_4/T}\) \(C_1>0\) Primary
7 Modified Strain Hardening \(\dot{\epsilon}_{cr}= \{ C_{1} \sigma^{C_2} \left[\left( C_3+1\right)\epsilon_{cr} \right]^{C_3} \}^{1/(C_3+1)} e^{-C_4/T}\) \(C_1>0\) Primary
8 Generalized Garofalo \(\dot{\epsilon}_{cr}=C_1\left[ sinh(C_2\sigma)\right]^{C_3} e^{-C_4/T}\) \(C_1>0\) Secondary
9 Exponential form \(\dot{\epsilon}_{cr}=C_1 e^{\sigma/C_2} e^{-C_3/T}\) \(C_1>0\) Secondary
10 Norton \(\dot{\epsilon}_{cr}=C_1 \sigma^{C_2} e^{-C_3/T}\) \(C_1>0\) Secondary
11 Combined Time Hardening \(\dot{\epsilon}_{cr}=\dfrac{C_1}{C_3+1} \sigma^{C_2} t^{C_3+1} e^{-C_4/T} + C_5 \sigma^{C_6}te^{-C_7/T}\) \(C_1>0\),
\(C_5>0\)		 Primary + Secondary
12 Rational Polynomial \(\dot{\epsilon}_{cr}=C_1 \dfrac{\partial\epsilon_c}{\partial t}\), \(\epsilon_{c}=\dfrac{cpt}{1+pt}+\dot{\epsilon}_m t\)
\(\dot{\epsilon}_m=C_2(10)^{C_3\sigma}\sigma^{C_4}\)
\(c=C_7\dot{\epsilon}_m^{C_8}\sigma^{C_9}\), \(p=C_{10}\dot{\epsilon}_{m}^{C_{11}}\sigma^{C_{12}}\)		 \(C_2>0\) Primary + Secondary
13 Generalized Time Hardening \(\dot{\epsilon}_{cr}=ft^r e^{-C_6/T}\)
\(f=C_1\sigma+C_2\sigma^2+C_3\sigma^3\)
\(r=C_4 + C_5\sigma\)		 - Primary

where \(\epsilon_{cr}\) is equivalent creep strain, \(\dot{\epsilon}_{cr}\) is the change in equivalent creep strain with respect to time, \(\sigma\) is equivalent stress. \(T\) is temperature. \(C_1\) through \(C_{12}\) are creep constants. \(t\) is time at end of substep. \(e\) is natural logarithm base.

\ No newline at end of file + Structures with material nonlinearities - WelSim Documentation
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Structures with material nonlinearities

Material nonlinearities occur because of the nonlinear relationship between stress and strain; that is, the stress is a nonlinear function of the strain. The relationship is also path-dependent (except for the case of nonlinear elasticity and hyperelasticity), so that the stress depends on the strain history as well as the strain itself.

The program can account for many material nonlinearities, as follows:

  1. Rate-independent plasticity is characterized by the irreversible instantaneous straining that occurs in a material.

  2. Rate-dependent plasticity allows the plastic-strains to develop over a time interval. It is also termed viscoplasticity.

  3. Creep is also an irreversible straining that occurs in a material and is rate-dependent so that the strains develop over time. The time frame for creep is usually much larger than that for rate-dependent plasticity.

  4. Nonlinear elasticity allows a nonlinear stress-strain relationship to be specified. All straining is reversible.

  5. Hyperelasticity is defined by a strain-energy density potential that characterizes elastomeric and foam-type materials. All straining is reversible.

  6. Viscoelasticity is a rate-dependent material characterization that includes a viscous contribution to the elastic straining.

When the material applicable for analysis is an elastoplastic material, the updated Lagrange method is applied, and the total Lagrange method is applied for hyperelastic material. Moreover, the Newton-Raphson method is applied to the repetitive analysis method.

Strain definitions

For the case of nonlinear materials, the definition of elastic strain given in Equation \(\eqref{eq:ch4_theory_stress_strain_relation}\) expands to

\[ \begin{align} \label{eq:ch4_guide_strain_full} \{\epsilon\}=\{\epsilon^{el}\}+\{\epsilon^{th}\}+\{e^{pl}\}+\{\epsilon^{cr}\}+\{\epsilon^{sw}\} \end{align} \]

where \(\epsilon\) is the total strain vector, \(\epsilon^{el}\) is elastic strain vector, \(\epsilon^{th}\) is the thermal strain vector, \(\epsilon^{pl}\) is the plastic strain vector, \(\epsilon^{cr}\) is the creep strain vector, and \(\epsilon^{sw}\) is the swelling strain vector.

Hyperelasticity

The elastic potential energy in hyperelastic material can be obtained from the initial state with no stress activation. Therefore, we have the main invariable terms of the right Cauchy-Green deformation tensor C(\(I_{1}\), \(I_{2}\), \(I_{3}\)), or the main invariable of the deformation tensor excluding the volume changes (\(\bar{I}_{1}\), \(\bar{I}_{2}\), \(\bar{I}_{3}\)). The potential can be expressed as \(\mathbf{W}=\mathbf{W}(I_{1},I_{2},I_{3})\), or \(\mathbf{W}=\mathbf{W}(\bar{I}_{1},\bar{I}_{2},\bar{I}_{3})\).

The nonlinear constitutive relation of hyperelastic material is defined by the relation between the second order Piola-Kirchhoff stress and the Green-Lagrange strain, the total Lagrange method is more efficient in solving such models.

When the elastic potential energy \(W\) of the hyperelasticity is known, the second Piola-Kirchhoff stress and strain-stress relationship can be calculated as follows

\[ S=2\dfrac{\partial W}{\partial C} \]
\[ C=4\dfrac{\partial^{2}W}{\partial C\partial C} \]

Arruda-Boyce model

The form of the strain-energy potential for Arruda-Boyce model is

\[ \begin{array}{ccc} W & = & [\dfrac{1}{2}(\bar{I}_{1}-3)+\dfrac{1}{20\lambda_{m}^{2}}(\bar{I_{1}^{2}}-9)+\dfrac{11}{1050\lambda_{m}^{4}}(\bar{I_{1}^{3}}-27)\\ & + & \dfrac{19}{7000\lambda_{m}^{6}}(\bar{I_{1}^{4}}-81)+\dfrac{519}{673750\lambda_{m}^{8}}(\bar{I_{1}^{5}}-243)]+\dfrac{1}{D_1}(\dfrac{J^{2}-1}{2}-\mathrm{ln}J) \end{array} \]

where \(\lambda_{m}\) is limiting network stretch, and \(D_1\) is the material incompressibility parameter.

The initial shear modulus is

\[ \mu=\dfrac{\mu_{0}}{1+\dfrac{3}{5\lambda_{m}^{2}}+\dfrac{99}{175\lambda_{m}^{4}}+\dfrac{513}{875\lambda_{m}^{6}}+\dfrac{42039}{67375\lambda_{m}^{8}}} \]

The initial bulk modulus is

\[ K=\dfrac{2}{D_1} \]

As the parameter \(\lambda_L\) goes to infinity, the model is equivalent to neo-Hookean form.

Blatz-Ko foam model

The form of strain-energy potential for the Blatz-Ko model is:

\[ W=\frac{\mu}{2}\left(\frac{I_{2}}{I_{3}}+2\sqrt{I_{3}}-5\right) \]

where \(\mu\) is initla shear modulus of material. The initial bulk modulus is defined as :

\[ K = \frac{5}{3}\mu \]

Extended tube model

The elastic strain-energy potential for the extended tube model is:

\[ \begin{array}{ccc} W & = & \frac{G_{c}}{2}\left[\frac{\left(1-\delta^{2}\right)\left(\bar{I}_{1}-3\right)}{1-\delta^{2}\left(\bar{I}_{1}-3\right)}+\mathrm{ln}\left(1-\delta^{2}\left(\bar{I}_{1}-3\right)\right)\right]\\ & + & \frac{2G_{e}}{\beta^{2}}\sum_{i=1}^{3}\left(\bar{\lambda}_{i}^{-\beta}-1\right)+\frac{1}{D_1}\left(J-1\right)^{2} \end{array} \]

where the initial shear modulus is \(G\)=\(G_c\) + \(G_e\), and \(G_e\) is constraint contribution to modulus, \(G_c\) is crosslinked contribution to modulus, \(\delta\) is extensibility parameter, \(\beta\) is empirical parameter (0\(\leq \beta \leq\)1), and \(D_1\) is material incompressibility parameter.

Extended tube model is equivalent ot a two-term Ogden model with the following parameters:

\[ \begin{array}{cccc} \alpha_1 = 2 &, & \alpha_2=-\beta\\ \mu_1=G_c &, & \mu_2=-\dfrac{2}{\beta}G_e, & \delta=0 \end{array} \]

Gent model

The form of the strian-energy potential for the Gent model is:

\[ W=-\frac{\mu J_{m}}{2}\mathrm{ln}\left(1-\frac{\bar{I}_{1}-3}{J_{m}}\right)+\frac{1}{D_1}\left(\frac{J^{2}-1}{2}-\mathrm{ln}J\right) \]

where \(\mu\) is initial shear modulus of material, \(J_m\) is limiting value of \(\bar{I}_1-3\), \(D_1\) is material incompressibility parameter.

The initial bulk modulus is

\[ K=\dfrac{2}{D_1} \]

When the parameter \(J_m\) goes to infinity, the Gent model is equivalent to neo-Hookean form.

Mooney-Rivlin model

This model includes two-, three-, five-, and nine-terma Mooney-Rivlin models. The form of the strain-energy potential for a two-parameter Mooney-Rivlin model is

\[ W=C_{10}\left(\bar{I}_{1}-3\right)+C_{01}\left(\bar{I}_{2}-3\right)+\frac{1}{D_1}\left(J-1\right)^{2} \]

where \(C_{10}\), \(C_{01}\), and \(D_{1}\) are the material constants.

The form of strain-energy potential for a three-parameter Mooney-Rivlin model is

\[ W=C_{10}\left(\bar{I}_{1}-3\right)+C_{01}\left(\bar{I}_{2}-3\right)+C_{11}\left(\bar{I}_{1}-3\right)\left(\bar{I}_{2}-3\right)+\frac{1}{D_1}\left(J-1\right)^{2} \]

where \(C_{10}\), \(C_{01}\), \(C_{11}\), and \(D_1\) are material ocnstants.

The form of strain-energy potential for a five-parameter Mooney-Rivlin model is

\[ \begin{array}{ccc} W & = & C_{10}\left(\bar{I}_{1}-3\right)+C_{01}\left(\bar{I}_{2}-3\right)+C_{20}\left(\bar{I}_{1}-3\right)^{2}\\ & + & C_{11}\left(\bar{I}_{1}-3\right)\left(\bar{I}_{2}-3\right)+C_{02}\left(\bar{I}_{2}-3\right)^{2}+\frac{1}{D_1}\left(J-1\right)^{2} \end{array} \]

where \(C_{10}\), \(C_{01}\), \(C_{20}\), \(C_{11}\), \(C_{02}\), and \(D_1\) are material ocnstants.

The form of strain-energy potential for a nine-parameter Mooney-Rivlin model is

\[ \begin{array}{ccc} W & = & C_{10}\left(\bar{I}_{1}-3\right)+C_{01}\left(\bar{I}_{2}-3\right)+C_{20}\left(\bar{I}_{1}-3\right)^{2}\\ & + & C_{11}\left(\bar{I}_{1}-3\right)\left(\bar{I}_{2}-3\right)+C_{02}\left(\bar{I}_{2}-3\right)^{2}+C_{30}\left(\bar{I}_{1}-3\right)^{3}\\ & + & C_{21}\left(\bar{I}_{1}-3\right)^{2}\left(\bar{I}_{2}-3\right)+C_{12}\left(\bar{I}_{1}-3\right)\left(\bar{I}_{2}-3\right)^{2}+C_{03}\left(\bar{I}_{2}-3\right)^{3}+\frac{1}{D_1}\left(J-1\right)^{2} \end{array} \]

where \(C_{10}\), \(C_{01}\), \(C_{20}\), \(C_{11}\), \(C_{02}\), \(C_{30}\), \(C_{21}\), \(C_{12}\), \(C_{03}\), and \(D_1\) are material ocnstants.

The initial shear modulus is given by:

\[ \mu=2(C_{10}+C_{01}) \]

The initial bulk modulus is

\[ K=\dfrac{2}{D_1} \]

Neo-Hookean model

The Neo-Hookean model is a well-known hyperelastic model with an expanded linear rule (Hooke rule) having isotropy so that it can respond to finite deformation problems. The elastic potential is as follows.

\[ W=\frac{\mu}{2}(\bar{I}_{1}-3)+\dfrac{1}{D_{1}}(J-1)^{2} \]

where \(\mu\) is initial shear modulus of materials, \(D_{1}\) is the material constant.

The initial bulk modulus is given by:

\[ K=\dfrac{2}{D_1} \]

Ogden compressible foam model

The strain-energy potential of the Ogden compressible foam model is based on the principal stretches of left Cauchy strain tensor, which has the form:

\[ W=\sum_{i=1}^{N}\frac{\mu_{i}}{\alpha_{i}}\left(J^{\alpha_{i}/3}\left(\bar{\lambda}_{1}^{\alpha_{i}}+\bar{\lambda}_{2}^{\alpha_{i}}+\bar{\lambda}_{3}^{\alpha_{i}}\right)-3\right)+\sum_{i=1}^{N}\frac{\mu_{i}}{\alpha_{i}\beta_{i}}\left(J^{-\alpha_{i}\beta_{i}}-1\right) \]

where N determines the order of the polynomial, \(\mu_i\), \(\alpha_i\) are material constants, \(D_k\) is incompressiblity parameter. The reduced principal strench is defined by:

\[ \bar{\lambda}_{p}=J^{-\frac{1}{3}}\lambda_p,\; J=(\lambda_{1}\lambda_{2}\lambda_{3})^{\frac{1}{2}} \]

The initial shear modulus is given by:

\[ \mu=\dfrac{\sum_{i=1}^{N}\mu_{i}\alpha_{i}}{2} \]

The initial bulk modulus K is defined by

\[ K = \sum_{i=1}^{N}\mu_{i}\alpha_{i}\left(\dfrac{1}{3}+\beta_{i}\right) \]

When parameters N=1, \(\alpha_1\)=-2, \(\mu_1\)=-\(\mu\), and \(\beta\)=0.5, the Ogden compressible model is converted to the Blatz-Ko model.

Ogden model

The strain-energy potential of the Ogden compressible foam model is based on the principal stretches of left Cauchy strain tensor, which has the form:

\[ W=\sum_{i=1}^{N}\frac{\mu_{i}}{\alpha_{i}}\left(\bar{\lambda}_{1}^{\alpha_{i}}+\bar{\lambda}_{2}^{\alpha_{i}}+\bar{\lambda}_{3}^{\alpha_{i}}-3\right)+\sum_{k=1}^{N}\frac{1}{D_{k}}\left(J-1\right)^{2k} \]

where N determines the order of the polynomial, \(\mu_i\), \(\alpha_i\) are material constants, \(D_k\) is incompressiblity parameter. The reduced principal strench is defined by:

\[ \bar{\lambda}_{p}=J^{-\frac{1}{3}}\lambda_p,\; J=(\lambda_{1}\lambda_{2}\lambda_{3})^{\frac{1}{2}} \]

The initial shear modulus is given by:

\[ \mu=\dfrac{\sum_{i=1}^{N}\mu_{i}\alpha_{i}}{2} \]

The initial bulk modulus K is defined by

\[ K = \dfrac{2}{D_1} \]

When parameters N=1, \(\alpha_1\)=2, the Ogden model is converted to the neo-Hookean model. When parameters N=2, \(\alpha_1\)=2 and \(\alpha_2\)=-2, the Ogden model is converted to the 2-parameter Mooney-Rivlin model.

Polynomial form

The polynomial form of strain-energy potential is:

\[ W=\sum_{i+j=1}^{N}c_{ij}\left(\bar{I}_{1}-3\right)^{i}\left(\bar{I_{2}}-3\right)^{j}+\sum_{k=1}^{N}\frac{1}{D_{k}}\left(J-1\right)^{2k} \]

where \(N\) determines the order of polynomial, \(c_{ij}\), \(D_k\) are material constants.

The initial shear modulus is given by:

\[ \mu=2\left(C_{10}+C_{01}\right) \]

The initial bulk modulus K is defined by

\[ K = \dfrac{2}{D_1} \]

The Polynomial model is converted to following models with specific paramters:

Parameters of Polynomial model Equivalent model
N=1, \(C_{01}\)=0 neo-Hookean
N=1 2-parameter Mooney-Rivlin
N=2 5-parameter Mooney-Rivlin
N=3 9-parameter Mooney-Rivlin

Yeoh model

The Yeoh model is also called the reduced polynomial form. The strain-energy potential is

\[ W=\sum_{i=1}^{N}c_{i0}\left(\bar{I}_{1}-3\right)^{i}+\sum_{k=1}^{N}\frac{1}{D_{k}}\left(J-1\right)^{2k} \]

where N denotes the order of polynomial, \(C_{i0}\) and \(D_k\) are material constants. When N=1, Yeoh becomes neo-Hookean model.

The initial shear modulus is defined:

\[ \mu=2c_{10} \]

The initial bulk modulus is:

\[ K=\frac{2}{D_1} \]

Rate-independent plasticity

The elastoplasticity based on the flow rule is applied in this program. The constitutive relation between Jaumman rate and the deformation rate tensor of the Kirchhoff stress is numerically solved using the updated Lagrange method.

Elastoplastic constitutive equation

The yield criteria of an elasto-plastic solid can be written into math formulas. The initial yield criteria are

\[ F(\sigma,\sigma_{y0})=0 \]

The Consecutive yield criteria are

\[ F(\sigma,\sigma_{y}(e^{-p}))=0 \]

where \(F\) is the yield function, \(\sigma_{y0}\) is initial yield stress, \(\sigma_{y}\) is consecutive yield stress, \(\sigma\) is stress tensor, \(\mathbf{e}\) is the infinitesimal strain tensor, \(\mathbf{e}^{p}\) is the plastic strain tensor, \(\bar{\mathbf{e}}^{p}\) is equivalent plastic strain.

The yield stress-equivalent plastic strain relationship is assumed to conform to the stress-plastic strain relation in a single axis state. The stress-plastic strain relation about one single axis state is:

\[ \sigma=H(e^{p}) \]
\[ \dfrac{d\sigma}{de^{p}}=H' \]

where \(H'\) is the strain hardening factor. The equivalent stress-equivalent plastic strain relation is :

\[ \bar{\sigma}=H(\bar{e}^{p}) \]
\[ \dot{\bar{\sigma}}=H'\dot{\bar{e^{p}}} \]

The consecutive yield function is generally a function of temperature and plastic strain work. In this program, this function is assumed to be related to the equivalent plastic strain \bar{e}^{p}. Since condition F=0 holds during the plastic deformation, we have

\[ \begin{align} \label{eq:ch5_plastic_gov1} \dot{F}=\dfrac{\partial F}{\partial\sigma}\colon\dot{\sigma}+\dfrac{\partial F}{\partial\mathbf{e}^{p}}\colon\dot{\mathbf{e}}^{p}=0 \end{align} \]

where \(\dot{F}\) is the time derivative function of \(F\).

In this case, we assume the existence of the plastic potential \(\Theta\), the plastic strain rate is

\[ \dot{\mathbf{e}}^{p}=\dot{\lambda}\dfrac{\partial\Theta}{\partial\sigma} \]

where \(\dot{\lambda}\) is the factor. Moreover, assuming the plastic potential \(\Theta\) is equivalent to yield function \(F\), the associated flow rule is assumed as

\[ \dot{\mathbf{e}}^{p}=\dot{\lambda}\dfrac{\partial F}{\partial\sigma} \]

which is substituted with equation \(\eqref{eq:ch5_plastic_gov1}\), we have

\[ \dot{\lambda}=\dfrac{\mathbf{a}^{T}\colon\mathbf{d}_{D}}{A+\mathbf{a}^{T}\colon\mathbf{D}\colon\mathbf{a}}\mathbf{\dot{\mathbf{e}}} \]

where \(\mathbf{D}\) is the elastic matrix, and

\[ \mathbf{a}^{T}=\dfrac{\partial F}{\partial\sigma}\quad\mathbf{d}_{D}=\mathbf{D}\mathbf{a}^{T}\quad A=-\dfrac{1}{\dot{\lambda}}\dfrac{\partial F}{\partial\mathbf{\mathbf{e}}^{p}}\colon\dot{\mathbf{e}}^{p} \]

The stress-strain relation for elastoplasicity can be rewritten to

\[ \begin{align} \label{eq:ch5_plastic_yield_func1} \dot{\sigma}=\{\mathbf{D}-\dfrac{\mathbf{d}_{D}\otimes\mathbf{d}_{D}^{T}}{A+\mathbf{d}_{D}^{T}\mathbf{a}}\}\colon\dot{\mathbf{e}} \end{align} \]

Here we give the explicit form of several yield functions that are applied in the program.

Von-Mises yield function

\[ F=\sqrt{3\mathbf{J}_{2}}-\sigma_{y} = 0 \]

Mohr-Coulomb yield function

\[ F=\sigma_{1}-\sigma_{3}+(\sigma_{1}+\sigma_{3})\mathrm{sin}\phi-2c\mathrm{cos}\phi = 0 \]

Drucker-Prager yield function

\[ F=\sqrt{\mathbf{J}_{2}}-\alpha\sigma\colon\mathbf{I}-\sigma_{y}=0 \]

where material constant \(\alpha\) and \(\sigma_{y}\) are calculated from the viscosity and friction angle of the material as shown below

\[ \alpha=\dfrac{2\mathrm{sin}\phi}{3+\mathrm{sin}\phi},\quad\sigma_{y}=\dfrac{6c\mathrm{cos}\phi}{3+\mathrm{sin}\phi} \]

Viscoelasticity

A material is viscoelastic if the material has both elastic (recoverable) and viscous (nonrecoverable) parts. Upon loads, the elastic deformation is instantaneous while the viscous part occurs over time. A viscoelastic model can depicts the deformation behavior of glass or glass-like materials and simulate heating and cooling processing of such materials.

Constitutive Equations

A generalized Maxwell model is applied for viscoelasticity in this program. The constitutive equation becomes a function of deviatoric strain \(\mathbf{e}\) and deviatoric viscosity strain \(\mathbf{q}\),

\[ \sigma(t)=K\thinspace tr(\epsilon\mathbf{I})+2G(\mu_{0}\mathbf{e}+\mu\mathbf{q}) \]

where

\[ \mu\mathbf{q}=\sum_{m=1}^{M}\mu_{m}\mathbf{q}^{(m)};\quad\sum_{m=0}^{M}\mu_{m}=1 \]

moveover, the deviatoric viscosity strain \(\mathbf{q}\) can be calculated by

\[ \dot{\mathbf{q}}\thinspace^{(m)}+\dfrac{1}{\tau_{m}}\mathbf{q}^{(m)}=\dot{\mathbf{e}} \]

where \(\tau_{m}\) is the relaxation time. The shear and volumetric relaxation coefficient \(G\) is represented by the following Prony series:

\[ G(t)=G[\mu_{0}^{G}+\sum_{i=1}^{M}\mu_{i}^{G}e^{-(t/\tau_{i}^{G})}] \]
\[ K(t)=K[\mu_{0}^{K}+\sum_{i=1}^{M}\mu_{i}^{K} e^{-\frac{t}{\tau_{i}^{K}}}] \]

where \(\tau_{i}^{G}\) and \(\tau_{i}^{K}\) are relaxation times for each Prony component, \(G_i\) and \(K_i\) are shear and volumetric moduli, respectively.

Themorheological Simplicity

Viscous material depends strongly on temperature. For instance, A glass-like material turninto viscous fluids at high temperatures and behave like a solid material at low temperatures. The thermorheological simplicity is proposed to assumes that material response to a load at a high temperature over a short duration is identical to that at lower temperature but over a longer duration. Essentially, the relaxation times in Prony components oby the scaling law:

\[ \tau_{i}^{G}(T) = \dfrac{\tau_{i}^{G}(T_r)}{A(T,T_r)} ,\qquad \tau_{i}^{K}(T) = \dfrac{\tau_{i}^{K}(T_r)}{A(T,T_r)} \]

where \(A(T,T_r)\) is called the shift function.

Shift Functions

WELSIM offers the following forms of the shift function:

  • Williams-Landel-Ferry Shift Function

Williams-Landel-Ferry Shift Function

The Williams-Landel-Ferry (WLF) shift function is defined by

\[ log_{10}(A) = \dfrac{C1(T-T_r)}{C2+T-T_r} \]

where T is temperature, \(T_r\) is reference temperature, \(C_1\) and \(C_2\) are the WLF constants.

Rate-dependent plasticity (including creep and viscoplasticity)

The creep is a deformation phenomenon that the displacement depends on the time even under constant stress condition. The viscoelasticity can be viewed as linear creep. Several nonlinear creep are described in this section. In the mathematical theory, we define creep strain \(\epsilon^{c}\) and creep strain rate \(\dot{\epsilon}^{c}\)

\[ \begin{align} \label{eq:ch5_creep_gov1} \dot{\epsilon}^{c}=\dfrac{\partial\epsilon^{c}}{\partial t}=\beta(\sigma,\epsilon^{c}) \end{align} \]

In this case, if the instantaneous strain is assumed as the elasticity strain \(\epsilon^{e}\), the total strain can be expressed as the summary of elastic and creep strains

\[ \epsilon=\epsilon^{e}+\epsilon^{c} \]

where the elastic strain can be calculated by

\[ \epsilon^{e}=\mathbf{c}^{e-1}\colon\sigma \]

When the creep occurs in the deformation, the stress becomes

\[ \sigma_{n+1}=\mathbf{c}\colon(\epsilon_{n+1}-\epsilon_{n+1}^{c}) \]
\[ \epsilon_{n+1}^{c}=\epsilon_{n}^{c}+\triangle t\beta_{n+\theta} \]

where \(\beta_{n+\theta}\) becomes

\[ \beta_{n+\theta}=(1+\theta)\beta_{n}+\theta\beta_{n+1} \]

The incremental creep strain \(\triangle\epsilon^{c}\) can be simplified to a nonlinear equation

\[ \mathbf{R}_{n+1}=\epsilon_{n+1}-\mathbf{c}^{-1}\colon\sigma_{n+1}-\epsilon_{n}^{c}-\triangle t\beta_{n+\theta}=0 \]

The Newton-Raphson method is applied to solve the nonlinear conditions. The iterative scheme in the finite element framework is

\[ \begin{align} \label{eq:ch5_creep_gov2} \mathbf{R}_{n+1}^{(k+1)}=0=\mathbf{R}_{n+1}^{(k)}-(\mathbf{c}^{-1}+\triangle t\mathbf{c}_{n+1}^{c})d\sigma_{n+1}^{(k)} \end{align} \]

which yields

\[ \begin{align} \label{eq:ch5_creep_gov3} \mathbf{c}_{n+1}^{c}=\dfrac{\partial\beta}{\partial\sigma}\mid_{n+\theta}=\theta\dfrac{\partial\beta}{\partial\sigma}\mid_{n+1} \end{align} \]

The above equations \(\eqref{eq:ch5_creep_gov2}\) and \(\eqref{eq:ch5_creep_gov3}\) are used in the iterative scheme. As the residual \(\mathbf{R}\) gets close to zero, the stress \(\sigma_{n+1}\) and tangent tensile modulus are

\[ \mathbf{c}_{n+1}^{*}=[\mathbf{c}^{-1}+\triangle t\mathbf{c}_{n+1}^{c}]^{-1} \]

To solve the equation \(\eqref{eq:ch5_creep_gov1}\), the following Norton model is applied in the program. The equivalent clip strain \(\dot{\epsilon}^{cr}\) is defined to be the function of Mises stress \(q\) and time \(t\).

\[ \dot{\epsilon}^{cr}=Aq^{n}t^{m} \]

where \(A\), \(m\), \(n\) are the material coefficients.

Creep

Creep is the inelastic, irreversible deformation of structures during time. It is a life limiting factor and depends on stress, strain, temperature and time. This dependency can be modeled as followed:

\[ \dot{\epsilon}^{cr}=f(\sigma,\epsilon,T,t) \]

Creep can occur in all crystalline materials, such as metal or glass, has various impacts on the behavior of the material.

Three types of creep

Creep can be divided in three different stages: primary creep, secondary creep and irradiation induced creep.

Primary creep (0<m<1) starts rapidly with an infinite creep rate at the initialization. Here is m the time index. It occurs after a certain amount of time and slows down constantly. It occurs in the first hour after applying the load and is essential in calculating the relaxation over time.

Secondary creep (m=1) follows right after the primary creep stage. The strain rate is now constant over a long period of time.

The strain rate in the irradiation induced creep stage is growing rapidly until failure. This happens in a short period of time and is not of great interest. Therefore only primary and secondary creep are modeled in WelSim.

Creep models

WELSIM supports implicit creep models including Strain Hardening, Time Hardening, Generalized Exponentia, Generalized Graham, Generalized Blackburn, Modified Time Hardening, Modified Strain Hardening, Generalized Garofalo, Exponential form, Norton, Combined Time Hardening, Rational polynomial, and Generalized Time Hardening. The details of these models are given in the table below.

Creep Model
(index)		 Name Equations Parameters Type
1 Strain Hardening \(\dot{\epsilon}_{cr}=C_{1}\sigma^{C_2}\epsilon_{cr}^{C_3}e^{-C_4/T}\) \(C_1>0\) Primary
2 Time Hardening \(\dot{\epsilon}_{cr}=C_{1}\sigma^{C_2}t^{C_3}e^{-C_4/T}\) \(C_1>0\) Primary
3 Generalized Exponential \(\dot{\epsilon}_{cr}=C_{1}\sigma^{C_2}re^{-rt}\), \(r=C_{5}\sigma^{C_3}e^{-C4/T}\) \(C_1>0\)
\(C_5>0\)		 Primary
4 Generalized Graham \(\dot{\epsilon}_{cr}=C_{1}\sigma^{C_2}\left( t^{C_3} + C_{4}t^{C_5} + C_{6}t^{C_7} \right) e^{-C_8/T}\) \(C_1>0\) Primary
5 Generalized Blackburn \(\dot{\epsilon}_{cr} = f\left(1-e^{-rt}\right)+gt\)
\(f=C_{1}e^{C_2\sigma}\), \(r=C_3\left(\sigma/C_4\right)^{C_5}\), \(g=C_{6}e^{C_{7}\sigma}\)		 \(C_1>0\)
\(C_3>0\)
\(C_6>0\)		 Primary
6 Modified Time Hardening \(\dot{\epsilon}_{cr}=\dfrac{C_{1}}{C_3+1}\sigma^{C_2}t^{C_3+1}e^{-C_4/T}\) \(C_1>0\) Primary
7 Modified Strain Hardening \(\dot{\epsilon}_{cr}= \{ C_{1} \sigma^{C_2} \left[\left( C_3+1\right)\epsilon_{cr} \right]^{C_3} \}^{1/(C_3+1)} e^{-C_4/T}\) \(C_1>0\) Primary
8 Generalized Garofalo \(\dot{\epsilon}_{cr}=C_1\left[ sinh(C_2\sigma)\right]^{C_3} e^{-C_4/T}\) \(C_1>0\) Secondary
9 Exponential form \(\dot{\epsilon}_{cr}=C_1 e^{\sigma/C_2} e^{-C_3/T}\) \(C_1>0\) Secondary
10 Norton \(\dot{\epsilon}_{cr}=C_1 \sigma^{C_2} e^{-C_3/T}\) \(C_1>0\) Secondary
11 Combined Time Hardening \(\dot{\epsilon}_{cr}=\dfrac{C_1}{C_3+1} \sigma^{C_2} t^{C_3+1} e^{-C_4/T} + C_5 \sigma^{C_6}te^{-C_7/T}\) \(C_1>0\),
\(C_5>0\)		 Primary + Secondary
12 Rational Polynomial \(\dot{\epsilon}_{cr}=C_1 \dfrac{\partial\epsilon_c}{\partial t}\), \(\epsilon_{c}=\dfrac{cpt}{1+pt}+\dot{\epsilon}_m t\)
\(\dot{\epsilon}_m=C_2(10)^{C_3\sigma}\sigma^{C_4}\)
\(c=C_7\dot{\epsilon}_m^{C_8}\sigma^{C_9}\), \(p=C_{10}\dot{\epsilon}_{m}^{C_{11}}\sigma^{C_{12}}\)		 \(C_2>0\) Primary + Secondary
13 Generalized Time Hardening \(\dot{\epsilon}_{cr}=ft^r e^{-C_6/T}\)
\(f=C_1\sigma+C_2\sigma^2+C_3\sigma^3\)
\(r=C_4 + C_5\sigma\)		 - Primary

where \(\epsilon_{cr}\) is equivalent creep strain, \(\dot{\epsilon}_{cr}\) is the change in equivalent creep strain with respect to time, \(\sigma\) is equivalent stress. \(T\) is temperature. \(C_1\) through \(C_{12}\) are creep constants. \(t\) is time at end of substep. \(e\) is natural logarithm base.

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Modal analysis

Generalized eigenvalue problem

When conducting a free oscillation analysis of the continuum, assuming no damping in the free vibration. The governing eqatuion is

\[ \begin{align} \label{eq:ch5_modal_gov} \mathbf{M}\ddot{\mathbf{u}}+\mathbf{Ku}=0 \end{align} \]

where \(\mathbf{u}\) is the generated displacement vector, \(\mathbf{M}\) is the mass matrix and \(\mathbf{K}\) is the stiffness matrix. The solution is assumed to

\[ \begin{align} \label{eq:ch5_eigenvalue_vector} \mathbf{u}(t)=(asin\omega t+bcos\omega t)\mathbf{x} \end{align} \]

where \(\omega\) is the natural angular frequency, \(a\) and \(b\) are the arbitrary constants. Herein, the second order differential of equation \(\eqref{eq:ch5_eigenvalue_vector}\) is

\[ \begin{align} \label{eq:ch5_modal_acceleration} \ddot{\mathbf{u}}(t)=\omega(asin\omega t-bsin\omega t)\mathbf{x} \end{align} \]

Combining equations \(\eqref{eq:ch5_modal_gov}\), \(\eqref{eq:ch5_eigenvalue_vector}\), and \(\eqref{eq:ch5_modal_acceleration}\), we have

\[ \begin{align} \label{eq:ch5_modal_gov3} \mathbf{M}\ddot{\mathbf{u}}+\mathbf{Ku}=(a\mathrm{sin}\omega t+b\mathrm{cos}\omega t)(-\omega^{2}\mathbf{M}+\mathbf{K}\mathbf{x})=(-\lambda\mathbf{M}\mathbf{x}+\mathbf{K}\mathbf{x})=0 \end{align} \]

which simplifies

\[ \mathbf{K}\mathbf{x}=\lambda\mathbf{M}\mathbf{x} \]

which indicates that if factor \(\lambda(=\omega^{2})\) and vector \(\mathbf{x}\) satisfies equation \(\eqref{eq:ch5_modal_gov3}\), function \(\mathbf{u}(t)\) becomes the solution of equation \(\eqref{eq:ch5_modal_gov}\). The factor \(\lambda\) is called the eigenvalue, vector \(\mathbf{x}\) is called the eigenvector.

Problem settings

Equation \(\eqref{eq:ch5_modal_acceleration}\) can be expanded to calculate arbitrary order frequencies, which may appear at real engineering practices. To solve various physical problems, we assume the system is Hermitian(Matrix Symmetrical). Thus, a complex matrix can be transposed into a conjugate complex number and a real symmetric matrix. The relationship can be expressed by the equation below

\[ k_{ij}=\bar{k}_{ji} \]

In this manual, the matrix in modal analysis is assumed to be symmetrical and positive definite. A positively definite matrix always yields to positive eigenvalues. Thus a matrix in the modal system always satisfies the following equation

\[ \mathbf{x}^{T}\mathbf{Ax}>0 \]

Shifted inverse iteration method

In the practical structural modal analysis, not all eigen values are required. There are many cases that some low order eigenvalues are sufficient for the engineering analysis. In the large scale problem that contains large sparse matrix, efficiently calculate the eigenvalues of the low order modes becomes important.

When the lower limit of the eigenvalue is given, the equation \(\eqref{eq:ch5_modal_gov3}\) can be derived to:

\[ \begin{align} \label{eq:ch5_modal_gov4} (\mathbf{K}-\sigma\mathbf{M})^{-1}\mathbf{M}\mathbf{x}=[1/(\lambda-\sigma)]\mathbf{x} \end{align} \]

this formation of the equations has following advantages in numerical calculation:

  • The mode is reversed.
  • The eigenvalue around \mathbf{\sigma} is maximized.

In the computing practice, the maximum eigenvalue may be calculated by first. For this reason, we use the equation \(\eqref{eq:ch5_modal_gov4}\) rather than equation \(\eqref{eq:ch5_modal_gov3}\) to calculate the eigenvalues around \sigma. This scheme is called the shifted inverse iteration.

Lanczos method

In the WELSIM application, the Lanczos method is applied to solve the eigenvalues. Lanczos method is a numerical method performing tridiagonalization of matrices. It has capabilities of :

  • an iterative method, has advantages in solving sparse matrices.
  • the algorithm is well structured with matrix and vector operations, and naturally fits for parallel computing.
  • is suitable for the geometric domain decomposition method (DDM) that is embedded finite element mesh.
  • calculate arbitrary number of the eigenvalues and modes.

The Lanczos method calculates the base of partial spaces by creating orthogonal vectors from the initial vectors. This method has advantages of computation speed over the subspace method. However, Lanczos method is easily affected by numerical errors. It is essential to check the solution with the numerical errors.

Geometric meaning in the lanczos method

Based on equation \(\eqref{eq:ch5_modal_gov4}\), we define

\[ \begin{align} \label{eq:ch5_modal_gov5} \begin{cases} \mathbf{A}=(\mathbf{K}-\sigma\mathbf{M})^{-1}\\{} [1/(\lambda-\sigma)]=\zeta \end{cases} \end{align} \]

which can be rewritten to the following equation

\[ \mathbf{Ax}=\zeta\mathbf{x} \]

The algorithm of the Lanczos method is the Gram-Schmidt orthogonalization for column vectors. Those column vectors are also called the columns of Krylov, and the space created by this scheme is called the Krylov subspace. When the Gram-Schmidt orthogonalization is performed in this space, the vectors can be acquired using the two nearest vectors. This is called the principle of Lanczos.

\ No newline at end of file + Modal analysis (eiginvalue) - WelSim Documentation
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Modal analysis

Generalized eigenvalue problem

When conducting a free oscillation analysis of the continuum, assuming no damping in the free vibration. The governing eqatuion is

\[ \begin{align} \label{eq:ch5_modal_gov} \mathbf{M}\ddot{\mathbf{u}}+\mathbf{Ku}=0 \end{align} \]

where \(\mathbf{u}\) is the generated displacement vector, \(\mathbf{M}\) is the mass matrix and \(\mathbf{K}\) is the stiffness matrix. The solution is assumed to

\[ \begin{align} \label{eq:ch5_eigenvalue_vector} \mathbf{u}(t)=(asin\omega t+bcos\omega t)\mathbf{x} \end{align} \]

where \(\omega\) is the natural angular frequency, \(a\) and \(b\) are the arbitrary constants. Herein, the second order differential of equation \(\eqref{eq:ch5_eigenvalue_vector}\) is

\[ \begin{align} \label{eq:ch5_modal_acceleration} \ddot{\mathbf{u}}(t)=\omega(asin\omega t-bsin\omega t)\mathbf{x} \end{align} \]

Combining equations \(\eqref{eq:ch5_modal_gov}\), \(\eqref{eq:ch5_eigenvalue_vector}\), and \(\eqref{eq:ch5_modal_acceleration}\), we have

\[ \begin{align} \label{eq:ch5_modal_gov3} \mathbf{M}\ddot{\mathbf{u}}+\mathbf{Ku}=(a\mathrm{sin}\omega t+b\mathrm{cos}\omega t)(-\omega^{2}\mathbf{M}+\mathbf{K}\mathbf{x})=(-\lambda\mathbf{M}\mathbf{x}+\mathbf{K}\mathbf{x})=0 \end{align} \]

which simplifies

\[ \mathbf{K}\mathbf{x}=\lambda\mathbf{M}\mathbf{x} \]

which indicates that if factor \(\lambda(=\omega^{2})\) and vector \(\mathbf{x}\) satisfies equation \(\eqref{eq:ch5_modal_gov3}\), function \(\mathbf{u}(t)\) becomes the solution of equation \(\eqref{eq:ch5_modal_gov}\). The factor \(\lambda\) is called the eigenvalue, vector \(\mathbf{x}\) is called the eigenvector.

Problem settings

Equation \(\eqref{eq:ch5_modal_acceleration}\) can be expanded to calculate arbitrary order frequencies, which may appear at real engineering practices. To solve various physical problems, we assume the system is Hermitian(Matrix Symmetrical). Thus, a complex matrix can be transposed into a conjugate complex number and a real symmetric matrix. The relationship can be expressed by the equation below

\[ k_{ij}=\bar{k}_{ji} \]

In this manual, the matrix in modal analysis is assumed to be symmetrical and positive definite. A positively definite matrix always yields to positive eigenvalues. Thus a matrix in the modal system always satisfies the following equation

\[ \mathbf{x}^{T}\mathbf{Ax}>0 \]

Shifted inverse iteration method

In the practical structural modal analysis, not all eigen values are required. There are many cases that some low order eigenvalues are sufficient for the engineering analysis. In the large scale problem that contains large sparse matrix, efficiently calculate the eigenvalues of the low order modes becomes important.

When the lower limit of the eigenvalue is given, the equation \(\eqref{eq:ch5_modal_gov3}\) can be derived to:

\[ \begin{align} \label{eq:ch5_modal_gov4} (\mathbf{K}-\sigma\mathbf{M})^{-1}\mathbf{M}\mathbf{x}=[1/(\lambda-\sigma)]\mathbf{x} \end{align} \]

this formation of the equations has following advantages in numerical calculation:

  • The mode is reversed.
  • The eigenvalue around \mathbf{\sigma} is maximized.

In the computing practice, the maximum eigenvalue may be calculated by first. For this reason, we use the equation \(\eqref{eq:ch5_modal_gov4}\) rather than equation \(\eqref{eq:ch5_modal_gov3}\) to calculate the eigenvalues around \sigma. This scheme is called the shifted inverse iteration.

Lanczos method

In the WELSIM application, the Lanczos method is applied to solve the eigenvalues. Lanczos method is a numerical method performing tridiagonalization of matrices. It has capabilities of :

  • an iterative method, has advantages in solving sparse matrices.
  • the algorithm is well structured with matrix and vector operations, and naturally fits for parallel computing.
  • is suitable for the geometric domain decomposition method (DDM) that is embedded finite element mesh.
  • calculate arbitrary number of the eigenvalues and modes.

The Lanczos method calculates the base of partial spaces by creating orthogonal vectors from the initial vectors. This method has advantages of computation speed over the subspace method. However, Lanczos method is easily affected by numerical errors. It is essential to check the solution with the numerical errors.

Geometric meaning in the lanczos method

Based on equation \(\eqref{eq:ch5_modal_gov4}\), we define

\[ \begin{align} \label{eq:ch5_modal_gov5} \begin{cases} \mathbf{A}=(\mathbf{K}-\sigma\mathbf{M})^{-1}\\{} [1/(\lambda-\sigma)]=\zeta \end{cases} \end{align} \]

which can be rewritten to the following equation

\[ \mathbf{Ax}=\zeta\mathbf{x} \]

The algorithm of the Lanczos method is the Gram-Schmidt orthogonalization for column vectors. Those column vectors are also called the columns of Krylov, and the space created by this scheme is called the Krylov subspace. When the Gram-Schmidt orthogonalization is performed in this space, the vectors can be acquired using the two nearest vectors. This is called the principle of Lanczos.

\ No newline at end of file diff --git a/welsim/theory/shapefunction/index.html b/welsim/theory/shapefunction/index.html index 0b654d6..cd23eaf 100755 --- a/welsim/theory/shapefunction/index.html +++ b/welsim/theory/shapefunction/index.html @@ -1 +1 @@ - Shape functions - WelSim Documentation
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Shape functions

This chapter describes the shape functions for the finite elements.

Understanding shape function notations

The notations used in shape functions are listed below:

  • u: displacement in x (or s) direction.
  • v: displacement in y (or t) direction.
  • w: displacement in z (or s) direction.
  • \(\theta_{x}\): Rotation about x direction.
  • \(\theta_{y}\): Rotation about y direction.
  • \(\theta_{z}\): Rotation about z direction.
  • \(A_{x}\): x-component of vector magnetic potential.
  • \(A_{y}\): y-component of vector magnetic potential.
  • \(A_{z}\): z-component of vector magnetic potential.
  • C: Concentration.
  • P: Pressure.
  • T: Temperature.
  • V: Electric potential or source current.
  • For the shell element, the u and v represent in-plane motions, and w denotes the out-of-plane motion.

3D shell elements

This section describes the shape functions for 3D shell elements that are applied in the WELSIM application.

3-Node triangle

The shape functions for the 3-node triangular shell elements are:

\[ u=u_{0}L_{0}+u_{1}L_{1}+u_{2}L_{2} \]
\[ v=v_{0}L_{0}+v_{1}L_{1}+v_{2}L_{2} \]
\[ w=w_{0}L_{0}+w_{1}L_{1}+w_{2}L_{2} \]
\[ A_{x}=A_{x0}L_{0}+A_{x1}L_{1}+A_{x2}L_{2} \]
\[ A_{y}=A_{y0}L_{0}+A_{y1}L_{1}+A_{y2}L_{2} \]
\[ A_{z}=A_{z0}L_{0}+A_{z1}L_{1}+A_{z2}L_{2} \]
\[ T=T_{0}L_{0}+T_{1}L_{1}+T_{2}L_{2} \]
\[ V=V_{0}L_{0}+V_{1}L_{1}+V_{2}L_{2} \]

6-Node triangle

The shape functions for the 6-node triangular shell elements are:

\[ u=u_{0}(2L_{0}-1)L_{0}+u_{1}(2L_{1}-1)L_{1}+u_{2}(2L_{2}-1)L_{2}+u_{3}(4L_{0}L_{1})+u_{4}(4L_{1}L_{2})+u_{5}(4L_{2}L_{0}) \]
\[ v=v_{0}(2L_{0}-1)L_{0}+v_{1}(2L_{1}-1)L_{1}+v_{2}(2L_{2}-1)L_{2}+v_{3}(4L_{0}L_{1})+v_{4}(4L_{1}L_{2})+v_{5}(4L_{2}L_{0}) \]
\[ w=w_{0}(2L_{0}-1)L_{0}+w_{1}(2L_{1}-1)L_{1}+w_{2}(2L_{2}-1)L_{2}+w_{3}(4L_{0}L_{1})+w_{4}(4L_{1}L_{2})+w_{5}(4L_{2}L_{0}) \]

3D solid elements

This section describes the shape functions for the 3D solid elements that are applied in the WELSIM application.

4-Node tetrahedra

The 4-node tetrahedra is also called liner tetrahedra element. The shape functions are:

\[ u=u_{0}L_{0}+u_{1}L_{1}+u_{2}L_{2}+u_{3}L_{3} \]
\[ v=v_{0}L_{0}+v_{1}L_{1}+v_{2}L_{2}+v_{3}L_{3} \]
\[ w=w_{0}L_{0}+w_{1}L_{1}+w_{2}L_{2}+w_{3}L_{3} \]

10-Node tetrahedra

The 10-node tetrahedra is also called bilinear tetrahedra element. The shape functions are:

\[ u=u_{0}(2L_{0}-1)L_{0}+u_{1}(2L_{1}-1)L_{1}+u_{2}(2L_{2}-1)L_{2}+u_{3}(2L_{3}-1)L_{3}+4u_{4}L_{0}L_{1}+u_{5}L_{1}L_{2}+u_{6}L_{0}L_{2}+u_{7}L_{0}L_{3}+u_{8}L_{1}L_{3}+u_{9}L_{2}L_{3} \]
\[ v=...\text{(analogous to u)} \]
\[ w=...\text{(analogous to u)} \]
\ No newline at end of file + Shape functions - WelSim Documentation
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Shape functions

This chapter describes the shape functions for the finite elements.

Understanding shape function notations

The notations used in shape functions are listed below:

  • u: displacement in x (or s) direction.
  • v: displacement in y (or t) direction.
  • w: displacement in z (or s) direction.
  • \(\theta_{x}\): Rotation about x direction.
  • \(\theta_{y}\): Rotation about y direction.
  • \(\theta_{z}\): Rotation about z direction.
  • \(A_{x}\): x-component of vector magnetic potential.
  • \(A_{y}\): y-component of vector magnetic potential.
  • \(A_{z}\): z-component of vector magnetic potential.
  • C: Concentration.
  • P: Pressure.
  • T: Temperature.
  • V: Electric potential or source current.
  • For the shell element, the u and v represent in-plane motions, and w denotes the out-of-plane motion.

3D shell elements

This section describes the shape functions for 3D shell elements that are applied in the WELSIM application.

3-Node triangle

The shape functions for the 3-node triangular shell elements are:

\[ u=u_{0}L_{0}+u_{1}L_{1}+u_{2}L_{2} \]
\[ v=v_{0}L_{0}+v_{1}L_{1}+v_{2}L_{2} \]
\[ w=w_{0}L_{0}+w_{1}L_{1}+w_{2}L_{2} \]
\[ A_{x}=A_{x0}L_{0}+A_{x1}L_{1}+A_{x2}L_{2} \]
\[ A_{y}=A_{y0}L_{0}+A_{y1}L_{1}+A_{y2}L_{2} \]
\[ A_{z}=A_{z0}L_{0}+A_{z1}L_{1}+A_{z2}L_{2} \]
\[ T=T_{0}L_{0}+T_{1}L_{1}+T_{2}L_{2} \]
\[ V=V_{0}L_{0}+V_{1}L_{1}+V_{2}L_{2} \]

6-Node triangle

The shape functions for the 6-node triangular shell elements are:

\[ u=u_{0}(2L_{0}-1)L_{0}+u_{1}(2L_{1}-1)L_{1}+u_{2}(2L_{2}-1)L_{2}+u_{3}(4L_{0}L_{1})+u_{4}(4L_{1}L_{2})+u_{5}(4L_{2}L_{0}) \]
\[ v=v_{0}(2L_{0}-1)L_{0}+v_{1}(2L_{1}-1)L_{1}+v_{2}(2L_{2}-1)L_{2}+v_{3}(4L_{0}L_{1})+v_{4}(4L_{1}L_{2})+v_{5}(4L_{2}L_{0}) \]
\[ w=w_{0}(2L_{0}-1)L_{0}+w_{1}(2L_{1}-1)L_{1}+w_{2}(2L_{2}-1)L_{2}+w_{3}(4L_{0}L_{1})+w_{4}(4L_{1}L_{2})+w_{5}(4L_{2}L_{0}) \]

3D solid elements

This section describes the shape functions for the 3D solid elements that are applied in the WELSIM application.

4-Node tetrahedra

The 4-node tetrahedra is also called liner tetrahedra element. The shape functions are:

\[ u=u_{0}L_{0}+u_{1}L_{1}+u_{2}L_{2}+u_{3}L_{3} \]
\[ v=v_{0}L_{0}+v_{1}L_{1}+v_{2}L_{2}+v_{3}L_{3} \]
\[ w=w_{0}L_{0}+w_{1}L_{1}+w_{2}L_{2}+w_{3}L_{3} \]

10-Node tetrahedra

The 10-node tetrahedra is also called bilinear tetrahedra element. The shape functions are:

\[ u=u_{0}(2L_{0}-1)L_{0}+u_{1}(2L_{1}-1)L_{1}+u_{2}(2L_{2}-1)L_{2}+u_{3}(2L_{3}-1)L_{3}+4u_{4}L_{0}L_{1}+u_{5}L_{1}L_{2}+u_{6}L_{0}L_{2}+u_{7}L_{0}L_{3}+u_{8}L_{1}L_{3}+u_{9}L_{2}L_{3} \]
\[ v=...\text{(analogous to u)} \]
\[ w=...\text{(analogous to u)} \]
\ No newline at end of file diff --git a/welsim/theory/structures/index.html b/welsim/theory/structures/index.html index 41ad1ee..fd30c85 100755 --- a/welsim/theory/structures/index.html +++ b/welsim/theory/structures/index.html @@ -1 +1 @@ - Structures - WelSim Documentation
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Structures

This section describes the mathematical and numerical theories used in this finite element analysis program. In the stress analysis of solids, the infinitesimal deformation linear elasticity static analysis method is discussed by first. The geometric nonlinearity and elastoplasticity are introduced to describe the finite deformation in solids.

Infinitesimal deformation linear elasticity static analysis

The infinitesimal deformation theory is the essential formulation for the linear elasticity, which assumes the stress-strain constitutive relation is linear. The equilibrium equation of solid mechanics, boundary conditions are given by the following equation.

\[ \begin{align} \label{eq:ch5_equilibrium_eqn1} \nabla\cdot\mathbf{\sigma}+\mathbf{b}=0\quad\mathrm{in}V \end{align} \]
\[ \begin{align} \label{eq:ch5_equilibrium_eqn2} \sigma\cdot\mathbf{n}=\mathbf{t}\quad\mathrm{on}\thinspace S_{t} \end{align} \]
\[ \begin{align} \label{eq:ch5_equilibrium_eqn3} \mathbf{u}=\mathbf{u}_{0}\quad\mathrm{on}\thinspace S_{u} \end{align} \]

where \(\sigma\) is the stress, \(\mathbf{t}\) is the surface force, \(\mathbf{b}\) is the body force, and S_{t} expresses the dynamic boundary and the \(S_{u}\) expresses the geometric boundary. The strain and displacement relation in the infinitesimal deformation is given

\[ \epsilon=\nabla_{s}\mathbf{u} \]

The stress and strain constitutive relation in the linear elastic body is given

\[ \sigma=\mathbf{C}\colon\epsilon \]

where \(\mathbf{C}\) is the fourth order elasticity tensor.

Principle of virtual work

The principle of the virtual work regarding the equilibrium equations \(\eqref{eq:ch5_equilibrium_eqn1}\), \(\eqref{eq:ch5_equilibrium_eqn2}\), and \(\eqref{eq:ch5_equilibrium_eqn3}\) is

\[ \begin{align} \label{eq:ch5_equilibrium_virtual1} \int_{V}\sigma\colon\delta\epsilon dV=\int_{S_{t}}\mathbf{t}\cdot\delta\mathbf{u}dS+\int_{V}\mathbf{b}\cdot\delta\mathbf{u}dV \end{align} \]
\[ \delta\mathbf{u}=0\quad\mathrm{on}\quad S_{u} \]

which can be rewritten into

\[ \begin{align} \label{eq:ch5_equilibrium_virtual2} \int_{V}(\mathbf{C}\colon\epsilon)\colon\delta\epsilon dV=\int_{S_{t}}\mathbf{t}\cdot\delta\mathbf{u}dS+\int_{V}\mathbf{b}\cdot\delta\mathbf{u}dV \end{align} \]

where \(\epsilon\) is the strain tensor, \(\sigma\) is the stress tensor, and \(\mathbf{C}\) is the fourth order elasticity tensor. The strain tensor \(\epsilon\) and stress tensor \(\sigma\) can be rewritten into vector forms \(\hat{\epsilon}\) and \(\hat{\sigma}\), respectively. Then we have

\[ \begin{align} \label{eq:ch4_theory_stress_strain_relation} \hat{\sigma}=\mathbf{D}\hat{\epsilon} \end{align} \]

where \(\mathbf{D}\) is the elasticity matrix. Given the strain and stress in the vector form, we can rewrite the governing equation ([eq:ch5_equilibrium_virtual1]) into

\[ \begin{align} \label{eq:ch5_equilibrium_virtual3} \int_{V}\hat{\epsilon}^{T}\mathbf{D}\delta\hat{\epsilon}dV=\int_{S_{t}}\delta\mathbf{u^{T}}\mathbf{t}dS+\int_{V}\delta\mathbf{u}^{T}\mathbf{b}dV \end{align} \]

Equation ([eq:ch5_equilibrium_virtual3]) is the principles of the virtual work applied in this software program.

Finite element formulation

The principle governing equation ([eq:ch5_equilibrium_virtual3]) of the virtual work can be discreted for each finite element:

\[ \begin{align} \label{eq:ch5_equilibrium_fe_form1} \sum_{e}\int_{V^{e}}\hat{\epsilon}^{T}\mathbf{D}\delta\hat{\epsilon}dV=\sum_{e}\int_{S_{t}^{e}}\delta\mathbf{u}^{T}\mathbf{t}dS+\sum_{e}\int_{V^{e}}\delta\mathbf{u}^{T}\mathbf{b}dV \end{align} \]

where the displacement field is interpolated for each element

\[ \begin{align} \label{eq:ch5_equilibrium_fe_form2} \mathbf{u}=\sum_{i=1}^{m}N_{i}\mathbf{u}_{i}=\mathbf{NU} \end{align} \]

Similarly, the strain component can be expressed as

\[ \begin{align} \label{eq:ch5_equilibrium_fe_form3} \hat{\epsilon}=\mathbf{BU} \end{align} \]

Substituting equations \(\eqref{eq:ch5_equilibrium_fe_form2}\) and \(\eqref{eq:ch5_equilibrium_fe_form3}\) into \(\eqref{eq:ch5_equilibrium_fe_form1}\), we have

\[ \begin{align} \label{eq:ch5_equilibrium_fe_form4} \sum_{e}\delta\mathbf{U}^{T}(\int_{V^{e}}\mathbf{B}^{T}\mathbf{DB}dV)\mathbf{U}=\sum_{e}\delta\mathbf{U}^{T}\cdot\int_{S_{t}^{e}}\mathbf{N}^{T}\mathbf{t}dS+\sum_{e}\delta\mathbf{U}^{T}\int_{V^{e}}\mathbf{N}^{T}\mathbf{b}dV \end{align} \]

The equation above can be summarized as

\[ \begin{align} \label{eq:ch5_equilibrium_fe_form5} \delta\mathbf{U}^{T}\mathbf{KU}=\delta\mathbf{U}^{T}\mathbf{F} \end{align} \]

where

\[ \begin{align} \label{eq:ch5_equilibrium_fe_form6} \mathbf{K}=\sum_{e}\int_{V^{e}}\mathbf{B}^{T}\mathbf{DB}dV \end{align} \]
\[ \begin{align} \label{eq:ch5_equilibrium_fe_form7} \mathbf{F}=\sum\int_{S_{t}^{e}}\mathbf{N}^{T}\mathbf{t}dS+\int_{V^{e}}\mathbf{N}^{T}\mathbf{b}dV \end{align} \]

The components of the matrix and vectors defined by equations \(\eqref{eq:ch5_equilibrium_fe_form6}\) and \(\eqref{eq:ch5_equilibrium_fe_form7}\) can be calculated for each finite element. For arbitrary virtual displacement \(\delta\mathbf{U}\), equation \(\eqref{eq:ch5_equilibrium_fe_form5}\) can be rewritten into

\[ \mathbf{KU=F} \]
\ No newline at end of file + Structures - WelSim Documentation
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Structures

This section describes the mathematical and numerical theories used in this finite element analysis program. In the stress analysis of solids, the infinitesimal deformation linear elasticity static analysis method is discussed by first. The geometric nonlinearity and elastoplasticity are introduced to describe the finite deformation in solids.

Infinitesimal deformation linear elasticity static analysis

The infinitesimal deformation theory is the essential formulation for the linear elasticity, which assumes the stress-strain constitutive relation is linear. The equilibrium equation of solid mechanics, boundary conditions are given by the following equation.

\[ \begin{align} \label{eq:ch5_equilibrium_eqn1} \nabla\cdot\mathbf{\sigma}+\mathbf{b}=0\quad\mathrm{in}V \end{align} \]
\[ \begin{align} \label{eq:ch5_equilibrium_eqn2} \sigma\cdot\mathbf{n}=\mathbf{t}\quad\mathrm{on}\thinspace S_{t} \end{align} \]
\[ \begin{align} \label{eq:ch5_equilibrium_eqn3} \mathbf{u}=\mathbf{u}_{0}\quad\mathrm{on}\thinspace S_{u} \end{align} \]

where \(\sigma\) is the stress, \(\mathbf{t}\) is the surface force, \(\mathbf{b}\) is the body force, and S_{t} expresses the dynamic boundary and the \(S_{u}\) expresses the geometric boundary. The strain and displacement relation in the infinitesimal deformation is given

\[ \epsilon=\nabla_{s}\mathbf{u} \]

The stress and strain constitutive relation in the linear elastic body is given

\[ \sigma=\mathbf{C}\colon\epsilon \]

where \(\mathbf{C}\) is the fourth order elasticity tensor.

Principle of virtual work

The principle of the virtual work regarding the equilibrium equations \(\eqref{eq:ch5_equilibrium_eqn1}\), \(\eqref{eq:ch5_equilibrium_eqn2}\), and \(\eqref{eq:ch5_equilibrium_eqn3}\) is

\[ \begin{align} \label{eq:ch5_equilibrium_virtual1} \int_{V}\sigma\colon\delta\epsilon dV=\int_{S_{t}}\mathbf{t}\cdot\delta\mathbf{u}dS+\int_{V}\mathbf{b}\cdot\delta\mathbf{u}dV \end{align} \]
\[ \delta\mathbf{u}=0\quad\mathrm{on}\quad S_{u} \]

which can be rewritten into

\[ \begin{align} \label{eq:ch5_equilibrium_virtual2} \int_{V}(\mathbf{C}\colon\epsilon)\colon\delta\epsilon dV=\int_{S_{t}}\mathbf{t}\cdot\delta\mathbf{u}dS+\int_{V}\mathbf{b}\cdot\delta\mathbf{u}dV \end{align} \]

where \(\epsilon\) is the strain tensor, \(\sigma\) is the stress tensor, and \(\mathbf{C}\) is the fourth order elasticity tensor. The strain tensor \(\epsilon\) and stress tensor \(\sigma\) can be rewritten into vector forms \(\hat{\epsilon}\) and \(\hat{\sigma}\), respectively. Then we have

\[ \begin{align} \label{eq:ch4_theory_stress_strain_relation} \hat{\sigma}=\mathbf{D}\hat{\epsilon} \end{align} \]

where \(\mathbf{D}\) is the elasticity matrix. Given the strain and stress in the vector form, we can rewrite the governing equation ([eq:ch5_equilibrium_virtual1]) into

\[ \begin{align} \label{eq:ch5_equilibrium_virtual3} \int_{V}\hat{\epsilon}^{T}\mathbf{D}\delta\hat{\epsilon}dV=\int_{S_{t}}\delta\mathbf{u^{T}}\mathbf{t}dS+\int_{V}\delta\mathbf{u}^{T}\mathbf{b}dV \end{align} \]

Equation ([eq:ch5_equilibrium_virtual3]) is the principles of the virtual work applied in this software program.

Finite element formulation

The principle governing equation ([eq:ch5_equilibrium_virtual3]) of the virtual work can be discreted for each finite element:

\[ \begin{align} \label{eq:ch5_equilibrium_fe_form1} \sum_{e}\int_{V^{e}}\hat{\epsilon}^{T}\mathbf{D}\delta\hat{\epsilon}dV=\sum_{e}\int_{S_{t}^{e}}\delta\mathbf{u}^{T}\mathbf{t}dS+\sum_{e}\int_{V^{e}}\delta\mathbf{u}^{T}\mathbf{b}dV \end{align} \]

where the displacement field is interpolated for each element

\[ \begin{align} \label{eq:ch5_equilibrium_fe_form2} \mathbf{u}=\sum_{i=1}^{m}N_{i}\mathbf{u}_{i}=\mathbf{NU} \end{align} \]

Similarly, the strain component can be expressed as

\[ \begin{align} \label{eq:ch5_equilibrium_fe_form3} \hat{\epsilon}=\mathbf{BU} \end{align} \]

Substituting equations \(\eqref{eq:ch5_equilibrium_fe_form2}\) and \(\eqref{eq:ch5_equilibrium_fe_form3}\) into \(\eqref{eq:ch5_equilibrium_fe_form1}\), we have

\[ \begin{align} \label{eq:ch5_equilibrium_fe_form4} \sum_{e}\delta\mathbf{U}^{T}(\int_{V^{e}}\mathbf{B}^{T}\mathbf{DB}dV)\mathbf{U}=\sum_{e}\delta\mathbf{U}^{T}\cdot\int_{S_{t}^{e}}\mathbf{N}^{T}\mathbf{t}dS+\sum_{e}\delta\mathbf{U}^{T}\int_{V^{e}}\mathbf{N}^{T}\mathbf{b}dV \end{align} \]

The equation above can be summarized as

\[ \begin{align} \label{eq:ch5_equilibrium_fe_form5} \delta\mathbf{U}^{T}\mathbf{KU}=\delta\mathbf{U}^{T}\mathbf{F} \end{align} \]

where

\[ \begin{align} \label{eq:ch5_equilibrium_fe_form6} \mathbf{K}=\sum_{e}\int_{V^{e}}\mathbf{B}^{T}\mathbf{DB}dV \end{align} \]
\[ \begin{align} \label{eq:ch5_equilibrium_fe_form7} \mathbf{F}=\sum\int_{S_{t}^{e}}\mathbf{N}^{T}\mathbf{t}dS+\int_{V^{e}}\mathbf{N}^{T}\mathbf{b}dV \end{align} \]

The components of the matrix and vectors defined by equations \(\eqref{eq:ch5_equilibrium_fe_form6}\) and \(\eqref{eq:ch5_equilibrium_fe_form7}\) can be calculated for each finite element. For arbitrary virtual displacement \(\delta\mathbf{U}\), equation \(\eqref{eq:ch5_equilibrium_fe_form5}\) can be rewritten into

\[ \mathbf{KU=F} \]
\ No newline at end of file diff --git a/welsim/theory/thermal/index.html b/welsim/theory/thermal/index.html index 32ddf43..3f4ccf6 100755 --- a/welsim/theory/thermal/index.html +++ b/welsim/theory/thermal/index.html @@ -1 +1 @@ - Thermal analysis - WelSim Documentation
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Thermal analysis

This section discuss the theories used in the WESLIM thermal analysis.

Governing equations

The governing equations applied in thermal analysis are:

\[ \begin{align} \label{eq:ch5_thermal_gov} \rho c\frac{\partial T}{\partial t}=\nabla\cdot(k\nabla T) \end{align} \]

where \(\rho=\rho(x)\) is mass density, \(c=c(x,T)\) is the specific heat, \(T=T(x,t)\) is the temperature, \(K=k(x,T)\) is the thermal conductivity, \(Q=Q(x,T,t)\) is the calorific value. \(x\) is the position in the modeling domain, \(T\) is the temperature and \(t\) is the time.

The modeling domain is represented by S, and the boundary is represented by \(\varGamma\). When assuming the boundary conditions of either the Dirichlet or Neumann type, those boundary conditions can be mathematically expressed as

\[ T=T_{1}(x,t) \qquad X\in\Gamma_{1} \]
\[ k\frac{\partial T}{\partial n}=q(x,T,t) \qquad X\in\Gamma_{2} \]

where the term \(T_{1}\), \(q\) is already known. \(q\) is the heat flux outflow from the boundary. Three types of heat flux can be considered in WELSIM thermal module.

\[ q=-q_{s}+q_{c}+q_{r} \]
\[ q_{s}=q_{s}(x,t) \]
\[ q_{c}=hc(T-T_{c}) \]
\[ q_{r}=hc(T^{4}-T_{r}^{4}) \]

where \(q_{s}\) is the distributed heat flux, \(q_{c}\) is the heat flux by the convective heat transfer, and \(q_{r}\) is the heat flux by the radiant heat transfer. The other quantities are

  • \(T_{c}=T_{c}(x,t)\) Convective heat transfer coefficient ambient temperature
  • \(h_{c}=h_{c}(x,t)\) Convective heat transfer factor
  • \(T_{r}=T_{r}(x,t)\) Radiant heat transfer coefficient ambient temperature
  • \(h_{r}=\epsilon\sigma F=h_{r}(x,t)\) Radiant heat transfer factor. \(\epsilon\) is the radiant rate, \(\sigma\) is the Stefan-Boltzmann constant, \(F\) is the shape factor.

Derivation of heat flow matrices

When equation \(\eqref{eq:ch5_thermal_gov}\) is discreted by the Galerkin approximation, it becomes as follows,

\[ \begin{align} \label{eq:ch5_thermal_gov2} [\mathbf{K}]\{T\}+[\mathbf{M}]\frac{\partial T}{\partial t}=\{F\} \end{align} \]

where the matrices and vectors are

\[ \begin{array}{ccc} [\mathbf{K}] & = & \int(k_{xx}\dfrac{\partial\{N\}^{T}}{\partial x}\dfrac{\partial\{N\}}{\partial x}+k_{yy}\dfrac{\partial\{N\}^{T}}{\partial y}\dfrac{\partial\{N\}}{\partial y}+k_{zz}\dfrac{\partial\{N\}^{T}}{\partial z}\dfrac{\partial\{N\}}{\partial z})dV\\ & + & \int h_{c}\{N\}^{T}\{N\}ds+\int h_{r}\{N\}^{T}\{N\}ds \end{array} \]
\[ [\mathbf{M}]=\int\rho c\{N\}^{T}\{N\}dV \]
\[ \{F\}=\int Q\{N\}^{T}dV-\int q_{s}\{N\}^{T}dS+\int h_{c}T_{c}\{N\}^{T}dS+\int h_{r}T_{r}(T+T_{r})(T^{2}+T_{r}^{2})\{N\}^{T}dS \]

where shape function

\[ \{N\}=(N^{1},N^{2},.......),\thinspace N_{i}=N_{i}(x) \]

Equation \(\eqref{eq:ch5_thermal_gov2}\) is nonlinear and unsteady. When the time is discretized by the backward Euler's rule and the temperature at time t=t_{0} is known, the temperature at t=t_{0+\triangle t} is calculated using the following equation.

\[ \begin{align} \label{eq:ch5_thermal_gov_disc1} [\mathbf{K}]_{t=t_{0+\triangle t}}\{T\}_{t=t_{0+\triangle t}}+[\mathbf{M}]_{t=t_{0+\triangle t}}\dfrac{\{T\}_{t=t_{0+\triangle t}}-\{T\}_{t=t_{0}}}{\triangle t}=\{F\}_{t=t_{0+\triangle t}} \end{align} \]

The temperature vector can be expressed as

\[ \begin{align} \label{eq:ch5_thermal_gov_disc2} \{T\}_{t=t_{0}+\triangle t}=\{T\}_{t=t_{0}+\triangle t}^{(i)}+\{\triangle T\}_{t=t_{0}+\triangle t}^{(i)} \end{align} \]

The product of the heat conduction matrix and temperature vector, mass matrix and etc. are expressed in approximation as in the following equation.

\[ \begin{align} \label{eq:ch5_thermal_gov_disc3} [\mathbf{K}]_{t=t_{0+\triangle t}}\{T\}_{t=t_{0+\triangle t}}\cong[\mathbf{K}]_{t=t_{0+\triangle t}}^{(i)}\{T\}_{t=t_{0+\triangle t}}^{(i)}+\dfrac{\partial[\mathbf{K}]_{t=t_{0+\triangle t}}^{(i)}\{T\}_{t=t_{0+\triangle t}}^{(i)}}{\partial\{T\}_{t=t_{0+\triangle t}}^{(i)}}\{\triangle T\}_{t=t_{0+\triangle t}}^{(i)} \end{align} \]
\[ \begin{align} \label{eq:ch5_thermal_gov_disc4} [M]_{t=t_{0+\triangle t}}\cong[M]_{t=t_{0}+\triangle t}^{(i)}+\dfrac{\partial[M]_{t=t_{0}+\triangle t}^{(i)}}{\partial\{T\}_{t=t_{0+\triangle t}}^{\{i\}}}\{\triangle T\}_{t=t_{0+\triangle t}}^{(i)} \end{align} \]

Substituting equations \(\eqref{eq:ch5_thermal_gov_disc2}\), \(\eqref{eq:ch5_thermal_gov_disc3}\), and \(\eqref{eq:ch5_thermal_gov_disc4}\) into equation \(\eqref{eq:ch5_thermal_gov_disc1}\) and skipping the high order polynomial terms, we have

\[ (\dfrac{[\mathbf{M}]_{t=t_{0+\triangle t}}^{(i)}}{\triangle t}+\dfrac{\partial[\mathbf{M}]_{t=t_{0+\triangle t}}^{(i)}\{T\}_{t=t_{0}+\text{\triangle t}}^{(i)}}{\partial\{T\}_{t=t_{0}+\triangle t}^{(i)}}\dfrac{\{T\}_{t=t_{0}+\triangle t}^{(i)}-\{T\}_{t=t0}}{\triangle t}+\dfrac{\partial[\mathbf{K}]_{t=t_{0}+\triangle t}^{(i)}\{T\}_{t=t_{0}+\triangle t}^{(i)}}{\partial\{T\}_{t=t_{0}+\triangle t}^{(i)}})\{\triangle T\}_{t=t_{0}+\triangle t}^{(i)}\\=\{F\}_{t=t_{0}+\triangle t}-[\mathbf{M}]_{t=t_{0}+\triangle t}^{(i)}\dfrac{\{T\}_{t=t_{0}+\triangle t}^{(i)}-\{T\}_{t=t_{0}}}{\triangle t}-[\mathbf{K}]_{t=t_{0}+\triangle t}^{(i)}\{T\}_{t=t_{0}+\triangle t}^{(i)} \]

Furthermore, an approximation evaluation for the left hand side factor is given below,

\[ [\mathbf{K}^{*}]^{(i)}=\dfrac{[M]_{t=t_{0}+\triangle t}^{(i)}}{\triangle t}+\dfrac{\partial[\mathbf{K}]_{t=t_{0}+\triangle t}^{(t)}}{\partial\{T\}_{t=t_{0}+\triangle t}^{(i)}}\{T\}_{t=t_{0}+\triangle t}^{(i)}=\dfrac{[M]_{t=t_{0}+\triangle t}^{(i)}}{\triangle t}+[\mathbf{K}_{T}]_{t=t_{0}+\triangle t}^{(i)} \]

where \([\mathbf{K}_{T}]_{t=t_{0}+\triangle t}^{(i)}\) tangent stiffness matrix.

Eventually, the temperature at time \(t=t_{0}+\triangle t\) can be calculated by iterative solver using the following scheme:

\[ \begin{array}{cc} [\mathbf{K}^{*}]^{(i)}\{T\}_{t=t_{0}+\triangle t}^{(i)}=\{F\}_{t=t_{0}+\triangle t}-[\mathbf{M}]_{t=t_{0}+\triangle t}^{(i)}\dfrac{\{T\}_{t=t_{0}+\triangle t}^{(i)}-\{T\}_{t=t_{0}}}{\triangle t}-[\mathbf{K}]_{t=t_{0}+\triangle t}^{(i)}\\ \{T\}_{t=t_{0}+\triangle t}^{(i+1)}=\{T\}_{t=t_{0}+\triangle t}^{(i)}+\{\triangle T\}_{t=t_{0}+\triangle t}^{(i)} \end{array} \]

For the steady state analysis, the iteration algorithm is given below

\[ \begin{array}{cc} [\mathbf{K}_{T}]^{(i)}\{\triangle T\}_{t=\infty}^{(i)}=\{F\}_{t=\infty}-[\mathbf{K}_{T}]^{(i)}\{\triangle T\}_{t=\infty}^{(i)}\\ \{T\}_{t=\infty}^{(i+1)}=\{T\}_{t=\infty}^{(i)}+\{\triangle T\}_{t=\infty}^{(i)} \end{array} \]

Since the implicit time solver is applied in the program, the selection of incremental time \(\triangle t\) is relatively flexible. However, if the magnitude of \(\triangle t\) is too large, the convergence frequency will be decreased in the iterative computation. The program contains automatic incremental functions to monitor the size of the residual vectors during the iterations. As the convergence rate becomes slow, the incremental time \(\triangle t\) is automatically reduced. When the convergence rate becomes high, the program increases the incremental time \(\triangle t\). Doing this automatic scheme can improve the numerical performance and saving computational time.

\ No newline at end of file + Thermal analysis - WelSim Documentation
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Thermal analysis

This section discuss the theories used in the WESLIM thermal analysis.

Governing equations

The governing equations applied in thermal analysis are:

\[ \begin{align} \label{eq:ch5_thermal_gov} \rho c\frac{\partial T}{\partial t}=\nabla\cdot(k\nabla T) \end{align} \]

where \(\rho=\rho(x)\) is mass density, \(c=c(x,T)\) is the specific heat, \(T=T(x,t)\) is the temperature, \(K=k(x,T)\) is the thermal conductivity, \(Q=Q(x,T,t)\) is the calorific value. \(x\) is the position in the modeling domain, \(T\) is the temperature and \(t\) is the time.

The modeling domain is represented by S, and the boundary is represented by \(\varGamma\). When assuming the boundary conditions of either the Dirichlet or Neumann type, those boundary conditions can be mathematically expressed as

\[ T=T_{1}(x,t) \qquad X\in\Gamma_{1} \]
\[ k\frac{\partial T}{\partial n}=q(x,T,t) \qquad X\in\Gamma_{2} \]

where the term \(T_{1}\), \(q\) is already known. \(q\) is the heat flux outflow from the boundary. Three types of heat flux can be considered in WELSIM thermal module.

\[ q=-q_{s}+q_{c}+q_{r} \]
\[ q_{s}=q_{s}(x,t) \]
\[ q_{c}=hc(T-T_{c}) \]
\[ q_{r}=hc(T^{4}-T_{r}^{4}) \]

where \(q_{s}\) is the distributed heat flux, \(q_{c}\) is the heat flux by the convective heat transfer, and \(q_{r}\) is the heat flux by the radiant heat transfer. The other quantities are

  • \(T_{c}=T_{c}(x,t)\) Convective heat transfer coefficient ambient temperature
  • \(h_{c}=h_{c}(x,t)\) Convective heat transfer factor
  • \(T_{r}=T_{r}(x,t)\) Radiant heat transfer coefficient ambient temperature
  • \(h_{r}=\epsilon\sigma F=h_{r}(x,t)\) Radiant heat transfer factor. \(\epsilon\) is the radiant rate, \(\sigma\) is the Stefan-Boltzmann constant, \(F\) is the shape factor.

Derivation of heat flow matrices

When equation \(\eqref{eq:ch5_thermal_gov}\) is discreted by the Galerkin approximation, it becomes as follows,

\[ \begin{align} \label{eq:ch5_thermal_gov2} [\mathbf{K}]\{T\}+[\mathbf{M}]\frac{\partial T}{\partial t}=\{F\} \end{align} \]

where the matrices and vectors are

\[ \begin{array}{ccc} [\mathbf{K}] & = & \int(k_{xx}\dfrac{\partial\{N\}^{T}}{\partial x}\dfrac{\partial\{N\}}{\partial x}+k_{yy}\dfrac{\partial\{N\}^{T}}{\partial y}\dfrac{\partial\{N\}}{\partial y}+k_{zz}\dfrac{\partial\{N\}^{T}}{\partial z}\dfrac{\partial\{N\}}{\partial z})dV\\ & + & \int h_{c}\{N\}^{T}\{N\}ds+\int h_{r}\{N\}^{T}\{N\}ds \end{array} \]
\[ [\mathbf{M}]=\int\rho c\{N\}^{T}\{N\}dV \]
\[ \{F\}=\int Q\{N\}^{T}dV-\int q_{s}\{N\}^{T}dS+\int h_{c}T_{c}\{N\}^{T}dS+\int h_{r}T_{r}(T+T_{r})(T^{2}+T_{r}^{2})\{N\}^{T}dS \]

where shape function

\[ \{N\}=(N^{1},N^{2},.......),\thinspace N_{i}=N_{i}(x) \]

Equation \(\eqref{eq:ch5_thermal_gov2}\) is nonlinear and unsteady. When the time is discretized by the backward Euler's rule and the temperature at time t=t_{0} is known, the temperature at t=t_{0+\triangle t} is calculated using the following equation.

\[ \begin{align} \label{eq:ch5_thermal_gov_disc1} [\mathbf{K}]_{t=t_{0+\triangle t}}\{T\}_{t=t_{0+\triangle t}}+[\mathbf{M}]_{t=t_{0+\triangle t}}\dfrac{\{T\}_{t=t_{0+\triangle t}}-\{T\}_{t=t_{0}}}{\triangle t}=\{F\}_{t=t_{0+\triangle t}} \end{align} \]

The temperature vector can be expressed as

\[ \begin{align} \label{eq:ch5_thermal_gov_disc2} \{T\}_{t=t_{0}+\triangle t}=\{T\}_{t=t_{0}+\triangle t}^{(i)}+\{\triangle T\}_{t=t_{0}+\triangle t}^{(i)} \end{align} \]

The product of the heat conduction matrix and temperature vector, mass matrix and etc. are expressed in approximation as in the following equation.

\[ \begin{align} \label{eq:ch5_thermal_gov_disc3} [\mathbf{K}]_{t=t_{0+\triangle t}}\{T\}_{t=t_{0+\triangle t}}\cong[\mathbf{K}]_{t=t_{0+\triangle t}}^{(i)}\{T\}_{t=t_{0+\triangle t}}^{(i)}+\dfrac{\partial[\mathbf{K}]_{t=t_{0+\triangle t}}^{(i)}\{T\}_{t=t_{0+\triangle t}}^{(i)}}{\partial\{T\}_{t=t_{0+\triangle t}}^{(i)}}\{\triangle T\}_{t=t_{0+\triangle t}}^{(i)} \end{align} \]
\[ \begin{align} \label{eq:ch5_thermal_gov_disc4} [M]_{t=t_{0+\triangle t}}\cong[M]_{t=t_{0}+\triangle t}^{(i)}+\dfrac{\partial[M]_{t=t_{0}+\triangle t}^{(i)}}{\partial\{T\}_{t=t_{0+\triangle t}}^{\{i\}}}\{\triangle T\}_{t=t_{0+\triangle t}}^{(i)} \end{align} \]

Substituting equations \(\eqref{eq:ch5_thermal_gov_disc2}\), \(\eqref{eq:ch5_thermal_gov_disc3}\), and \(\eqref{eq:ch5_thermal_gov_disc4}\) into equation \(\eqref{eq:ch5_thermal_gov_disc1}\) and skipping the high order polynomial terms, we have

\[ (\dfrac{[\mathbf{M}]_{t=t_{0+\triangle t}}^{(i)}}{\triangle t}+\dfrac{\partial[\mathbf{M}]_{t=t_{0+\triangle t}}^{(i)}\{T\}_{t=t_{0}+\text{\triangle t}}^{(i)}}{\partial\{T\}_{t=t_{0}+\triangle t}^{(i)}}\dfrac{\{T\}_{t=t_{0}+\triangle t}^{(i)}-\{T\}_{t=t0}}{\triangle t}+\dfrac{\partial[\mathbf{K}]_{t=t_{0}+\triangle t}^{(i)}\{T\}_{t=t_{0}+\triangle t}^{(i)}}{\partial\{T\}_{t=t_{0}+\triangle t}^{(i)}})\{\triangle T\}_{t=t_{0}+\triangle t}^{(i)}\\=\{F\}_{t=t_{0}+\triangle t}-[\mathbf{M}]_{t=t_{0}+\triangle t}^{(i)}\dfrac{\{T\}_{t=t_{0}+\triangle t}^{(i)}-\{T\}_{t=t_{0}}}{\triangle t}-[\mathbf{K}]_{t=t_{0}+\triangle t}^{(i)}\{T\}_{t=t_{0}+\triangle t}^{(i)} \]

Furthermore, an approximation evaluation for the left hand side factor is given below,

\[ [\mathbf{K}^{*}]^{(i)}=\dfrac{[M]_{t=t_{0}+\triangle t}^{(i)}}{\triangle t}+\dfrac{\partial[\mathbf{K}]_{t=t_{0}+\triangle t}^{(t)}}{\partial\{T\}_{t=t_{0}+\triangle t}^{(i)}}\{T\}_{t=t_{0}+\triangle t}^{(i)}=\dfrac{[M]_{t=t_{0}+\triangle t}^{(i)}}{\triangle t}+[\mathbf{K}_{T}]_{t=t_{0}+\triangle t}^{(i)} \]

where \([\mathbf{K}_{T}]_{t=t_{0}+\triangle t}^{(i)}\) tangent stiffness matrix.

Eventually, the temperature at time \(t=t_{0}+\triangle t\) can be calculated by iterative solver using the following scheme:

\[ \begin{array}{cc} [\mathbf{K}^{*}]^{(i)}\{T\}_{t=t_{0}+\triangle t}^{(i)}=\{F\}_{t=t_{0}+\triangle t}-[\mathbf{M}]_{t=t_{0}+\triangle t}^{(i)}\dfrac{\{T\}_{t=t_{0}+\triangle t}^{(i)}-\{T\}_{t=t_{0}}}{\triangle t}-[\mathbf{K}]_{t=t_{0}+\triangle t}^{(i)}\\ \{T\}_{t=t_{0}+\triangle t}^{(i+1)}=\{T\}_{t=t_{0}+\triangle t}^{(i)}+\{\triangle T\}_{t=t_{0}+\triangle t}^{(i)} \end{array} \]

For the steady state analysis, the iteration algorithm is given below

\[ \begin{array}{cc} [\mathbf{K}_{T}]^{(i)}\{\triangle T\}_{t=\infty}^{(i)}=\{F\}_{t=\infty}-[\mathbf{K}_{T}]^{(i)}\{\triangle T\}_{t=\infty}^{(i)}\\ \{T\}_{t=\infty}^{(i+1)}=\{T\}_{t=\infty}^{(i)}+\{\triangle T\}_{t=\infty}^{(i)} \end{array} \]

Since the implicit time solver is applied in the program, the selection of incremental time \(\triangle t\) is relatively flexible. However, if the magnitude of \(\triangle t\) is too large, the convergence frequency will be decreased in the iterative computation. The program contains automatic incremental functions to monitor the size of the residual vectors during the iterations. As the convergence rate becomes slow, the incremental time \(\triangle t\) is automatically reduced. When the convergence rate becomes high, the program increases the incremental time \(\triangle t\). Doing this automatic scheme can improve the numerical performance and saving computational time.

\ No newline at end of file diff --git a/welsim/theory/transient/index.html b/welsim/theory/transient/index.html index 827a1b6..3236b95 100755 --- a/welsim/theory/transient/index.html +++ b/welsim/theory/transient/index.html @@ -1 +1 @@ - Structures with transient analysis - WelSim Documentation
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Structures with transient analysis

The time integration method applied in structural transient analysis is described in the section.

Formulation of implicit method

In the direct time integration, the equation of motion can be expressed as follows

\[ \begin{align} \label{eq:ch5_time_solver_imp1} \mathbf{M}(t+\triangle t)\ddot{\mathbf{U}}(t+\triangle t)+\mathbf{C}(t+\triangle t)\dot{\mathbf{U}}(t+\triangle t)+\mathbf{Q}(t+\triangle t)=\mathbf{F}(t+\triangle t) \end{align} \]

where \(\mathbf{M}\) and \(\mathbf{C}\) is the mass matrix and damping matrix, respectively. The \(\mathbf{Q}\) and \(\mathbf{F}\) are the internal force vector, and external force vector, respectively. Note that, the mass density is consistent in the structural analysis, thus the mass matrix keep constants regardless of the deformation in non-linearity.

In the Newmark-\(\beta\) method, the displacement, velocity, and acceleration at the each time incremental \(\triangle t\) are

\[ \begin{align} \label{eq:ch5_time_solver_imp2} \dot{\mathbf{U}}(t+\triangle t)=\dfrac{\gamma}{\beta\triangle t}\triangle\mathbf{U}(t+\triangle t)-\dfrac{\gamma-\beta}{\beta}\dot{\mathbf{U}}(t)-\triangle t\dfrac{\gamma-2\beta}{2\beta}\ddot{\mathbf{U}}(t) \end{align} \]
\[ \begin{align} \label{eq:ch5_time_solver_imp3} \ddot{\mathbf{U}}(t+\triangle t)=\dfrac{\text{1}}{\beta\triangle t^{2}}\triangle\mathbf{U}(t+\triangle t)-\dfrac{1}{\beta\triangle t}\dot{\mathbf{U}}(t)-\dfrac{1-2\beta}{2\beta}\ddot{\mathbf{U}}(t) \end{align} \]

where \(\gamma\) and \(\beta\) are time solver parameters. Given the specific values, the numerical algorithm becomes linear acceleration method, or the trapezoid rule.

\[ \gamma=\frac{1}{2},\thinspace\beta=\frac{1}{6},\quad\mathrm{Linear}\thinspace\mathrm{acceleration\thinspace\mathrm{method}} \]
\[ \gamma=\frac{1}{2},\thinspace\beta=\frac{1}{4},\quad\mathrm{Trapezoid}\thinspace\mathrm{rule} \]

substituting equations \(\eqref{eq:ch5_time_solver_imp2}\) and \(\eqref{eq:ch5_time_solver_imp3}\) into equation \(\eqref{eq:ch5_time_solver_imp1}\), the following equation can be acquired

\[ \begin{array}{ccc} (\dfrac{1}{\beta\triangle t^{2}}\mathbf{M}+\dfrac{\gamma}{\beta\triangle t}\mathbf{C}+\mathbf{K})\triangle\mathbf{U}(t+\triangle t) & = & \mathbf{F}(t+\triangle t)-\mathbf{Q}(t+\triangle t)\\ & + & \dfrac{1}{\beta\triangle t}\mathbf{\mathbf{M}\dot{\mathbf{U}}}(t)+\dfrac{1-2\beta}{2\beta}\mathbf{M}\ddot{\mathbf{U}}(t)+\dfrac{\gamma-\beta}{\beta}\mathbf{C}\dot{\mathbf{U}}(t)\\ & + & \triangle t\dfrac{\gamma-2\beta}{2\beta}\mathbf{C}\ddot{\mathbf{U}}(t) \end{array} \]

when we use linear stiffness matrix \(\mathbf{K}_{L}\) for a linear problem, the equation above becomes \(\mathbf{Q}(t+\triangle t)=\mathbf{K}_{L}\mathbf{U}(t+\triangle t)\). Substituting this term into the equation (), we have

\[ \begin{array}{ccc} \{\mathbf{M}(-\dfrac{1}{(\triangle t)^{2}\beta}\mathbf{U}(t)-\dfrac{1}{(\triangle t)\beta}\dot{\mathbf{U}}(t)-\dfrac{1-2\beta}{2\beta}\ddot{\mathbf{U}}(t))\\ +\mathbf{C}(-\dfrac{\gamma}{(\triangle t)\beta}\mathbf{U}(t)+(1-\dfrac{\gamma}{\beta})\dot{\mathbf{U}}(t)+\triangle t\dfrac{2\beta-\gamma}{2\beta}\ddot{\mathbf{U}}(t))\}\\ +\{\dfrac{1}{(\triangle t)^{2}\beta}\mathbf{M}+\dfrac{\gamma}{(\triangle t)\beta}\mathbf{C}+\mathbf{K}_{L}\}\mathbf{U}(t+\triangle t) & = & \mathbf{F}(t+\triangle t) \end{array} \]

In the analysis practice, the acceleration and velocity boundary conditions are imposed. Then the displacement of the following equation can be derived from equation \(\eqref{eq:ch5_time_solver_imp1}\).

\[ u_{is}(t+\triangle t)=u_{is}(t)+\triangle t\dot{u}_{is}(t)+(\triangle t)^{2}(\frac{1}{2}-\beta)\ddot{u}_{is}(t+\triangle t) \]

where \(u_{is}(t+\triangle t)\) is the nodal displacement at time \(t+\triangle t\), \(\dot{u}{}_{is}(t+\triangle t)\) is the nodal velocity, \(\ddot{u}{}_{is}(t+\triangle t)\) is the nodal acceleration, i is the degree of freedom per node, s is the node number.

The mass and damping terms are treated as follows

  1. The lumped mass matrix is used at most of cases in this program.
  2. The damping matrix is treated using Rayleigh algorithm \(\mathbf{C}=R_{m}\mathbf{M}+R_{k}\mathbf{K}_{L}\).

Formulation of explicit method

This section discuss how the explicit time solver is formulation to solve the governing equation below

\[ \begin{align} \label{eq:ch5_time_solver_exp1} \mathbf{M}\ddot{\mathbf{U}}(t)+\mathbf{C}\text{(t)}\dot{\mathbf{U}(t)+\mathbf{Q}(t)=\mathbf{F}(t)} \end{align} \]

where the displacement at the time \(t+\triangle t\) and \(t-\triangle t\) can be expressed by the Taylor's expansion at time t with the second order truncation.

\[ \begin{align} \label{eq:ch5_time_solver_exp2} \mathbf{U}(t+\triangle t)=\mathbf{U}(t)+\dot{\mathbf{U}}(t)(\triangle t)+\dfrac{1}{2!}\ddot{\mathbf{U}}(t)(\triangle t)^{2} \end{align} \]
\[ \begin{align} \label{eq:ch5_time_solver_exp3} \mathbf{U}(t-\triangle t)=\mathbf{U}(t)-\dot{\mathbf{U}}(t)(\triangle t)+\dfrac{1}{2!}\ddot{\mathbf{U}}(t)(\triangle t)^{2} \end{align} \]

Differentiating equations \(\eqref{eq:ch5_time_solver_exp2}\) and \(\eqref{eq:ch5_time_solver_exp3}\), we have

\[ \begin{align} \label{eq:ch5_time_solver_exp4} \dot{\mathbf{U}}(t)=\dfrac{1}{2\triangle t}(\mathbf{U}(t+\triangle t)-\mathbf{U}(t-\triangle t)) \end{align} \]
\[ \begin{align} \label{eq:ch5_time_solver_exp5} \ddot{\mathbf{U}}(t)=\dfrac{1}{(\triangle t)^{2}}(\mathbf{U}(t+\triangle t)-2\mathbf{U}(t)+\mathbf{U}(t-\triangle t)) \end{align} \]

Substituting equations \(\eqref{eq:ch5_time_solver_exp4}\) and \(\eqref{eq:ch5_time_solver_exp5}\) into \(\eqref{eq:ch5_time_solver_exp1}\), we have

\[ (\dfrac{1}{\triangle t^{2}}\mathbf{M}+\dfrac{1}{2\triangle t}\mathbf{C})\mathbf{U}(t+\triangle t)=\mathbf{F}(t)-\mathbf{Q}(t)-\dfrac{1}{\triangle t^{2}}\mathbf{M}[2\mathbf{U}(t)-\mathbf{U}(t-\triangle t)]-\dfrac{1}{2\triangle t}\mathbf{CU}(t-\triangle t) \]

For the linear problem, we also have condition \(\mathbf{Q}(t)=\mathbf{K}_{L}\mathbf{U}(t)\) for equation. Finally, the displacement at \(t+\triangle t\) is:

\[ \mathbf{U}(t+\triangle t)=\dfrac{1}{(\frac{1}{\triangle t^{2}}\mathbf{M}+\frac{1}{2\triangle t}\mathbf{C})}\{\mathbf{F}(t)-\mathbf{Q}(t)-\dfrac{1}{\triangle t^{2}}\mathbf{M}[2\mathbf{U}(t)-\mathbf{U}(t-\triangle t)]-\dfrac{1}{2\triangle t}\mathbf{C}(t-\triangle t)\mathbf{U}\} \]
\ No newline at end of file + Structures with transient analysis - WelSim Documentation
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Structures with transient analysis

The time integration method applied in structural transient analysis is described in the section.

Formulation of implicit method

In the direct time integration, the equation of motion can be expressed as follows

\[ \begin{align} \label{eq:ch5_time_solver_imp1} \mathbf{M}(t+\triangle t)\ddot{\mathbf{U}}(t+\triangle t)+\mathbf{C}(t+\triangle t)\dot{\mathbf{U}}(t+\triangle t)+\mathbf{Q}(t+\triangle t)=\mathbf{F}(t+\triangle t) \end{align} \]

where \(\mathbf{M}\) and \(\mathbf{C}\) is the mass matrix and damping matrix, respectively. The \(\mathbf{Q}\) and \(\mathbf{F}\) are the internal force vector, and external force vector, respectively. Note that, the mass density is consistent in the structural analysis, thus the mass matrix keep constants regardless of the deformation in non-linearity.

In the Newmark-\(\beta\) method, the displacement, velocity, and acceleration at the each time incremental \(\triangle t\) are

\[ \begin{align} \label{eq:ch5_time_solver_imp2} \dot{\mathbf{U}}(t+\triangle t)=\dfrac{\gamma}{\beta\triangle t}\triangle\mathbf{U}(t+\triangle t)-\dfrac{\gamma-\beta}{\beta}\dot{\mathbf{U}}(t)-\triangle t\dfrac{\gamma-2\beta}{2\beta}\ddot{\mathbf{U}}(t) \end{align} \]
\[ \begin{align} \label{eq:ch5_time_solver_imp3} \ddot{\mathbf{U}}(t+\triangle t)=\dfrac{\text{1}}{\beta\triangle t^{2}}\triangle\mathbf{U}(t+\triangle t)-\dfrac{1}{\beta\triangle t}\dot{\mathbf{U}}(t)-\dfrac{1-2\beta}{2\beta}\ddot{\mathbf{U}}(t) \end{align} \]

where \(\gamma\) and \(\beta\) are time solver parameters. Given the specific values, the numerical algorithm becomes linear acceleration method, or the trapezoid rule.

\[ \gamma=\frac{1}{2},\thinspace\beta=\frac{1}{6},\quad\mathrm{Linear}\thinspace\mathrm{acceleration\thinspace\mathrm{method}} \]
\[ \gamma=\frac{1}{2},\thinspace\beta=\frac{1}{4},\quad\mathrm{Trapezoid}\thinspace\mathrm{rule} \]

substituting equations \(\eqref{eq:ch5_time_solver_imp2}\) and \(\eqref{eq:ch5_time_solver_imp3}\) into equation \(\eqref{eq:ch5_time_solver_imp1}\), the following equation can be acquired

\[ \begin{array}{ccc} (\dfrac{1}{\beta\triangle t^{2}}\mathbf{M}+\dfrac{\gamma}{\beta\triangle t}\mathbf{C}+\mathbf{K})\triangle\mathbf{U}(t+\triangle t) & = & \mathbf{F}(t+\triangle t)-\mathbf{Q}(t+\triangle t)\\ & + & \dfrac{1}{\beta\triangle t}\mathbf{\mathbf{M}\dot{\mathbf{U}}}(t)+\dfrac{1-2\beta}{2\beta}\mathbf{M}\ddot{\mathbf{U}}(t)+\dfrac{\gamma-\beta}{\beta}\mathbf{C}\dot{\mathbf{U}}(t)\\ & + & \triangle t\dfrac{\gamma-2\beta}{2\beta}\mathbf{C}\ddot{\mathbf{U}}(t) \end{array} \]

when we use linear stiffness matrix \(\mathbf{K}_{L}\) for a linear problem, the equation above becomes \(\mathbf{Q}(t+\triangle t)=\mathbf{K}_{L}\mathbf{U}(t+\triangle t)\). Substituting this term into the equation (), we have

\[ \begin{array}{ccc} \{\mathbf{M}(-\dfrac{1}{(\triangle t)^{2}\beta}\mathbf{U}(t)-\dfrac{1}{(\triangle t)\beta}\dot{\mathbf{U}}(t)-\dfrac{1-2\beta}{2\beta}\ddot{\mathbf{U}}(t))\\ +\mathbf{C}(-\dfrac{\gamma}{(\triangle t)\beta}\mathbf{U}(t)+(1-\dfrac{\gamma}{\beta})\dot{\mathbf{U}}(t)+\triangle t\dfrac{2\beta-\gamma}{2\beta}\ddot{\mathbf{U}}(t))\}\\ +\{\dfrac{1}{(\triangle t)^{2}\beta}\mathbf{M}+\dfrac{\gamma}{(\triangle t)\beta}\mathbf{C}+\mathbf{K}_{L}\}\mathbf{U}(t+\triangle t) & = & \mathbf{F}(t+\triangle t) \end{array} \]

In the analysis practice, the acceleration and velocity boundary conditions are imposed. Then the displacement of the following equation can be derived from equation \(\eqref{eq:ch5_time_solver_imp1}\).

\[ u_{is}(t+\triangle t)=u_{is}(t)+\triangle t\dot{u}_{is}(t)+(\triangle t)^{2}(\frac{1}{2}-\beta)\ddot{u}_{is}(t+\triangle t) \]

where \(u_{is}(t+\triangle t)\) is the nodal displacement at time \(t+\triangle t\), \(\dot{u}{}_{is}(t+\triangle t)\) is the nodal velocity, \(\ddot{u}{}_{is}(t+\triangle t)\) is the nodal acceleration, i is the degree of freedom per node, s is the node number.

The mass and damping terms are treated as follows

  1. The lumped mass matrix is used at most of cases in this program.
  2. The damping matrix is treated using Rayleigh algorithm \(\mathbf{C}=R_{m}\mathbf{M}+R_{k}\mathbf{K}_{L}\).

Formulation of explicit method

This section discuss how the explicit time solver is formulation to solve the governing equation below

\[ \begin{align} \label{eq:ch5_time_solver_exp1} \mathbf{M}\ddot{\mathbf{U}}(t)+\mathbf{C}\text{(t)}\dot{\mathbf{U}(t)+\mathbf{Q}(t)=\mathbf{F}(t)} \end{align} \]

where the displacement at the time \(t+\triangle t\) and \(t-\triangle t\) can be expressed by the Taylor's expansion at time t with the second order truncation.

\[ \begin{align} \label{eq:ch5_time_solver_exp2} \mathbf{U}(t+\triangle t)=\mathbf{U}(t)+\dot{\mathbf{U}}(t)(\triangle t)+\dfrac{1}{2!}\ddot{\mathbf{U}}(t)(\triangle t)^{2} \end{align} \]
\[ \begin{align} \label{eq:ch5_time_solver_exp3} \mathbf{U}(t-\triangle t)=\mathbf{U}(t)-\dot{\mathbf{U}}(t)(\triangle t)+\dfrac{1}{2!}\ddot{\mathbf{U}}(t)(\triangle t)^{2} \end{align} \]

Differentiating equations \(\eqref{eq:ch5_time_solver_exp2}\) and \(\eqref{eq:ch5_time_solver_exp3}\), we have

\[ \begin{align} \label{eq:ch5_time_solver_exp4} \dot{\mathbf{U}}(t)=\dfrac{1}{2\triangle t}(\mathbf{U}(t+\triangle t)-\mathbf{U}(t-\triangle t)) \end{align} \]
\[ \begin{align} \label{eq:ch5_time_solver_exp5} \ddot{\mathbf{U}}(t)=\dfrac{1}{(\triangle t)^{2}}(\mathbf{U}(t+\triangle t)-2\mathbf{U}(t)+\mathbf{U}(t-\triangle t)) \end{align} \]

Substituting equations \(\eqref{eq:ch5_time_solver_exp4}\) and \(\eqref{eq:ch5_time_solver_exp5}\) into \(\eqref{eq:ch5_time_solver_exp1}\), we have

\[ (\dfrac{1}{\triangle t^{2}}\mathbf{M}+\dfrac{1}{2\triangle t}\mathbf{C})\mathbf{U}(t+\triangle t)=\mathbf{F}(t)-\mathbf{Q}(t)-\dfrac{1}{\triangle t^{2}}\mathbf{M}[2\mathbf{U}(t)-\mathbf{U}(t-\triangle t)]-\dfrac{1}{2\triangle t}\mathbf{CU}(t-\triangle t) \]

For the linear problem, we also have condition \(\mathbf{Q}(t)=\mathbf{K}_{L}\mathbf{U}(t)\) for equation. Finally, the displacement at \(t+\triangle t\) is:

\[ \mathbf{U}(t+\triangle t)=\dfrac{1}{(\frac{1}{\triangle t^{2}}\mathbf{M}+\frac{1}{2\triangle t}\mathbf{C})}\{\mathbf{F}(t)-\mathbf{Q}(t)-\dfrac{1}{\triangle t^{2}}\mathbf{M}[2\mathbf{U}(t)-\mathbf{U}(t-\triangle t)]-\dfrac{1}{2\triangle t}\mathbf{C}(t-\triangle t)\mathbf{U}\} \]
\ No newline at end of file diff --git a/welsim/troubleshooting/index.html b/welsim/troubleshooting/index.html index 8935191..32db1e3 100755 --- a/welsim/troubleshooting/index.html +++ b/welsim/troubleshooting/index.html @@ -1 +1 @@ - Troubleshooting - WelSim Documentation
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Troubleshooting

If you encounter an issue that cannot be resolved here, please send the project file (*.wsdb and the associated folder), and the system information to info@welsim.com. Your computer information can be acquired by clicking About button on the toolbar.

Graphical window issue

The graphics window fails to display items, and the context is all black. The screen capture of this issue is shown in Figure [fig:ch6_issue_opengl].

finite_element_analysis_welsim_troubleshooting_1

  • Cause: This issue is due to an unsupported graphics card or driver.

  • Solution: Set the environment variable QT_OPENGL=desktop then restart the WelSim application. The graphics window shall display the context correctly.

\ No newline at end of file + Troubleshooting - WelSim Documentation
Skip to content

Troubleshooting

If you encounter an issue that cannot be resolved here, please send the project file (*.wsdb and the associated folder), and the system information to info@welsim.com. Your computer information can be acquired by clicking About button on the toolbar.

Graphical window issue

The graphics window fails to display items, and the context is all black. The screen capture of this issue is shown in Figure below.

finite_element_analysis_welsim_troubleshooting_1

  • Cause: This issue is due to an unsupported graphics card or driver.

  • Solution: Set the environment variable QT_OPENGL=desktop then restart the WelSim application. The graphics window shall display the context correctly.

Result data matching issue

The result fails to display contours due to the dismatched mesh. The error message of this issue is shown in Figure below.

finite_element_analysis_welsim_result_data_point_error1

  • Cause: This issue is due to dismatched data between result and mesh.

  • Solution: This could be a software defect, send the model to the info@welsim.com for investigation.

\ No newline at end of file diff --git a/welsim/users/analysistypes/index.html b/welsim/users/analysistypes/index.html index 4912310..d6b415e 100755 --- a/welsim/users/analysistypes/index.html +++ b/welsim/users/analysistypes/index.html @@ -1 +1 @@ - Physics and analysis types - WelSim Documentation
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Physics and analysis types

WELSIM supports several types of finite element analyses. This section describes those analysis types that you can perform in the WELSIM user interface.

Static structural analysis

As one of the most widely used analysis types, a static structural analysis discloses the structural displacements, stresses, strains, and forces caused by loads or other mechanical effects. In this static analysis, the constant loading and response are assumed.

The static structural analysis can be either linear or nonlinear. The non-linearity can be introduced by the large deformations, in-elasticity, contact, hyperelasticity, etc. For the nonlinear problem, it is recommended to set multiple substeps in the Study Settings.

Conducting a static structural analysis

The following lists the general and specifics steps in conducting static structural analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Structural and Analysis Type to Static. Since the static structural analysis is the default analysis type, you do not need to change these properties if the analysis is newly created. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, the default setting is Solid. You need to change this property value accordingly if the geometry is Shell or other types. See Defining Part Behaviors for details.

  5. Setting bonnections: Optional. Contacts are supported in a static structural analysis. See Setting Connections for details.

  6. Applying mesh: It is recommended to generate Tet10 elements for Solid analysis and the Tri6 element for the Shell analysis. See Applying Mesh for details.

  7. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analyses such as nonlinear models, the analysis controls you can tune: Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  8. Setting up boundary conditions: For a static structural analysis, the applicable boundary conditions are Fixed Supported, Fixed Rotation, Displacement, Force, and Pressure. The following body conditions are supported: Body Force, Acceleration, Earth Gravity, and Rotational Velocity. See Setting up Boundary Conditions for details.

  9. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  10. Evaluating results: For a static structural analysis, the applicable results are Deformations, Stresses, Strains, Rotations, Reaction Forces, and Reaction Moments. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

Transient structural analysis

In the transient structural analysis, the dynamic response is updated and is a function of time. You can impose general time-dependent boundary conditions on the model and obtain the time-varying responded to these transient loads or constraints. The inertia or damping effects play important roles in this analysis type, if the inertia and damping effects are minimal, you could use the static analysis instead.

The transient structural analysis can be either linear or nonlinear. The non-linearity can be introduced by the large deformations, inelasticity, contact, hyperelasticity, etc. For the nonlinear problem, it is recommended to set multiple substeps for each load step in the Study Settings.

Conducting a transient structural analysis

The following lists the general and specifics steps in conducting transient structural analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Structural and Analysis Type to Transient. You can choose either Implicit or Explicit time integration solver. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. You need to change this property value accordingly if the geometry is Shell or other types. See Defining Part Behaviors for details.

  5. Setting connections: Optional. Contacts are supported in a transient structural analysis. See Setting Connections for details.

  6. Applying mesh: It is recommended to generate Tet10 elements for Solid analysis and the Tri6 element for the Shell analysis. See Applying Mesh for details.

  7. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analyses such as nonlinear models, the analysis controls you can tune are Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  8. Defining initial conditions: Optional. In the transient structural analysis, you can define the initial status of boundary and body conditions. The Initial Status property provides two options: None and Equal to Step 1. The default option None set the initial value to zero, the option Equal to Step 1 set the initial value to that of step 1. See Defining Initial Conditions for details.

  9. Setting up boundary conditions: For the transient structural analysis, the applicable boundary conditions are Fixed Supported, Fixed Rotation, Displacement, Force, Pressure, Velocity, and Acceleration. The following body conditions are supported: Body Force, Acceleration, Earth Gravity, and Rotational Velocity. See Setting up Boundary Conditions for details.

  10. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  11. Evaluating results: For the transient structural analysis, the applicable results are: Deformations, Stresses, Strains, Rotations, Reaction Forces, Reaction Moments, Velocity, and Acceleration. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

finite_element_analysis_welsim_structural_tran_prop

The modal analysis investigates the vibration characteristics of a structure or component. You can obtain the natural frequencies and mode shapes, which serve as a starting pointing for dynamic analysis of the target structure.

Conducting a modal structural analysis

The following lists the general and specifics steps in conducting modal structural analysis:

  1. Creating analysis environment: From the properties view of FEM Project object, set the Physics Type to Structural and Analysis Type to Modal. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. However, the nonlinearity in the modal analysis is ignored due to the characteristics of eigen solver algorithms. You must define the sufficient properties that are required in the solving process. For example, the mass density parameter must be defined. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. You need to change this property value accordingly if the geometry is Shell or other types. See Defining Part Behaviors for details.

  5. Setting connections: Optional. The Bonded Contacts are supported in a modal structural analysis. See Setting Connections for details.

  6. Applying mesh: It is recommended to generate the Tet10 elements for Solid analysis and the Tri6 element for the Shell analysis. See Applying Mesh for details.

  7. Configuring study settings: You typically do not need to change these settings for simple modal analyses. The default number of modes is 6, increasing this value yields to calculate more natural frequency modes, while it requires more computational resources. See Configuring Study Settings for details.

  8. Setting up boundary conditions: For the modal structural analysis, the applicable boundary conditions are Fixed Supported, Fixed Rotation, zero Displacement. The following body conditions are supported: Body Force, Acceleration, Earth Gravity, and Rotational Velocity. Note that only constraint-type boundaries are applicable in modal analysis. See Setting up Boundary Conditions for details.

  9. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  10. Evaluating results: For the modal structural analysis, the applicable results are Deformations, and Frequencies. Note that deformation results here are just relative quantities intended to show the shape modes. The Tabular Data and Chart windows display the frequencies and related mode numbers. See Evaluating Results for details.

finite_element_analysis_welsim_modal_study_ana_prop

Steady-state thermal analysis

In the steady-state thermal analysis, you can determine the temperatures in objects that are impacted by the time-invariant thermal loads. Users are recommended to perform a steady-state analysis before conducting a transient study in a complex model.

The static thermal analysis can be either linear or nonlinear. The nonlinearity can be introduced by the temperature-depend material properties, or radiation and convection coefficient. For the nonlinear problem, it is recommended to set multiple substeps in the Study Settings.

Conducting a static structural analysis

The following lists the general and specifics steps in conducting static structural analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Thermal and Analysis Type to Static. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. You need to change this property value accordingly if the geometry is Shell or other types. See Defining Part Behaviors for details.

  5. Setting connections: Optional. The steady-state thermal analysis supports the Bonded Contact. See Setting Connections for details.

  6. Applying mesh: It is recommended to generate the Tet10 elements for Solid analysis, and the Tri6 element for the Shell analysis. See Applying Mesh for details.

  7. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analysis such as nonlinear models, the analysis controls you can tune are Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  8. Setting up boundary conditions: In the steady-state thermal analysis, the applicable boundary conditions are: Temperature, Heat Flux, Convection, and Radiation. See Setting up Boundary Conditions for details.

  9. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  10. Evaluating results: In steady-state thermal analysis, the applicable results are Temperature. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

Transient thermal analysis

In the transient thermal analysis, you can obtain the temperatures of objects that vary over time. Many heat transfer applications such as coiling or quenching problems, and so on involve transient thermal analysis. The transient thermal analysis can be either linear or nonlinear. The nonlinearity can be introduced by the temperature-dependent material properties or convection and radiation boundary conditions. For the nonlinear problem, it is recommended to define multiple substeps for each load step in the Study Settings.

Conducting a transient thermal analysis

The following lists the general and specifics steps in conducting transient thermal analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Thermal and Analysis Type to Transient. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. You need to change this property value accordingly if the geometry is Shell or other types. See Defining Part Behaviors for details.

  5. Setting connections: Optional. In the transient thermal analysis, the Bonded Contact is supported. See Setting Connections for details.

  6. Applying mesh: It is recommended to generate the Tet10 elements for Solid analysis and the Tri6 element for the Shell analysis. See Applying Mesh for details.

  7. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analysis such as nonlinear models, the analysis controls you can tune are Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  8. Setting up boundary conditions: In the transient thermal analysis, the applicable boundary conditions are: Temperature, Heat Flux, Convection, and Radiation. See Setting up Boundary Conditions for details.

  9. Defining initial conditions: You can define the global initial temperature condition for the analysis. In the transient thermal analysis, you can define the initial status of boundary and body conditions. The Initial Status property provides two options: None and Equal to Step 1. The default option None set the initial value to zero, the option Equal to Step 1 set the initial value to that of step 1. See Defining Initial Conditions for details.

  10. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  11. Evaluating results: In the transient thermal analysis, the applicable results are Temperature. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

ElectroStatic Analysis

The electrostatic analysis can be applied to determine the distribution of electric potential in a conducting body under voltage or current conditions. You can obtain the solution results such as voltage, electric field, etc. The electrostatic analysis supports the single body analysis.

An electrostatic analysis could be either linear or nonlinear. The electric field dependent material properties can introduce the nonlinearity. For the nonlinear problem, it is recommended to set multiple substeps in the Study Settings.

Conducting an electrostatic analysis

The following lists the general and specifics steps in conducting electrostatic analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Electromagnetic and Analysis Type to ElectroStatic. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. An electrostatic analysis only supports the Solid geometry type. See Defining Part Behaviors for details.

  5. Applying mesh: It is recommended to generate Tet10 elements for Solid analysis. See Applying Mesh for details.

  6. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analysis such as nonlinear models, the analysis controls you can tune are Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  7. Setting up boundary conditions: In the electrostatic analysis, the applicable boundary conditions are Ground, Voltage, Symmetry, Zero Charge, Surface Charge Density, and Electric Displacement. See Setting up Boundary Conditions for details.

  8. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  9. Evaluating results: In the electrostatic analysis, the applicable results are Voltage, Electric Field, Electric Displacement, and Energy Density. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

MagnetoStatic analysis

The magnetostatic analysis determines the magnetic field in and around a magnetic body.

A magnetostatic analysis requires the medium such as air surrounding the geometry be included as part of the entire simulation domain. In many cases, the full model can be reduced to the symmetric model by applying a symmetric boundary condition on the symmetric surface.

Conducting a magnetostatic analysis

The following lists the general and specifics steps in conducting magnetostatic analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Electromagnetic and Analysis Type to MagnetoStatic. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. A magnetostatic analysis only supports the Solid geometry type. See Defining Part Behaviors for details.

  5. Applying mesh: It is recommended to generate the Tet10 elements for magnetostatic analysis. See Applying Mesh for details.

  6. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analysis such as nonlinear models, the analysis controls you can tune are Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  7. Setting up boundary conditions: In the magnetostatic analysis, the applicable boundary conditions are Insulating, Symmetry, Magnetic Potential, and Magnetic Flux Density. See Setting up Boundary Conditions for details.

  8. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  9. Evaluating results: In the magnetostatic analysis, the applicable results are Magnetic Potential, Magnetic Field, Magnetic Induction Field, and Energy Density. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

finite_element_analysis_welsim_mat_ui_lib

finite_element_analysis_welsim_mat_ui_build

The following describes the widget components in the material editor interface:

  • Library Outline Tab: Display the available pre-defined material data for you to select. All materials are classified into several categories including General Materials, Nonlinear Materials, Hyperelastic Materials, Thermal Materials, Electromagnetic Materials, and Acoustic Materials.

  • Build Outline Tab: Display the available properties for you to add to the material. All properties are classified into several categories including Baisc, Linear Elastic, Hyper-elastic, Plastic, Creep, Visco-elastic, and Electromagnetic. The toggled properties are added to the material data and shown in the Property Pane.

  • Material Properties View Pane: Displays the properties of the selected properties items. You can modify the values of the properties. Click OK button to close the spreadsheet and save the material data into the Material Object.

Library outline tab

The Library Outline Tab shows an outline of the contents of the selectable material sources. You can directly load a material data from this pre-defined source by one of the methods below:

  • Double click a material entry.
  • Select a material entry, and press the Import button.
\ No newline at end of file + Physics and analysis types - WelSim Documentation
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Physics and analysis types

WELSIM supports several types of finite element analyses. This section describes those analysis types that you can perform in the WELSIM user interface.

Static structural analysis

As one of the most widely used analysis types, a static structural analysis discloses the structural displacements, stresses, strains, and forces caused by loads or other mechanical effects. In this static analysis, the constant loading and response are assumed.

The static structural analysis can be either linear or nonlinear. The non-linearity can be introduced by the large deformations, in-elasticity, contact, hyperelasticity, etc. For the nonlinear problem, it is recommended to set multiple substeps in the Study Settings.

Conducting a static structural analysis

The following lists the general and specifics steps in conducting static structural analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Structural and Analysis Type to Static. Since the static structural analysis is the default analysis type, you do not need to change these properties if the analysis is newly created. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, the default setting is Solid. You need to change this property value accordingly if the geometry is Shell or other types. See Defining Part Behaviors for details.

  5. Setting bonnections: Optional. Contacts are supported in a static structural analysis. See Setting Connections for details.

  6. Applying mesh: It is recommended to generate Tet10 elements for Solid analysis and the Tri6 element for the Shell analysis. See Applying Mesh for details.

  7. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analyses such as nonlinear models, the analysis controls you can tune: Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  8. Setting up boundary conditions: For a static structural analysis, the applicable boundary conditions are Fixed Supported, Fixed Rotation, Displacement, Force, and Pressure. The following body conditions are supported: Body Force, Acceleration, Earth Gravity, and Rotational Velocity. See Setting up Boundary Conditions for details.

  9. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  10. Evaluating results: For a static structural analysis, the applicable results are Deformations, Stresses, Strains, Rotations, Reaction Forces, and Reaction Moments. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

Transient structural analysis

In the transient structural analysis, the dynamic response is updated and is a function of time. You can impose general time-dependent boundary conditions on the model and obtain the time-varying responded to these transient loads or constraints. The inertia or damping effects play important roles in this analysis type, if the inertia and damping effects are minimal, you could use the static analysis instead.

The transient structural analysis can be either linear or nonlinear. The non-linearity can be introduced by the large deformations, inelasticity, contact, hyperelasticity, etc. For the nonlinear problem, it is recommended to set multiple substeps for each load step in the Study Settings.

Conducting a transient structural analysis

The following lists the general and specifics steps in conducting transient structural analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Structural and Analysis Type to Transient. You can choose either Implicit or Explicit time integration solver. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. You need to change this property value accordingly if the geometry is Shell or other types. See Defining Part Behaviors for details.

  5. Setting connections: Optional. Contacts are supported in a transient structural analysis. See Setting Connections for details.

  6. Applying mesh: It is recommended to generate Tet10 elements for Solid analysis and the Tri6 element for the Shell analysis. See Applying Mesh for details.

  7. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analyses such as nonlinear models, the analysis controls you can tune are Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  8. Defining initial conditions: Optional. In the transient structural analysis, you can define the initial status of boundary and body conditions. The Initial Status property provides two options: None and Equal to Step 1. The default option None set the initial value to zero, the option Equal to Step 1 set the initial value to that of step 1. See Defining Initial Conditions for details.

  9. Setting up boundary conditions: For the transient structural analysis, the applicable boundary conditions are Fixed Supported, Fixed Rotation, Displacement, Force, Pressure, Velocity, and Acceleration. The following body conditions are supported: Body Force, Acceleration, Earth Gravity, and Rotational Velocity. See Setting up Boundary Conditions for details.

  10. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  11. Evaluating results: For the transient structural analysis, the applicable results are: Deformations, Stresses, Strains, Rotations, Reaction Forces, Reaction Moments, Velocity, and Acceleration. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

finite_element_analysis_welsim_structural_tran_prop

The modal analysis investigates the vibration characteristics of a structure or component. You can obtain the natural frequencies and mode shapes, which serve as a starting pointing for dynamic analysis of the target structure.

Conducting a modal structural analysis

The following lists the general and specifics steps in conducting modal structural analysis:

  1. Creating analysis environment: From the properties view of FEM Project object, set the Physics Type to Structural and Analysis Type to Modal. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. However, the nonlinearity in the modal analysis is ignored due to the characteristics of eigen solver algorithms. You must define the sufficient properties that are required in the solving process. For example, the mass density parameter must be defined. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. You need to change this property value accordingly if the geometry is Shell or other types. See Defining Part Behaviors for details.

  5. Setting connections: Optional. The Bonded Contacts are supported in a modal structural analysis. See Setting Connections for details.

  6. Applying mesh: It is recommended to generate the Tet10 elements for Solid analysis and the Tri6 element for the Shell analysis. See Applying Mesh for details.

  7. Configuring study settings: You typically do not need to change these settings for simple modal analyses. The default number of modes is 6, increasing this value yields to calculate more natural frequency modes, while it requires more computational resources. See Configuring Study Settings for details.

  8. Setting up boundary conditions: For the modal structural analysis, the applicable boundary conditions are Fixed Supported, Fixed Rotation, zero Displacement. The following body conditions are supported: Body Force, Acceleration, Earth Gravity, and Rotational Velocity. Note that only constraint-type boundaries are applicable in modal analysis. See Setting up Boundary Conditions for details.

  9. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  10. Evaluating results: For the modal structural analysis, the applicable results are Deformations, and Frequencies. Note that deformation results here are just relative quantities intended to show the shape modes. The Tabular Data and Chart windows display the frequencies and related mode numbers. See Evaluating Results for details.

finite_element_analysis_welsim_modal_study_ana_prop

Steady-state thermal analysis

In the steady-state thermal analysis, you can determine the temperatures in objects that are impacted by the time-invariant thermal loads. Users are recommended to perform a steady-state analysis before conducting a transient study in a complex model.

The static thermal analysis can be either linear or nonlinear. The nonlinearity can be introduced by the temperature-depend material properties, or radiation and convection coefficient. For the nonlinear problem, it is recommended to set multiple substeps in the Study Settings.

Conducting a static structural analysis

The following lists the general and specifics steps in conducting static structural analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Thermal and Analysis Type to Static. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. You need to change this property value accordingly if the geometry is Shell or other types. See Defining Part Behaviors for details.

  5. Setting connections: Optional. The steady-state thermal analysis supports the Bonded Contact. See Setting Connections for details.

  6. Applying mesh: It is recommended to generate the Tet10 elements for Solid analysis, and the Tri6 element for the Shell analysis. See Applying Mesh for details.

  7. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analysis such as nonlinear models, the analysis controls you can tune are Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  8. Setting up boundary conditions: In the steady-state thermal analysis, the applicable boundary conditions are: Temperature, Heat Flux, Convection, and Radiation. See Setting up Boundary Conditions for details.

  9. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  10. Evaluating results: In steady-state thermal analysis, the applicable results are Temperature. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

Transient thermal analysis

In the transient thermal analysis, you can obtain the temperatures of objects that vary over time. Many heat transfer applications such as coiling or quenching problems, and so on involve transient thermal analysis. The transient thermal analysis can be either linear or nonlinear. The nonlinearity can be introduced by the temperature-dependent material properties or convection and radiation boundary conditions. For the nonlinear problem, it is recommended to define multiple substeps for each load step in the Study Settings.

Conducting a transient thermal analysis

The following lists the general and specifics steps in conducting transient thermal analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Thermal and Analysis Type to Transient. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. You need to change this property value accordingly if the geometry is Shell or other types. See Defining Part Behaviors for details.

  5. Setting connections: Optional. In the transient thermal analysis, the Bonded Contact is supported. See Setting Connections for details.

  6. Applying mesh: It is recommended to generate the Tet10 elements for Solid analysis and the Tri6 element for the Shell analysis. See Applying Mesh for details.

  7. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analysis such as nonlinear models, the analysis controls you can tune are Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  8. Setting up boundary conditions: In the transient thermal analysis, the applicable boundary conditions are: Temperature, Heat Flux, Convection, and Radiation. See Setting up Boundary Conditions for details.

  9. Defining initial conditions: You can define the global initial temperature condition for the analysis. In the transient thermal analysis, you can define the initial status of boundary and body conditions. The Initial Status property provides two options: None and Equal to Step 1. The default option None set the initial value to zero, the option Equal to Step 1 set the initial value to that of step 1. See Defining Initial Conditions for details.

  10. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  11. Evaluating results: In the transient thermal analysis, the applicable results are Temperature. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

ElectroStatic Analysis

The electrostatic analysis can be applied to determine the distribution of electric potential in a conducting body under voltage or current conditions. You can obtain the solution results such as voltage, electric field, etc. The electrostatic analysis supports the single body analysis.

An electrostatic analysis could be either linear or nonlinear. The electric field dependent material properties can introduce the nonlinearity. For the nonlinear problem, it is recommended to set multiple substeps in the Study Settings.

Conducting an electrostatic analysis

The following lists the general and specifics steps in conducting electrostatic analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Electromagnetic and Analysis Type to ElectroStatic. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. An electrostatic analysis only supports the Solid geometry type. See Defining Part Behaviors for details.

  5. Applying mesh: It is recommended to generate Tet10 elements for Solid analysis. See Applying Mesh for details.

  6. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analysis such as nonlinear models, the analysis controls you can tune are Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  7. Setting up boundary conditions: In the electrostatic analysis, the applicable boundary conditions are Ground, Voltage, Symmetry, Zero Charge, Surface Charge Density, and Electric Displacement. See Setting up Boundary Conditions for details.

  8. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  9. Evaluating results: In the electrostatic analysis, the applicable results are Voltage, Electric Field, Electric Displacement, and Energy Density. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

MagnetoStatic analysis

The magnetostatic analysis determines the magnetic field in and around a magnetic body.

A magnetostatic analysis requires the medium such as air surrounding the geometry be included as part of the entire simulation domain. In many cases, the full model can be reduced to the symmetric model by applying a symmetric boundary condition on the symmetric surface.

Conducting a magnetostatic analysis

The following lists the general and specifics steps in conducting magnetostatic analysis:

  1. Creating analysis environment: In the Properties View of the FEM Project object, set the Physics Type to Electromagnetic and Analysis Type to MagnetoStatic. See Creating Analysis Environment for details.

  2. Defining materials: The material properties can be either linear or nonlinear. You must define the sufficient properties that are required in the solving process. See Defining Materials for details.

  3. Specifying geometries: See Specifying Geometries for details.

  4. Defining part behaviors: The Structure Type property of the Part object determines the successive meshing and solving algorithms, and the default setting is Solid. A magnetostatic analysis only supports the Solid geometry type. See Defining Part Behaviors for details.

  5. Applying mesh: It is recommended to generate the Tet10 elements for magnetostatic analysis. See Applying Mesh for details.

  6. Configuring study settings: You usually do not need to change these settings for simple linear analyses. For the complex analysis such as nonlinear models, the analysis controls you can tune are Step Controls in Study object, Substep Controls and Nonlinear Controls in Study Settings object. See Configuring Study Settings for details.

  7. Setting up boundary conditions: In the magnetostatic analysis, the applicable boundary conditions are Insulating, Symmetry, Magnetic Potential, and Magnetic Flux Density. See Setting up Boundary Conditions for details.

  8. Solving: Output window continuously updates messages from the solvers and provides information on the numerical steps in solving the given problem. The convergence data is also explicitly shown in the Output window. See Solving for details.

  9. Evaluating results: In the magnetostatic analysis, the applicable results are Magnetic Potential, Magnetic Field, Magnetic Induction Field, and Energy Density. The Tabular Data and Chart windows display the maximum and minimum result values along the time/set number. See Evaluating Results for details.

finite_element_analysis_welsim_mat_ui_lib

finite_element_analysis_welsim_mat_ui_build

The following describes the widget components in the material editor interface:

  • Library Outline Tab: Display the available pre-defined material data for you to select. All materials are classified into several categories including General Materials, Nonlinear Materials, Hyperelastic Materials, Thermal Materials, Electromagnetic Materials, and Acoustic Materials.

  • Build Outline Tab: Display the available properties for you to add to the material. All properties are classified into several categories including Baisc, Linear Elastic, Hyper-elastic, Plastic, Creep, Visco-elastic, and Electromagnetic. The toggled properties are added to the material data and shown in the Property Pane.

  • Material Properties View Pane: Displays the properties of the selected properties items. You can modify the values of the properties. Click OK button to close the spreadsheet and save the material data into the Material Object.

Library outline tab

The Library Outline Tab shows an outline of the contents of the selectable material sources. You can directly load a material data from this pre-defined source by one of the methods below:

  • Double click a material entry.
  • Select a material entry, and press the Import button.
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Setting up boundary conditions

Boundary or Body conditions are essential conditions for the most analyses. A boundary condition is imposed on the boundary of the geometry. For example, a displacement condition imposed on the face of the 3D solid geometry. A body condition is imposed on the entire body. For example, the rotational velocity imposed on the body.

Each analysis type has its boundary and body conditions. These boundary and body conditions will be described separately regarding structural, thermal, and electromagnetic analyses.

Note

The boundary condition here includes both boundary and body conditions.

Add boundary condition

Adding boundary and body conditions in WELSIM application is straightforward. The following describes the adding method and its behaviors.

  • Adding new conditions from the Menu.
  • Adding new conditions from the Toolbar.
  • Right clicking on the Study or its children objects and selecting the condition item from the context menu.

Scoping method

The scoping method supports the geometry selection, and you can select the target geometry entities and set to the properties. A voltage boundary condition scoping is illustrated in Figure below. You can select multiple geometry entities such as bodies, faces, edges, or vertices to a Geometry property, but all these entities must be the same type.

finite_element_analysis_welsim_bc_voltage_prop

Tips in geometry selection

The following describes the tips in selecting geometries for boundary and body conditions:

  • You can first select geometries and then apply to Geometry Selection property, or you can click the Geometry Selection property then select the geometries from the Graphics window.
  • You can select multiple entities by pressing the Ctrl or Shift key.
  • For the body conditions, you only select the volumes or bodies.
  • For the boundary conditions, you only can select the faces or edges.

Types of boundary conditions

This section describes the boundary conditions that are provided in the WELSIM application.

Displacement

Displacement determines the spatial motion of one or more faces, edges, or vertices for their original location. This boundary condition is available for all structural analysis.

Boundary condition application

To apply Displacement:

  1. On the menu or toolbar of the Structural, click Displacement button. Or, right-click the Study object in the tree and select Impose Conditions > Displacement.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Displacement components on X, Y, and Z directions.

Properties view

The available settings in the Properties View are described below.

  • Geometry selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Displacement vector: Component field allows you to input displacement values on X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Displacement example

Displacement boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_disp_full

Fixed support

Fixed Support is a special case of Displacement boundary condition. It essentially sets the displacement to zero at the scoped geometries. This boundary condition is available for all structural analysis.

Boundary condition application

To apply the Fixed Support:

  1. On the menu or toolbar of the Structural, click Fixed Support button. Or, right-click the Study object in the tree and select Impose Conditions > Fixed Support.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Determine the constraint status on X, Y, and Z directions.

Properties view

The available settings in the Properties View are described below.

  • Geometry selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Constraint status: Component field allows you to set the constraints on X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Fixed support example

Fixed support boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_fixed_support

Fixed rotation

Fixed Rotation constrains the rotation of the scoped geometry entities. This boundary condition is only available for Shell structural analysis.

Boundary condition application

To apply Fixed Rotation: 1. On the menu or toolbar of the Structural, click Fixed Rotation button. Or, right-click the Study object in the tree and select Impose Conditions > Fixed Rotation. 2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window. 3. Determine the constraint status on X, Y, and Z directions.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Constraint Status: Component field allows you to set the constraints on X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Fixed Rotation example

Fixed Rotation boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_fixed_rot

Pressure

A pressure boundary condition imposes a constant normal pressure to one or more surfaces. A positive pressure acts into the surface, which compresses the scoped body. Similarly, a negative pressure pulling away from the scoped surface. This boundary condition is available for all structural analysis.

Boundary condition application

To apply Pressure:

  1. On the menu or toolbar of the Structural, click Pressure button. Or, right-click the Study object in the tree and select Impose Conditions > Pressure.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Input the magnitude of normal pressure. A positive pressure acts into the surface, and a negative pressure pulls away from the surface.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Normal Pressure: Scalar value field allows you to pressure. A positive value indicates a compression pressure, and negative value denotes a tensile pressure.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Pressure example

Pressure boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_pressure

Force

A force boundary condition imposes a constant force to one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for all structural analysis.

Boundary condition application

To apply Force:

  1. On the menu or toolbar of the Structural, click Force button. Or, right-click the Study object in the tree and select Impose Conditions>Force.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Force components on X, Y, and Z directions.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Force Vector: Defines the Force component values on X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Force example

Force boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_force

Velocity

A velocity boundary condition imposes a constant velocity to one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for transient structural analysis.

Boundary condition application

To apply Velocity:

  1. On the menu or toolbar of the Structural, click Velocity button. Or, right-click the Study object in the tree and select Impose Conditions > Velocity.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Velocity components on X, Y, and Z directions.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Velocity Vector: Defines the Velocity component values on X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Velocity example

Velocity boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_velocity

Acceleration

An acceleration boundary condition imposes a constant acceleration to one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for transient structural analysis.

Boundary condition application

To apply Acceleration:

  1. On the menu or toolbar of the Structural, click Acceleration button. Or, right-click the Study object in the tree and select Impose Conditions>Acceleration.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Acceleration components on X, Y, and Z directions.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Acceleration Vector: Defines the Acceleration component values on X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Acceleration example

Acceleration boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_acceleration

Temperature

A temperature boundary condition imposes a constant temperature to one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for all thermal analysis.

Boundary condition application

To apply Temperature:

  1. On the menu or toolbar of the Thermal, click Temperature button. Or, right-click the Study object in the tree and select Impose Conditions>Temperature.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Temperature scalar value.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Temperature: Defines the Temperature value.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Temperature example

Temperature boundary condition is applied as shown in Figure below.

Heat flux

A Heat Flux boundary condition imposes a constant flux to one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for all thermal analysis.

Boundary condition application

To apply Heat Flux:

  1. On the menu or toolbar of the Thermal, click Heat Flux button. Or, right-click the Study object in the tree and select Impose Conditions>Heat Flux.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Heat Flux scalar value.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Heat Flux: Defines the flux value. A positive flux acts into the boundary, and a negative heat flux acts away from the boundary.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Heat flux example

Heat Flux boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_heat_flux

Heat convection

A heat convection boundary condition imposes a constant convection onto one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for all thermal analysis.

Boundary condition application

To apply Heat Convection:

  1. On the menu or toolbar of the Thermal, click Heat Convection button. Or, right-click the Study object in the tree and select Impose Conditions > Heat Convection.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Convection Coefficient and Ambient Temperature scalar values.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Convection Coefficient: Defines the convection value. A positive convection acts into the boundary, and a negative heat convection acts away from the boundary.
  • Ambient Temperature: Defines the ambient temperature value for the convection condition.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Heat convection example

Heat Convection boundary condition is applied in Figure below.

finite_element_analysis_welsim_bc_heat_convection

Heat radiation

A heat radiation boundary condition imposes a constant radiation onto one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for all thermal analysis.

Boundary condition application

To apply Heat Radiation:

  1. On the menu or toolbar of the Thermal, click Heat Radiation button. Or, right-click the Study object in the tree and select Impose Conditions>Heat Radiation.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Radiation Coefficient and Ambient Temperature scalar values.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Emissivity: Defines the radiation coefficient value.
  • Ambient Temperature: Defines the ambient temperature value.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Heat radiation example

Heat Radiation boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_heat_radiation

Initial temperature

Boundary condition application

To apply Initial Temperature:

  1. On the Menu or Toolbar of the Thermal, click Initial Temperature button. Or, right-click the Study object in the tree and select Impose Conditions > Heat Radiation.
  2. Set the Initial Temperature value or use the default value.

Properties view

The available settings in the Properties View are described below.

  • Initial temperature: Define initial temperature value.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Initial temperature example

Initial Temperature boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_initial_temp

Note

Initial Temperature should be added before any other boundary conditions in all kinds of thermal analyses.

Heat flow

Boundary condition application

To apply Heat Flow:

  1. On the Menu or Toolbar of the Thermal, click Heat Flow button. Or, right-click the Study object in the tree and select Impose Conditions > Heat Flow.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Set the Heat Flow value.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Heat Flow: Define the heat flow value.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Heat flow example

Heat Flow boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_heat_flow

Perfectly insulated

Boundary condition application

To apply Perfectly Insulated:

  1. On the Menu or Toolbar of the Thermal, click Heat Flow button. Or, right-click the Study object in the tree and select Impose Conditions > Heat Flow.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Perfectly insulated example

Perfectly Insulated boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_perfectly_insulated

Voltage

Voltage determines the electric potential to one or more faces or edges, or vertices. This boundary condition is available for the electrostatic analysis.

Boundary condition application

To apply Voltage:

  1. On the menu or toolbar of the Electromagnetic, click Voltage button. Or, right-click the Study object in the tree and select Impose Conditions>Voltage.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Voltage value.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Voltage: Scalar field allows you to input voltage value.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Voltage example

Voltage boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_voltage

Ground

A Ground boundary condition is a special case of Voltage boundary condition. It essentially sets the voltage to zero at the scoped geometries. This boundary condition is available for the electrostatic analysis.

Boundary condition application

To apply Ground:

  1. On the menu or toolbar of the Electromagnetic, click Ground command. Or, right-click the Study object in the tree and select Impose Conditions>Ground.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Ground example

Ground boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_ground

Symmetry

A Symmetry boundary condition defines the symmetric boundary for the scoped geometry. This boundary condition is available for electromagnetic analyses.

Boundary condition application

To apply Symmetry:

  1. On the menu or toolbar of the Electromagnetic, click Symmetry button. Or, right-click the Study object in the tree and select Impose Conditions>Symmetry.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Symmetry example

Symmetry boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_em_symmetry

Zero charge

A Zero Charge boundary condition defines the zero surface charge for the scoped geometry. This boundary condition is available for electrostatic analysis.

Boundary condition application

To apply Zero Charge:

  1. On the menu or toolbar of the Electromagnetic, click Zero Charge button. Or, right-click the Study object in the tree and select Impose Conditions>Zero Charge.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Zero charge example

Zero Charge boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_zero_charge

Surface charge density

A Surface Change Density boundary condition defines the surface charge density for the scoped geometry. This boundary condition is available for electrostatic analysis.

Boundary condition application

To apply Surface Charge Density:

  1. On the menu or toolbar of the Electromagnetic, click Surface Charge Density button. Or, right-click the Study object in the tree and select Impose Conditions>Surface Charge Density.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Charge Density: A scalar value field determines the surface charge density on the scoped geometry.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Surface charge density example

Surface Charge Density boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_charge_density

Electric displacement

An Electric Displacement boundary condition defines the electric displacement vector for the scoped geometry. This boundary condition is available for electrostatic analysis.

Boundary condition application

To apply Electric Displacement:

  1. On the menu or toolbar of the Electromagnetic, click Electric Displacement button. Or, right-click the Study object in the tree and select Impose Conditions>Electric Displacement.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Determine the values of Electric Displacement.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Electric Displacement: Component fields determine the electric displacement on the X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Electric displacement example

Electric Displacement boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_electric_displacement

Insulating

An Insulating boundary condition defines the zero magnetic field for the scoped geometry. This boundary condition is available for the magnetic analysis.

Boundary condition application

To apply Insulating:

  1. On the menu or toolbar of the Electromagnetic, click Insulating command. Or, right-click the Study object in the tree and select Impose Conditions>Insulating.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Insulating example

Insulating boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_insulating

Vector magnetic potential

A Vector Magnetic Potential boundary condition defines the magnetic potential vector for the scoped geometry. This boundary condition is available for magnetic analysis.

Boundary condition application

To apply Vector Magnetic Potential:

  1. On the menu or toolbar of the Electromagnetic, click Magnetic Potential button. Or, right-click the Study object in the tree and select Impose Conditions>Magnetic Potential.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Determine the value of Vector Magnetic Potential.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Magnetic Potential: A component field determines the magnetic potential on the X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Magnetic potential example

Magnetic Potential boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_magnetic_potential

Magnetic flux density

A Magnetic Flux Density boundary condition defines the magnetic flux density for the scoped geometry. This boundary condition is available for magnetic analysis.

Boundary condition application

To apply Magnetic Flux Density:

  1. On the menu or toolbar of the Electromagnetic, click Magnetic Flux Density button. Or, right-click the Study object in the tree and select Impose Conditions>Magnetic Flux Density.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Magnetic Flux Density: A component field determines the magnetic flux density on the X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Magnetic flux density example

Magnetic Flux Density boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_magnetic_flux_density

Types of body conditions

This section describes the Body Conditions that are provided in the WELSIM application.

Acceleration

The Acceleration body condition defines a linear acceleration of a structure in a particular direction. This body condition is available for all structural analysis.

If desired, acceleration body condition can be used to mimic the Earth Gravity. For example, the standard earth gravity is 9.80665 m/s\(^{2}\) toward the ground, you can add an acceleration body condition object and apply to all or the target bodies to represent the earth gravity.

Body condition application

To apply Acceleration:

  1. On the menu or toolbar of the Structural, click Acceleration button. Or, right-click the Study object in the tree and select Impose Conditions>Acceleration.
  2. Keep the All bodies Scoping Method, or choose the Geometry Selection and scope the geometric entities from Graphics window.
  3. Define the Acceleration magnitude on X, Y, and Z directions.

Properties view

The available settings in the Properties View are described below.

  • Scoping Method: Drop-down field has options All Bodies and Geometry Selection.
  • Geometry Selection: Selection field allows you to select the body entities. This property is shown if the Scoping Method property is set to Geometry Selection.
  • Acceleration: Component field allows you to input acceleration values on X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the body condition.

Acceleration example

Acceleration is applied as shown in Figure below.

finite_element_analysis_welsim_dc_acceleration

Earth gravity

The earth gravity condition defines gravitational effects on structure bodies. This body condition is available for all structural analysis. This condition is equivalent to the Acceleration body condition.

Body condition application

To apply Acceleration:

  1. On the menu or toolbar of the Structural, click Earth Gravity button. Or, right-click the Study object in the tree and select Impose Conditions>Earth Gravity.
  2. Keep the All bodies Scoping Method, or choose the Geometry Selection and scope the geometric entities from Graphics window.
  3. Define the Earth Gravity magnitude on X, Y, and Z directions.

Properties view

The available settings in the Properties View are described below.

  • Scoping Method: Drop-down field has options All Bodies and Geometry Selection.
  • Geometry Selection: Selection field allows you to select the body entities. This property is shown if the Scoping Method property is set to Geometry Selection.
  • Gravity: Component field allows you to input gravity values on X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the body condition.

Earth gravity example

The Earth Gravity body condition is applied as shown in Figure below.

finite_element_analysis_welsim_dc_gravity

Body force

The body force condition defines a linear force acting structure bodies. This body condition is available for all structural analysis. The contribution of body force to the governing equation can be seen at Infinitesimal deformation linear elasticity static analysis.

Body condition application

To apply Body Force:

  1. On the menu or toolbar of the Structural, click Body Force button. Or, right-click the Study object in the tree and select Impose Conditions>Body Force.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Body Force magnitude on X, Y, and Z directions.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the body entities.
  • Force Vector: Component field allows you to input body force values on X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the body condition.

Body force example

The Body Force is applied as shown in Figure below.

finite_element_analysis_welsim_body_force

Rotational velocity

The Rotational Velocity condition determines the centrifugal force generated from a part spinning at a constant rate. This body condition is available for all structural analysis.

Body condition application

To apply Rotational Velocity:

  1. On the menu or toolbar of the Structural, click Rotational Velocity button. Or, right-click the Study object in the tree and select Impose Conditions>Rotational Velocity.
  2. Keep the All bodies Scoping Method, or choose the Geometry Selection and scope the geometric entities from Graphics window.
  3. Define the coefficients of Angular Velocity, Rotating Axis.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the body entities. This property is shown if the Scoping Method property is set to Geometry Selection.
  • Angular Velocity: Defines the magnitude of the angular velocity.
  • Rotating Origin: Defines the origin location of the rotation axis.
  • Rotating Axis: Defines the direction vector of the rotation axis.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Rotational velocity example

The Rotational Velocity is applied as shown in Figure below.

finite_element_analysis_welsim_dc_rotational_velocity

Internal heat generation

The Internal Heat Generation condition determines the heat flow generated from the body. This body condition is available for all thermal analysis.

Internal heat generation application

To apply Internal Heat Generation:

  1. On the menu or toolbar of the Thermal, click Internal Heat Generation button. Or, right-click the Study object in the tree and select Impose Conditions > Internal Heat Generation.
  2. Keep the All bodies Scoping Method, or choose the Geometry Selection and scope the geometric entities from Graphics window.
  3. Define the coefficients of Heat Flow value.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the body entities. This property is shown if the Scoping Method property is set to Geometry Selection.
  • Heat Flow: Defines the magnitude of the volume heat generation.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Internal heat generation example

The Internal Heat Generation is applied as shown in Figure below.

\ No newline at end of file + Setting up boundary conditions - WelSim Documentation
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Setting up boundary conditions

Boundary or Body conditions are essential conditions for the most analyses. A boundary condition is imposed on the boundary of the geometry. For example, a displacement condition imposed on the face of the 3D solid geometry. A body condition is imposed on the entire body. For example, the rotational velocity imposed on the body.

Each analysis type has its boundary and body conditions. These boundary and body conditions will be described separately regarding structural, thermal, and electromagnetic analyses.

Note

The boundary condition here includes both boundary and body conditions.

Add boundary condition

Adding boundary and body conditions in WELSIM application is straightforward. The following describes the adding method and its behaviors.

  • Adding new conditions from the Menu.
  • Adding new conditions from the Toolbar.
  • Right clicking on the Study or its children objects and selecting the condition item from the context menu.

Scoping method

The scoping method supports the geometry selection, and you can select the target geometry entities and set to the properties. A voltage boundary condition scoping is illustrated in Figure below. You can select multiple geometry entities such as bodies, faces, edges, or vertices to a Geometry property, but all these entities must be the same type.

finite_element_analysis_welsim_bc_voltage_prop

Tips in geometry selection

The following describes the tips in selecting geometries for boundary and body conditions:

  • You can first select geometries and then apply to Geometry Selection property, or you can click the Geometry Selection property then select the geometries from the Graphics window.
  • You can select multiple entities by pressing the Ctrl or Shift key.
  • For the body conditions, you only select the volumes or bodies.
  • For the boundary conditions, you only can select the faces or edges.

Types of boundary conditions

This section describes the boundary conditions that are provided in the WELSIM application.

Displacement

Displacement determines the spatial motion of one or more faces, edges, or vertices for their original location. This boundary condition is available for all structural analysis.

Boundary condition application

To apply Displacement:

  1. On the menu or toolbar of the Structural, click Displacement button. Or, right-click the Study object in the tree and select Impose Conditions > Displacement.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Displacement components on X, Y, and Z directions.

Properties view

The available settings in the Properties View are described below.

  • Geometry selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Displacement vector: Component field allows you to input displacement values on X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Displacement example

Displacement boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_disp_full

Fixed support

Fixed Support is a special case of Displacement boundary condition. It essentially sets the displacement to zero at the scoped geometries. This boundary condition is available for all structural analysis.

Boundary condition application

To apply the Fixed Support:

  1. On the menu or toolbar of the Structural, click Fixed Support button. Or, right-click the Study object in the tree and select Impose Conditions > Fixed Support.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Determine the constraint status on X, Y, and Z directions.

Properties view

The available settings in the Properties View are described below.

  • Geometry selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Constraint status: Component field allows you to set the constraints on X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Fixed support example

Fixed support boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_fixed_support

Fixed rotation

Fixed Rotation constrains the rotation of the scoped geometry entities. This boundary condition is only available for Shell structural analysis.

Boundary condition application

To apply Fixed Rotation: 1. On the menu or toolbar of the Structural, click Fixed Rotation button. Or, right-click the Study object in the tree and select Impose Conditions > Fixed Rotation. 2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window. 3. Determine the constraint status on X, Y, and Z directions.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Constraint Status: Component field allows you to set the constraints on X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Fixed Rotation example

Fixed Rotation boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_fixed_rot

Pressure

A pressure boundary condition imposes a constant normal pressure to one or more surfaces. A positive pressure acts into the surface, which compresses the scoped body. Similarly, a negative pressure pulling away from the scoped surface. This boundary condition is available for all structural analysis.

Boundary condition application

To apply Pressure:

  1. On the menu or toolbar of the Structural, click Pressure button. Or, right-click the Study object in the tree and select Impose Conditions > Pressure.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Input the magnitude of normal pressure. A positive pressure acts into the surface, and a negative pressure pulls away from the surface.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Normal Pressure: Scalar value field allows you to pressure. A positive value indicates a compression pressure, and negative value denotes a tensile pressure.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Pressure example

Pressure boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_pressure

Force

A force boundary condition imposes a constant force to one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for all structural analysis.

Boundary condition application

To apply Force:

  1. On the menu or toolbar of the Structural, click Force button. Or, right-click the Study object in the tree and select Impose Conditions>Force.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Force components on X, Y, and Z directions.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Force Vector: Defines the Force component values on X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Force example

Force boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_force

Velocity

A velocity boundary condition imposes a constant velocity to one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for transient structural analysis.

Boundary condition application

To apply Velocity:

  1. On the menu or toolbar of the Structural, click Velocity button. Or, right-click the Study object in the tree and select Impose Conditions > Velocity.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Velocity components on X, Y, and Z directions.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Velocity Vector: Defines the Velocity component values on X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Velocity example

Velocity boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_velocity

Acceleration

An acceleration boundary condition imposes a constant acceleration to one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for transient structural analysis.

Boundary condition application

To apply Acceleration:

  1. On the menu or toolbar of the Structural, click Acceleration button. Or, right-click the Study object in the tree and select Impose Conditions>Acceleration.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Acceleration components on X, Y, and Z directions.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Acceleration Vector: Defines the Acceleration component values on X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Acceleration example

Acceleration boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_acceleration

Temperature

A temperature boundary condition imposes a constant temperature to one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for all thermal analysis.

Boundary condition application

To apply Temperature:

  1. On the menu or toolbar of the Thermal, click Temperature button. Or, right-click the Study object in the tree and select Impose Conditions>Temperature.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Temperature scalar value.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Temperature: Defines the Temperature value.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Temperature example

Temperature boundary condition is applied as shown in Figure below.

Heat flux

A Heat Flux boundary condition imposes a constant flux to one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for all thermal analysis.

Boundary condition application

To apply Heat Flux:

  1. On the menu or toolbar of the Thermal, click Heat Flux button. Or, right-click the Study object in the tree and select Impose Conditions>Heat Flux.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Heat Flux scalar value.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Heat Flux: Defines the flux value. A positive flux acts into the boundary, and a negative heat flux acts away from the boundary.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Heat flux example

Heat Flux boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_heat_flux

Heat convection

A heat convection boundary condition imposes a constant convection onto one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for all thermal analysis.

Boundary condition application

To apply Heat Convection:

  1. On the menu or toolbar of the Thermal, click Heat Convection button. Or, right-click the Study object in the tree and select Impose Conditions > Heat Convection.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Convection Coefficient and Ambient Temperature scalar values.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Convection Coefficient: Defines the convection value. A positive convection acts into the boundary, and a negative heat convection acts away from the boundary.
  • Ambient Temperature: Defines the ambient temperature value for the convection condition.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Heat convection example

Heat Convection boundary condition is applied in Figure below.

finite_element_analysis_welsim_bc_heat_convection

Heat radiation

A heat radiation boundary condition imposes a constant radiation onto one or more entities, such as surfaces, edges, or vertices. This boundary condition is available for all thermal analysis.

Boundary condition application

To apply Heat Radiation:

  1. On the menu or toolbar of the Thermal, click Heat Radiation button. Or, right-click the Study object in the tree and select Impose Conditions>Heat Radiation.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Radiation Coefficient and Ambient Temperature scalar values.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Emissivity: Defines the radiation coefficient value.
  • Ambient Temperature: Defines the ambient temperature value.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Heat radiation example

Heat Radiation boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_heat_radiation

Initial temperature

Boundary condition application

To apply Initial Temperature:

  1. On the Menu or Toolbar of the Thermal, click Initial Temperature button. Or, right-click the Study object in the tree and select Impose Conditions > Heat Radiation.
  2. Set the Initial Temperature value or use the default value.

Properties view

The available settings in the Properties View are described below.

  • Initial temperature: Define initial temperature value.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Initial temperature example

Initial Temperature boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_initial_temp

Note

Initial Temperature should be added before any other boundary conditions in all kinds of thermal analyses.

Heat flow

Boundary condition application

To apply Heat Flow:

  1. On the Menu or Toolbar of the Thermal, click Heat Flow button. Or, right-click the Study object in the tree and select Impose Conditions > Heat Flow.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Set the Heat Flow value.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Heat Flow: Define the heat flow value.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Heat flow example

Heat Flow boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_heat_flow

Perfectly insulated

Boundary condition application

To apply Perfectly Insulated:

  1. On the Menu or Toolbar of the Thermal, click Heat Flow button. Or, right-click the Study object in the tree and select Impose Conditions > Heat Flow.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Perfectly insulated example

Perfectly Insulated boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_perfectly_insulated

Voltage

Voltage determines the electric potential to one or more faces or edges, or vertices. This boundary condition is available for the electrostatic analysis.

Boundary condition application

To apply Voltage:

  1. On the menu or toolbar of the Electromagnetic, click Voltage button. Or, right-click the Study object in the tree and select Impose Conditions>Voltage.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Voltage value.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Voltage: Scalar field allows you to input voltage value.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Voltage example

Voltage boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_voltage

Ground

A Ground boundary condition is a special case of Voltage boundary condition. It essentially sets the voltage to zero at the scoped geometries. This boundary condition is available for the electrostatic analysis.

Boundary condition application

To apply Ground:

  1. On the menu or toolbar of the Electromagnetic, click Ground command. Or, right-click the Study object in the tree and select Impose Conditions>Ground.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Ground example

Ground boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_ground

Symmetry

A Symmetry boundary condition defines the symmetric boundary for the scoped geometry. This boundary condition is available for electromagnetic analyses.

Boundary condition application

To apply Symmetry:

  1. On the menu or toolbar of the Electromagnetic, click Symmetry button. Or, right-click the Study object in the tree and select Impose Conditions>Symmetry.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Symmetry example

Symmetry boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_em_symmetry

Zero charge

A Zero Charge boundary condition defines the zero surface charge for the scoped geometry. This boundary condition is available for electrostatic analysis.

Boundary condition application

To apply Zero Charge:

  1. On the menu or toolbar of the Electromagnetic, click Zero Charge button. Or, right-click the Study object in the tree and select Impose Conditions>Zero Charge.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Zero charge example

Zero Charge boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_zero_charge

Surface charge density

A Surface Change Density boundary condition defines the surface charge density for the scoped geometry. This boundary condition is available for electrostatic analysis.

Boundary condition application

To apply Surface Charge Density:

  1. On the menu or toolbar of the Electromagnetic, click Surface Charge Density button. Or, right-click the Study object in the tree and select Impose Conditions>Surface Charge Density.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Charge Density: A scalar value field determines the surface charge density on the scoped geometry.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Surface charge density example

Surface Charge Density boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_charge_density

Electric displacement

An Electric Displacement boundary condition defines the electric displacement vector for the scoped geometry. This boundary condition is available for electrostatic analysis.

Boundary condition application

To apply Electric Displacement:

  1. On the menu or toolbar of the Electromagnetic, click Electric Displacement button. Or, right-click the Study object in the tree and select Impose Conditions>Electric Displacement.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Determine the values of Electric Displacement.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Electric Displacement: Component fields determine the electric displacement on the X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Electric displacement example

Electric Displacement boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_electric_displacement

Insulating

An Insulating boundary condition defines the zero magnetic field for the scoped geometry. This boundary condition is available for the magnetic analysis.

Boundary condition application

To apply Insulating:

  1. On the menu or toolbar of the Electromagnetic, click Insulating command. Or, right-click the Study object in the tree and select Impose Conditions>Insulating.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Insulating example

Insulating boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_insulating

Vector magnetic potential

A Vector Magnetic Potential boundary condition defines the magnetic potential vector for the scoped geometry. This boundary condition is available for magnetic analysis.

Boundary condition application

To apply Vector Magnetic Potential:

  1. On the menu or toolbar of the Electromagnetic, click Magnetic Potential button. Or, right-click the Study object in the tree and select Impose Conditions>Magnetic Potential.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Determine the value of Vector Magnetic Potential.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Magnetic Potential: A component field determines the magnetic potential on the X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Magnetic potential example

Magnetic Potential boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_magnetic_potential

Magnetic flux density

A Magnetic Flux Density boundary condition defines the magnetic flux density for the scoped geometry. This boundary condition is available for magnetic analysis.

Boundary condition application

To apply Magnetic Flux Density:

  1. On the menu or toolbar of the Electromagnetic, click Magnetic Flux Density button. Or, right-click the Study object in the tree and select Impose Conditions>Magnetic Flux Density.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the Face, Edge, or Vertex entities. The selected entities must be the same type.
  • Magnetic Flux Density: A component field determines the magnetic flux density on the X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Magnetic flux density example

Magnetic Flux Density boundary condition is applied as shown in Figure below.

finite_element_analysis_welsim_bc_magnetic_flux_density

Types of body conditions

This section describes the Body Conditions that are provided in the WELSIM application.

Acceleration

The Acceleration body condition defines a linear acceleration of a structure in a particular direction. This body condition is available for all structural analysis.

If desired, acceleration body condition can be used to mimic the Earth Gravity. For example, the standard earth gravity is 9.80665 m/s\(^{2}\) toward the ground, you can add an acceleration body condition object and apply to all or the target bodies to represent the earth gravity.

Body condition application

To apply Acceleration:

  1. On the menu or toolbar of the Structural, click Acceleration button. Or, right-click the Study object in the tree and select Impose Conditions>Acceleration.
  2. Keep the All bodies Scoping Method, or choose the Geometry Selection and scope the geometric entities from Graphics window.
  3. Define the Acceleration magnitude on X, Y, and Z directions.

Properties view

The available settings in the Properties View are described below.

  • Scoping Method: Drop-down field has options All Bodies and Geometry Selection.
  • Geometry Selection: Selection field allows you to select the body entities. This property is shown if the Scoping Method property is set to Geometry Selection.
  • Acceleration: Component field allows you to input acceleration values on X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the body condition.

Acceleration example

Acceleration is applied as shown in Figure below.

finite_element_analysis_welsim_dc_acceleration

Earth gravity

The earth gravity condition defines gravitational effects on structure bodies. This body condition is available for all structural analysis. This condition is equivalent to the Acceleration body condition.

Body condition application

To apply Acceleration:

  1. On the menu or toolbar of the Structural, click Earth Gravity button. Or, right-click the Study object in the tree and select Impose Conditions>Earth Gravity.
  2. Keep the All bodies Scoping Method, or choose the Geometry Selection and scope the geometric entities from Graphics window.
  3. Define the Earth Gravity magnitude on X, Y, and Z directions.

Properties view

The available settings in the Properties View are described below.

  • Scoping Method: Drop-down field has options All Bodies and Geometry Selection.
  • Geometry Selection: Selection field allows you to select the body entities. This property is shown if the Scoping Method property is set to Geometry Selection.
  • Gravity: Component field allows you to input gravity values on X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the body condition.

Earth gravity example

The Earth Gravity body condition is applied as shown in Figure below.

finite_element_analysis_welsim_dc_gravity

Body force

The body force condition defines a linear force acting structure bodies. This body condition is available for all structural analysis. The contribution of body force to the governing equation can be seen at Infinitesimal deformation linear elasticity static analysis.

Body condition application

To apply Body Force:

  1. On the menu or toolbar of the Structural, click Body Force button. Or, right-click the Study object in the tree and select Impose Conditions>Body Force.
  2. Click the property of Geometry Selection, and scope the geometric entities from Graphics window.
  3. Define the Body Force magnitude on X, Y, and Z directions.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the body entities.
  • Force Vector: Component field allows you to input body force values on X, Y, and Z directions.
  • Suppressed: Include (False - default) or exclude (True) the body condition.

Body force example

The Body Force is applied as shown in Figure below.

finite_element_analysis_welsim_body_force

Rotational velocity

The Rotational Velocity condition determines the centrifugal force generated from a part spinning at a constant rate. This body condition is available for all structural analysis.

Body condition application

To apply Rotational Velocity:

  1. On the menu or toolbar of the Structural, click Rotational Velocity button. Or, right-click the Study object in the tree and select Impose Conditions>Rotational Velocity.
  2. Keep the All bodies Scoping Method, or choose the Geometry Selection and scope the geometric entities from Graphics window.
  3. Define the coefficients of Angular Velocity, Rotating Axis.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the body entities. This property is shown if the Scoping Method property is set to Geometry Selection.
  • Angular Velocity: Defines the magnitude of the angular velocity.
  • Rotating Origin: Defines the origin location of the rotation axis.
  • Rotating Axis: Defines the direction vector of the rotation axis.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Rotational velocity example

The Rotational Velocity is applied as shown in Figure below.

finite_element_analysis_welsim_dc_rotational_velocity

Internal heat generation

The Internal Heat Generation condition determines the heat flow generated from the body. This body condition is available for all thermal analysis.

Internal heat generation application

To apply Internal Heat Generation:

  1. On the menu or toolbar of the Thermal, click Internal Heat Generation button. Or, right-click the Study object in the tree and select Impose Conditions > Internal Heat Generation.
  2. Keep the All bodies Scoping Method, or choose the Geometry Selection and scope the geometric entities from Graphics window.
  3. Define the coefficients of Heat Flow value.

Properties view

The available settings in the Properties View are described below.

  • Geometry Selection: Selection field allows you to select the body entities. This property is shown if the Scoping Method property is set to Geometry Selection.
  • Heat Flow: Defines the magnitude of the volume heat generation.
  • Suppressed: Include (False - default) or exclude (True) the boundary condition.

Internal heat generation example

The Internal Heat Generation is applied as shown in Figure below.

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Setting connections

The Connections object acts as a group folder includes all connecting related settings, such as Contact Pair.

Connections group

The Connections group is a unique container in WELSIM application for all types of connection objects. As illustrated in Figure below, the Connections object includes multiple Contact Pair objects.

finite_element_analysis_welsim_connections_obj

Contact pairs

Contact Pairs are applied when two separate parts (solid, surface, and line bodies) in an assembly touch one another (they are mutually tangent). The contact bodies/surfaces:

  • Transmit normal forces and tangential frictional forces.
  • Can be bonded contact (Linear).
  • Can separate or collide (Nonlinear).
  • Do not penetrate one another in the structures.

As shown in Figure below, the Contact for structure analysis support three types of contact: Bonded, Frictionless, and Frictional. For the Frictionless and Frictional types, the contact pairs (surfaces, edges) are free to separate and move away from one another, which is called to have status-changing nonlinearity. The stiffness matrice in the solving change dramatically as the parts are touching or separated.

finite_element_analysis_welsim_contact_prop

Formulation of contact

Since the contact algorithms are complicated, it is recommended to use the default formulation method for your contact analysis. This section describes the theory of contact formulations: Lagrange and Augmented Lagrange methods. Those methods only exist in the structural analysis.

Bonded

For the Non-Separated Bonded contact, the MPC algorithm is applied internally to add constraint equations to the tied nodes on the contact entities (surfaces, edges). The bonded contact has no penetration, no separation behaviors during the motion.

Lagrange method

This formulation adds an extra contact pressure term to satisfy the contact compatibility. Thus the contact force is solved explicitly as an unknown degree of freedom.

Augmented lagrange method

Augmented Lagrange method is a penalty-based contact formulation. The finite contact force is

\[ F_{Normal}=k_{Normal}x_{Penetration}+\lambda \]

where \(k_{Normal}\) is the contact stiffness, \(x_{Penetration}\) is the penetration depth along the normal direction. The smaller the penetration depth, the more accurate numerical solutions. The exist of term \(\lambda\) is the difference between the traditional penalty method and the augmented Lagrange method.

Contact settings

When you select a Contact Pair object in the tree, the contact settings become available in the Properties view. The Target Geometry and Master Geometry properties allow you to scope the contact pairs from the Graphics window. Note that the valid Target and Master Geometries show in different colors. You can change the highlight color in the Display tab of the contact Properties View.

When you choose the Frictionless or Frictional option in the Contact Type property, the following properties shows:

  • Formulation: Provides two options: Lagrange and Augmented Lagrange methods. The default is the Lagrange method. The Formation property is described in Formulation of Contact.
  • Finite Sliding: Supports the finite sliding as the contact occurs. The default is false.
  • Normal Direction Tolerance: Determines the distance tolerance on the normal direction. The default value is 1e-5.
  • Tangential Direction Tolerance: Determines the distance tolerance on the tangential direction. The default value is 1e-3.
  • Normal Direction Penalty: Determines the penalty tolerance on the normal direction. The Default value is 1e3.
  • Tangential Direction Penalty: Determines the penalty tolerance on the tangential direction. The default value is 1e3.

Supported contact types

The Table below identifies the supported formulations for the various contact geometries.

Contact Geometry Face (Master) Edge (Master) Vertex (Master)
Face (Target) Yes Yes Not Supported for solving
Edge (Target) Yes Yes Not Supported for solving
Vertex (Target) Not Supported for solving Not Supported for solving Not Supported for solving

Ease of use contact

Flipping master and target scoping geometries

This feature provides you a command to quickly swap master and target geometries that are already scoped in the Properties View. You can achieve this by right clicking on the specific Contact Pair, and choosing Switch Target/Master Contacts from the context menu as shown in Figure below.

finite_element_analysis_welsim_contact_switch

Note

This feature is not applicable to Face to Edge contact where faces and edges are always designated as targets and masters, respectively.

\ No newline at end of file + Setting connections - WelSim Documentation
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Setting connections

The Connections object acts as a group folder includes all connecting related settings, such as Contact Pair.

Connections group

The Connections group is a unique container in WELSIM application for all types of connection objects. As illustrated in Figure below, the Connections object includes multiple Contact Pair objects.

finite_element_analysis_welsim_connections_obj

Contact pairs

Contact Pairs are applied when two separate parts (solid, surface, and line bodies) in an assembly touch one another (they are mutually tangent). The contact bodies/surfaces:

  • Transmit normal forces and tangential frictional forces.
  • Can be bonded contact (Linear).
  • Can separate or collide (Nonlinear).
  • Do not penetrate one another in the structures.

As shown in Figure below, the Contact for structure analysis support three types of contact: Bonded, Frictionless, and Frictional. For the Frictionless and Frictional types, the contact pairs (surfaces, edges) are free to separate and move away from one another, which is called to have status-changing nonlinearity. The stiffness matrice in the solving change dramatically as the parts are touching or separated.

finite_element_analysis_welsim_contact_prop

Formulation of contact

Since the contact algorithms are complicated, it is recommended to use the default formulation method for your contact analysis. This section describes the theory of contact formulations: Lagrange and Augmented Lagrange methods. Those methods only exist in the structural analysis.

Bonded

For the Non-Separated Bonded contact, the MPC algorithm is applied internally to add constraint equations to the tied nodes on the contact entities (surfaces, edges). The bonded contact has no penetration, no separation behaviors during the motion.

Lagrange method

This formulation adds an extra contact pressure term to satisfy the contact compatibility. Thus the contact force is solved explicitly as an unknown degree of freedom.

Augmented lagrange method

Augmented Lagrange method is a penalty-based contact formulation. The finite contact force is

\[ F_{Normal}=k_{Normal}x_{Penetration}+\lambda \]

where \(k_{Normal}\) is the contact stiffness, \(x_{Penetration}\) is the penetration depth along the normal direction. The smaller the penetration depth, the more accurate numerical solutions. The exist of term \(\lambda\) is the difference between the traditional penalty method and the augmented Lagrange method.

Contact settings

When you select a Contact Pair object in the tree, the contact settings become available in the Properties view. The Target Geometry and Master Geometry properties allow you to scope the contact pairs from the Graphics window. Note that the valid Target and Master Geometries show in different colors. You can change the highlight color in the Display tab of the contact Properties View.

When you choose the Frictionless or Frictional option in the Contact Type property, the following properties shows:

  • Formulation: Provides two options: Lagrange and Augmented Lagrange methods. The default is the Lagrange method. The Formation property is described in Formulation of Contact.
  • Finite Sliding: Supports the finite sliding as the contact occurs. The default is false.
  • Normal Direction Tolerance: Determines the distance tolerance on the normal direction. The default value is 1e-5.
  • Tangential Direction Tolerance: Determines the distance tolerance on the tangential direction. The default value is 1e-3.
  • Normal Direction Penalty: Determines the penalty tolerance on the normal direction. The Default value is 1e3.
  • Tangential Direction Penalty: Determines the penalty tolerance on the tangential direction. The default value is 1e3.

Supported contact types

The Table below identifies the supported formulations for the various contact geometries.

Contact Geometry Face (Master) Edge (Master) Vertex (Master)
Face (Target) Yes Yes Not Supported for solving
Edge (Target) Yes Yes Not Supported for solving
Vertex (Target) Not Supported for solving Not Supported for solving Not Supported for solving

Ease of use contact

Flipping master and target scoping geometries

This feature provides you a command to quickly swap master and target geometries that are already scoped in the Properties View. You can achieve this by right clicking on the specific Contact Pair, and choosing Switch Target/Master Contacts from the context menu as shown in Figure below.

finite_element_analysis_welsim_contact_switch

Note

This feature is not applicable to Face to Edge contact where faces and edges are always designated as targets and masters, respectively.

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Specifying geometry

Geometry fundamentals

Part is the fundamental object carries the geometry data. An assembly model may contain one or multiple parts. There is no limit of parts in WELSIM application, and large assemblie require more hardware resources to process the geometric operations. All parts object are grouped in the Geometry Group object.

Working with parts

The part has these attributes:

  • Each part object has a Material property, which determines the assigned material on the part.
  • Parts can be hidden/shown in the Graphics window.
  • Parts can be Suppressed/Unsuppressed for the successive analysis.
  • The imported part can adjust the size of geometry by tuning the Scale property value.

Color scheme of parts

The geometry is assigned with predefined random color. However, you can define the color of part to visually identify different components in an assembly. Click the Display tab from the Properties view of the Part Object, and click the Color By property to determine the color scheme. The following lists the available color schemes:

  • Part Color
  • Material

You can reset the colors back to the default color scheme by right click on the Geometry object in the tree and selecting Reset Body Colors.

Overview

The WELSIM geometry module's interface is similar to that most other features. The graphical user interface of geometry commands is consist of three regions:

  1. Toolbars: Located at the top of the interface, there is a toolbar.
  2. Geometry Menu: Located at the Menu, the Geometry Menu provides all geometry related commands.
  3. Context Menu: Popped up at Geometry tree objects, the context menu provides geometry related commands as shown in Figure below.

finite_element_analysis_welsim_context_menu_geometry

Creating primitive geometry

The system provides built-in commands to allow you to create primitive geometries. The following describes the supported geometries: Box, Cylinder, Plate, and Line.

Box

An example of a created box shape is shown in Figure [fig:ch3_guide_geom_box]. finite_element_analysis_welsim_geom_box

Cylinder

An example of a created cylinder shape is shown in Figure [fig:ch3_guide_geom_cylinder]. finite_element_analysis_welsim_geom_cylinder

Plate

An example of a created plate shape is shown in Figure [fig:ch3_guide_geom_plate]. finite_element_analysis_welsim_geom_plate

Line

An example of a created Line shape is shown in Figure [fig:ch3_guide_geom_line]. finite_element_analysis_welsim_geom_line

Importing and exporting geometry

Importing

The geometry importing feature supports the STEP and IGES format files, and the STEP file is recommended. The following lists the behaviors of importing geometry:

  • An imported STEP file may lead to creating multiple Part objects in the tree if the file contains an assembly.
  • IGES file contains the surface information only, you need to implement Make Solid command to the imported geometry to obtain the solid geometry.
  • Using the Scale property to tune the size of the imported geometry.

Exporting

The geometries in the tree can be exported to an external STEP file. The following methods show you how to export:

  • Click the Export... button from the Toolbar.
  • Click the Export... item from the Geometry Menu.
  • Right click on the target geometries and select the Export... from the context menu.

Boolean operations

The WELSIM geometry module supports fundamental Boolean operations, which allow users to manipulate the shape of geometries. The available operations are Union, Intersection, and Difference. You can select multiple geometry objects from the tree list and press the Boolean commands to implement the operations. You can hold Ctrl or Shift keys to select multiple geometry objects from the project tree.

Union

The union operation consolidates two or more geometry into one geometry. An example of Union geometry of a box and cylinder shape is shown in Figure below.

finite_element_analysis_welsim_geom_union

Intersection

The intersection operation keeps the commonly shared portions of two or more geometries. An example of Intersection geometry of a box and cylinder shape is shown in Figure below.

finite_element_analysis_welsim_geom_intersection

Difference

The Difference operation subtracts the secondly selected geometry from the first selected geometry. Thus the selection order plays an important role in the final generated geometry. You can see the results of two different selection orders in Figures below.

finite_element_analysis_welsim_geom_diff1 finite_element_analysis_welsim_geom_diff2

Geometry commands

In addition to the fundamental geometry commands, the following lists the commands that may be applied in the geometry modeling:

Generate solid

In the most of analysis, the model needs to be solid to generate the 3D solid finite element. If the imported geometry only contains the surface data, the mesher cannot generate solid elements. In this scenario, you need to convert a surface geometry to solid geometry. The Generate Solid command provides you with a tool to complete this conversion.

To convert a surface to solid geometry, you can follow the steps below:

  1. Select the surface geometry objects from the tree.
  2. Click the Generate Solid command from the Geometry Menu, or right click on the selected geometry objects, and select the Generate Solid command from the context menu.

Part structure types

Solid bodies

The solid bodies including parts and assembly support all simulation features of WELSIM application.

Surface bodies

The surface bodies are treated as Shell structure in the structural and thermal analyses. In the Properties View of the Shell part, you need to specify the thickness of the shell, as shown in Figure below.

finite_element_analysis_welsim_part_shell_thickness

\ No newline at end of file + Specifying geometry - WelSim Documentation
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Specifying geometry

Geometry fundamentals

Part is the fundamental object carries the geometry data. An assembly model may contain one or multiple parts. There is no limit of parts in WELSIM application, and large assemblie require more hardware resources to process the geometric operations. All parts object are grouped in the Geometry Group object.

Working with parts

The part has these attributes:

  • Each part object has a Material property, which determines the assigned material on the part.
  • Parts can be hidden/shown in the Graphics window.
  • Parts can be Suppressed/Unsuppressed for the successive analysis.
  • The imported part can adjust the size of geometry by tuning the Scale property value.

Color scheme of parts

The geometry is assigned with predefined random color. However, you can define the color of part to visually identify different components in an assembly. Click the Display tab from the Properties view of the Part Object, and click the Color By property to determine the color scheme. The following lists the available color schemes:

  • Part Color
  • Material

You can reset the colors back to the default color scheme by right click on the Geometry object in the tree and selecting Reset Body Colors.

Overview

The WELSIM geometry module's interface is similar to that most other features. The graphical user interface of geometry commands is consist of three regions:

  1. Toolbars: Located at the top of the interface, there is a toolbar.
  2. Geometry Menu: Located at the Menu, the Geometry Menu provides all geometry related commands.
  3. Context Menu: Popped up at Geometry tree objects, the context menu provides geometry related commands as shown in Figure below.

finite_element_analysis_welsim_context_menu_geometry

Creating primitive geometry

The system provides built-in commands to allow you to create primitive geometries. The following describes the supported geometries: Box, Cylinder, Plate, and Line.

Box

An example of a created box shape is shown in Figure [fig:ch3_guide_geom_box]. finite_element_analysis_welsim_geom_box

Cylinder

An example of a created cylinder shape is shown in Figure [fig:ch3_guide_geom_cylinder]. finite_element_analysis_welsim_geom_cylinder

Plate

An example of a created plate shape is shown in Figure [fig:ch3_guide_geom_plate]. finite_element_analysis_welsim_geom_plate

Line

An example of a created Line shape is shown in Figure [fig:ch3_guide_geom_line]. finite_element_analysis_welsim_geom_line

Importing and exporting geometry

Importing

The geometry importing feature supports the STEP and IGES format files, and the STEP file is recommended. The following lists the behaviors of importing geometry:

  • An imported STEP file may lead to creating multiple Part objects in the tree if the file contains an assembly.
  • IGES file contains the surface information only, you need to implement Make Solid command to the imported geometry to obtain the solid geometry.
  • Using the Scale property to tune the size of the imported geometry.

Exporting

The geometries in the tree can be exported to an external STEP file. The following methods show you how to export:

  • Click the Export... button from the Toolbar.
  • Click the Export... item from the Geometry Menu.
  • Right click on the target geometries and select the Export... from the context menu.

Boolean operations

The WELSIM geometry module supports fundamental Boolean operations, which allow users to manipulate the shape of geometries. The available operations are Union, Intersection, and Difference. You can select multiple geometry objects from the tree list and press the Boolean commands to implement the operations. You can hold Ctrl or Shift keys to select multiple geometry objects from the project tree.

Union

The union operation consolidates two or more geometry into one geometry. An example of Union geometry of a box and cylinder shape is shown in Figure below.

finite_element_analysis_welsim_geom_union

Intersection

The intersection operation keeps the commonly shared portions of two or more geometries. An example of Intersection geometry of a box and cylinder shape is shown in Figure below.

finite_element_analysis_welsim_geom_intersection

Difference

The Difference operation subtracts the secondly selected geometry from the first selected geometry. Thus the selection order plays an important role in the final generated geometry. You can see the results of two different selection orders in Figures below.

finite_element_analysis_welsim_geom_diff1 finite_element_analysis_welsim_geom_diff2

Geometry commands

In addition to the fundamental geometry commands, the following lists the commands that may be applied in the geometry modeling:

Generate solid

In the most of analysis, the model needs to be solid to generate the 3D solid finite element. If the imported geometry only contains the surface data, the mesher cannot generate solid elements. In this scenario, you need to convert a surface geometry to solid geometry. The Generate Solid command provides you with a tool to complete this conversion.

To convert a surface to solid geometry, you can follow the steps below:

  1. Select the surface geometry objects from the tree.
  2. Click the Generate Solid command from the Geometry Menu, or right click on the selected geometry objects, and select the Generate Solid command from the context menu.

Part structure types

Solid bodies

The solid bodies including parts and assembly support all simulation features of WELSIM application.

Surface bodies

The surface bodies are treated as Shell structure in the structural and thermal analyses. In the Properties View of the Shell part, you need to specify the thickness of the shell, as shown in Figure below.

finite_element_analysis_welsim_part_shell_thickness

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Application user interface

This section describes the fundamental components of the WELSIM application interface, their usage, and behaviors.

WELSIM application window

The functional components of the graphical user interface include the following as listed in Table below.

Window Component Description
Main Menus This menu includes all application level actions such as File and About
Standard Toolbar This toolbar contains commonly used actions such as Mesh and Solve
Graphics Toolbar This toolbar contains graphics related actions such as Zoom and Selection
Project Explorer (Tree) Window This window contains a list of simulation objects that represents the modeling settings. Since it contains the branches and trunk, this windows is also called tree outline. The context menu for each object could vary. The object can be renamed, deleted, duplicated, copied and pasted
Properties Window This window displays the properties of each object in the tree list. The user can view or edit the property values
Graphics View This window shows and manipulates the visual content of the simulation entities. This window can display: 3D geometry, mesh, annotation, coordinate system symbol, spreadsheet, etc
Output Window This window display the messages from the system or solvers
Tabular Data Window This window lists the data that is input from user or output from the solvers. The listed data is always consistent with the curves in the Chart window
Chart Window This window plots the graphics that is input from user or output from the solvers. The curves are always consistent with the table data in the Tabular Data window
Context Menu This menu shows up as user right mouse button click on objects, graphics, toolbars, etc. Different entities may show different context
Status Bar This widget shows the message and status on the bottom area of the application interface

Windows management

The WELSIM window owns panes that can carry project objects, properties, graphics, output, tabular data, and chart views.Window management functionalities enable you to dock, hide, show, move, and resize the windows.

Hiding and showing

The windows can be hidden or shown by setting the view controller. As shown in Figure [tab:ch3_guide_gui_windows], there are two ways to control the window views:

  1. Browse the View Menu > Windows, toggle the windows that you would show or hide.
  2. Right mouse button clicks on the Toolbar, you can toggle the windows.

You also can click the cross button on the title bar to hide the window.

finite_element_analysis_welsim_gui_window1 finite_element_analysis_welsim_gui_window2

Docking and undocking

You can drag a window's title bar to move a window pane. Once you start to drag the window, the activated window is moving with your mouse. You can release the button on the target area to settle the new docking area. You can double-click a window's title bar to move it around the screen. The size of the window can be adjusted easily by dragging the borders or corners. You also can click the undocking button on the title bar to undock the window.

Moving and resizing

You can drag a window's title bar to move and undock a window pane. Once you start to drag the window, the potential dock target area appears in the allowed space. At this moment, you can release the button to dock the window on the target area.

Main windows

Besides the menu and toolbar widgets of the user interface, some other widgets are available. Those windows appear by default or when specific options are activated. The availability of those windows is controlled by the VIEW > Windows menu. This section discusses the following windows:

  • Project Explorer (Tree list)
  • Properties View
  • Graphics Window
  • Output Window
  • Tabular Data Window
  • Chart Window
  • Spreadsheet Window

As the user selects a tree object in the Project Explorer window, all attributes for the selected object in Properties View, Tabular Data, and Chart Window are displayed or updated. The Properties window contains two tabs, and the Data tab shows the attributes about the object data, the Display tab lists the specifications about the graphics. The Graphics window shows the three-dimensional geometry model, depending on the tree object selection, shows information about the object details, highlighted areas, and annotations. The Output window displays the messages from the system or solvers. The Spreadsheet window shows the worksheet data for specific tree objects.

Those user interface components are described in the following sections:

Project explorer

The object Tree list represents the logical steps of the conducted simulation study. All branches relate to the parenting object. For instance, a key object called Study contains Study Settings and boundary condition objects. The user can right click on an object to activate a context menu that relates to the clicked object. The objects can be copied, pasted, duplicated, and renamed.

An example of the Project Explorer window is shown in Figure below.

finite_element_analysis_welsim_gui_tree1

Note

The tree outline contains all elements that applied in the simulation study. The root object displays the number of projects in the solution. The Material project node includes all material specification. The FEM project contains the analysis settings, multiple FEM projects are allowed in the solution.

Knowing the tree objects

The tree objects in the Project Explorer window have the following conventions:

  • Object Icon appears to the left of the object in the tree list. The icon is intended for users to identify the type of object. For example, icons for computational results always consist of three colors (red, green, and blue), which can help distinguish other objects.
  • A right-head arrow symbol to the left of the object indicates that this object contains child sub-objects. Clicking the arrow to expand the object and display the children.
  • A down-head arrow symbol to the left of the object indicates that the object expends all child objects. Clicking the arrow to collapse the sub-objects.
  • To delete an object from the tree list, you can right click on the target object and select Delete.

Object status symbols

The status icons are smaller than the tree object icon and located to the right bottom corner of the object icon. These symbols are intend to provide a quick visual reference to the status of the object. The details of the status symbols are described in Table below.

Status Name Symbol Icon Description
Underdefined finite_element_analysis_welsim_status_undefined A study object or its child objects requires user input values
Error finite_element_analysis_welsim_status_error A fixed supported object may stop the simulation due to the confliction with other settings, user needs to resolve the confliction to continue the modeling
OK finite_element_analysis_welsim_status_ok A mesh settings object is well defined or any action about this object is succeed
Suppressed finite_element_analysis_welsim_status_suppressed An object is suppressed, such object becomes deactivated and won't participate the simulation. User can unsuppress the object
Needs to be Updated finite_element_analysis_welsim_status_needtoupdate An answers object or its child objects are not evaluated. Waiting for user to update

Suppressing/Unsuppressing objects

Most of the objects in the Project Explorer window can be suppressed or unsuppressed by users. A suppressed object means that it is excluded from the further analysis. For example, suppressing a boundary condition excludes the boundary condition from the study and the further solutions. You also can unsuppress the object with the restored object attributes.

There are two ways to suppress/unsuppress an object:

  • Right-click the object, and then select Suppress from the context menu. Or
  • In the property view of the object, set the Suppressed option to True. Conversely, you can unsuppress objects by setting the Suppressed option to False.

Properties view

The Properties View is located in the bottom left corner of the main user interface by default, and the user can change the location by dragging the window pane. This view window provides the user with details and information that relate to the selected object in the Project Explorer. Some properties are read-only that cannot be changed by the users, and some properties allow users to input values. An example of Properties View of the object is shown in Figures below.

finite_element_analysis_welsim_properties_view1 finite_element_analysis_welsim_properties_view2

Features

The features of the Properties View include:

  • Resizable and movable.
  • Drop-down cells for Boolean or Enumeration list.
  • Buttons to display a dialog box (such as color picker).
  • OK/Cancel buttons for geometry selection.
  • Property cell can change background color according to the content.

Group property

The Group Property is a read-only and occupy the entire row of the Properties pane, as shown in Figure below.

finite_element_analysis_welsim_group_property

The group provides you better user experience by organizing the properties into distinct categories.

Undefined or invalid properties

In the Properties View, the undefined or invalid fields are highlighted in yellow as shown in Figure below.

finite_element_analysis_welsim_invalid_property

Once the property is well defined and becomes valid, highlight yellow color disappears.

The combo property shows the drop-down list as user clicks the attribute as shown in Figure below.

finite_element_analysis_welsim_dropdown_property

Note

You can adjust the width of the columns by dragging the separator between the columns.

Text entry

In the text entry field, you can input strings, numbers, or integers, depending on the type of the cell as shown in Figure below.

finite_element_analysis_welsim_text_property

The invalid value for the specific cell will be discarded, or the cell shows red background.

Geometry selection

Geometry Selection allows users to scope topological entities from the graphics window. An example of Geometry Selection property is shown in Figure below.

finite_element_analysis_welsim_property_sel2

After selecting appropriate geometry entities, you can click the OK button to set the current selection into the field. Clicking the Cancel button does not change the pre-existing selection.

Graphics window

The Graphics window displays the geometry, annotation, mesh, result, etc. The components in the graphics window could be:

  • 3D Graphics
  • A scale rule
  • A legend and a coutour controller (for result display)
  • 2D Annotations (for boundary conditions, result display)
  • 3D Annotations (for boundary conditions)
  • Global coordinate system symbol
  • Graphical toolbar
  • Multi-purpose tabs
  • WELSIM logo and version number

An example view of the Grpahics window is shown in Figure below.

finite_element_analysis_welsim_graphics_full

Tabular data window

Tabular Data window is designed in better reviewing the input and output data. When you select the following objects in the tree window, both Tabular Data and Chart windows display data on the interface.

  • Boundary conditions
  • Body conditions
  • Results
  • Probe Results

The listed data in Tabular Data window is consistent with the curves in the Chart window. As an example shown in Figure below, you can see the maximum and minimum values at all time steps are consistent between those two windows.

finite_element_analysis_welsim_tabular_data_view1

Chart window

The Chart window displays the curves for the selected tree object. The curves are consistent with the data in the Tabular Data window. An example of Chart window drawing the maximum and minimum values along time is shown in Figure below.

finite_element_analysis_welsim_chart_view1

Spreadsheet window

The spreadsheet window provides object data in the form of tables, charts, or text to you. This widget usually contains the summarized data for a collection of properties. Note that not all objects contain a spreadsheet window, only the object that has large data may own a spreadsheet window. The behaviors of the spreadsheet window are:

  1. A spreadsheet designed to show large data on one field does not automatically display the data. You can open the spreadsheet window by double-clicking specific objects, such as Material and Study Setting objects.
  2. A new tab shows up as the spreadsheet window is open. You can close the window by clicking the cross button on the tab, or by pressing the OK button on the spreadsheet.

An example of the spreadsheet window is shown in Figure below.

finite_element_analysis_welsim_spreadsheet_view1

Output window

The output window prompts you with feedback concerning the results of your actions in using WELSIM. In the current version, the output window mainly displays the message from the solvers. An example of output window displaying the solver messages is shown in Figure below.

finite_element_analysis_welsim_output_view1

The Output window pane contains several buttons, there are:

  • Save Output Text: saves the output text into an external file.
  • Clear Text: clears the text field.
  • Stop Interprocess: discontinues the solver process.

The main menus contain the following items as shown in Figure below.

finite_element_analysis_welsim_main_menu

File menu

The FILE menu includes the following actions:

  • New: Creates a new finite element analysis project.
  • Open: Resumes the WELSIM solution from an external “*.wsdb” file.
  • Save: stores the WELSIM solution to an external “.wsdb” file.
  • Save As: stores the WELSIM solution to another external “.wsdb” file.
  • Close Project: deletes the current finite element project.
  • Close All: deletes all projects in the solution.
  • Quit: Exit the application.

The items of the File menu is shown in Figure below.

finite_element_analysis_welsim_menu_file

View menu

The VIEW menu includes the following actions:

  • Zooms: adjusts display scale of the graphics field, contains sub-items: Zoom Extents, Zoom In, Zoom Out, Box Zoom.
  • Views: changes the viewpoint to the graphics display field. Includes sub-items: Isometric, Top, Right, Front.
  • Graphics Window: changes the mode of the graphics window. Includes sub-items: Docked, Undocked, and Full Screen.
  • Toolbars: determines to show the toolbars on the uesr interface. The available toolbars include File, Material, Geometry, FEM, Structural, Thermal, Electromagnetic, Tools, and Help.
  • Windows: controls the display of the windows. The options that can be toggled are Project Explorer, Properties, Output, Tabular Data, and Chart windows.
  • Status Bar: toggles the display of the status bar to the bottom of the main window.

The items of the View menu is shown in Figure below.

finite_element_analysis_welsim_menu_view

Material menu

The MATERIAL menu includes the following actions:

  • New Material Project: adds a new material project if the tree has no material project.
  • Add Material: defines a new material object.
  • Export Materials: outputs material data into an external file with JSON format.

The items of the Material Menu is shown in Figure below.

finite_element_analysis_welsim_menu_material

Geometry menu

The GEOMETRY menu includes the following actions:

  • Import: creates new geometries from the external files with STEP or IGES format.
  • Export: saves geometries into external STEP file.
  • Add Box: creates a new 3D box shape.
  • Add Cylinder: creates a new 3D cylinder shape.
  • Add Plate: creates a new 3D plate shape.
  • Add Line: creates a new 3D line shape.
  • Generate Solid: create a 3D solid shape according to the enclosed surface shape.
  • Union: consolidates multiple geometries into one geometry.
  • Intersection: creates a geometry that is the common area of multiple geometries.
  • Difference: creates a geometry that is differentiated between the selected geometries.
  • Show: displays the selected geometry objects.
  • Hide: hides the selected geometry objects.
  • Show All: displays all geometries.
  • Hide All: hides all geometries.

The items of the Geometry Menu is shown in Figure below.

finite_element_analysis_welsim_menu_geometry

FEM menu

The FEM Menu includes the following actions:

  • Mesh All: generates the mesh for the entire domain.
  • Clear Generated Mesh: removes all generated mesh.
  • Check Mesh: examines the quality of the generated mesh.
  • Add Mesh Settings: adds a global mesh settings object to the tree.
  • Add Mesh Method: adds a local mesh method object to the tree.
  • Mesh Method: generates the mesh for the geometries that are scoped in the mesh method object.
  • Connections: adds a Connections object if no connection object is presented.
  • Add Contact: adds a Contact Pair object to the tree.
  • Add Study Settings: adds a Study Settings object to the tree if no study settings object is presented.
  • Compute: solves the finite element model.
  • Clear Calculated Solution: remove the solved data in the current project.
  • User Defined Result: adds a user-defined result object to the tree.
  • Evaluate Result: evaluates the selected result objects.
  • Evaluate All: evaluate all result objects in current project.
  • Clear Result: remove the generated result data.
  • Export Result: export the result data into an external file in ASCII format.

The items of the FEM Menu is shown in Figure below.

finite_element_analysis_welsim_menu_fem

Structural menu

The STRUCTURAL menu includes the following actions:

  • Constraint: adds a fixed support boundary condition object. It essentially sets displacement to zero.
  • Displacement: adds a displacement boundary condition object.
  • Force: adds a force boundary condition object.
  • Pressure: adds a pressure boundary condition object.
  • Fixed Rotation: adds a fixed rotation boundary condition object, specifically for the shell model.
  • Velocity: adds a velocity boundary condition object, specifically for the transient structural analysis.
  • Acceleration: adds a velocity boundary condition object, specifically for the transient structural analysis.
  • Body Force: adds a body force condition object.
  • Acceleration: adds a body acceleration condition object.
  • Earth Gravity: adds a standard earth gravity condition object.
  • Rotational Velocity: adds a rotational velocity object.
  • Displacement Result: adds a displacement result object.
  • Stress Result: adds a stress result object.
  • Strain Result: adds a strain result object.
  • Velocity Result: adds a velocity result object. It is available for the transient structural analysis.
  • Acceleration Result: adds an acceleration result object. It is available for the transient structural analysis.
  • Rotation Result: adds a ratation result object. It is available for the shell structure.
  • Reaction Force Probe: adds a force reaction probe result.
  • Reaction Moment Probe: adds a moment reaction probe result. It is available for the shell structure.

The items of the Structural menu is shown in Figure below.

finite_element_analysis_welsim_menu_structural

Thermal menu

The THERMAL menu includes the following actions:

  • Temperature: adds a temperature boundary condition object.
  • Heat Flux: adds a heat flux boundary condition object.
  • Convection: adds a heat convection boundary condition object.
  • Radiation: adds a heat radiation boundary condition object.
  • Initial Temperature: adds a initial temperature condition object. It is available for transient thermal analysis.
  • Temperature Result: adds a temperature result object.

The items on the Thermal menu is shown in Figure below.

finite_element_analysis_welsim_menu_thermal

Electromagnetic menu

The ELECTROMAGNETIC menu includes the following actions:

  • Ground: adds a ground boundary condition object. It essentially sets the voltage to zero.
  • Voltage: adds a voltage boundary condition object.
  • Symmetry: adds a symmetry boundary condition object.
  • Zero Charge: adds a zero charge boundary condition object.
  • Surface Charge Density: adds a surface charge density boundary condition object.
  • Electric Displacement: adds an electric displacement boundary condition object.
  • Insulating: adds an insulating boundary condition object. It essentially sets zero magnetic potential.
  • Magnetic Potential: adds a magnetic potential boundary condition object.
  • Magnetic Flux Density: adds a magnetic flux density boundary condition object.
  • Voltage Result: adds a voltage result object.
  • Electric Field Result: adds an electric field result object.
  • Electric Displacement Result: adds an electric displacement result object.
  • Magnetic Potential Result: adds a magnetic potential result object.
  • Magnetic Field Result: adds a magnetic field result object.
  • Magnetic Induction Field Result: adds a magnetic induction field result object.
  • Energy Density Result: adds an energy density result object.

The items of the Electromagnetic menu is shown in Figure below.

finite_element_analysis_welsim_menu_em

Tools menu

The TOOLS menu includes the following actions:

  • Export Input Script: generates solver input scripts to the designated directory.
  • Reveal Files in Explorer: opens the local directory that contains project files.

The items of the Tools menu is shown in Figure below.

finite_element_analysis_welsim_menu_tools

Help menu

The HELP menu includes the following actions:

  • Documentation: opens the default internet web browser, and visits online documentation.
  • Website: opens the default internet web browser, and visits official website.
  • License Manager: opens WELSIM license manager interface. You can activate the application with the license key or update the license here.
  • About: provides copyright and application version information.

The items of the Help menu is shown in Figure below.

finite_element_analysis_welsim_menu_help

Toolbars

Toolbars are displayed across the top of the main user interface. Toolbars are dockable, and you can drag the toolbar to your preferred field.

File toolbar

The File toolbar contains application-level commands as shown in Figure below. Each icon button and its description follows:

  • finite_element_analysis_welsim_gui_newdoc: creates a new finite element analysis project.
  • finite_element_analysis_welsim_gui_save: saves solution into an external “*.wsdb” file.
  • finite_element_analysis_welsim_gui_opendoc: resumes solution from an external “*.wsdb” file.
  • finite_element_analysis_welsim_gui_closedoc: closes the current analysis project.

finite_element_analysis_welsim_toolbar_file

Material toolbar

The Material toolbar contains material-related simulation commands as shown in Figure below. Each icon button and its description follows:

  • finite_element_analysis_welsim_materialobject: creates a new material object.
  • finite_element_analysis_welsim_exportmaterial: exports all material data into an external JSON file.

finite_element_analysis_welsim_toolbar_material

Geometry toolbar

The Geometry toolbar contains geometry-related commands as shown in Figure below. Each icon button and its description follows:

  • finite_element_analysis_welsim_gui_import: imports the geometries from an external STEP or IGES file.
  • finite_element_analysis_welsim_gui_export_part: exports the geometries into an external STEP file.
  • finite_element_analysis_welsim_part_box: creates a box shape.
  • finite_element_analysis_welsim_part_cylinder: creates a cylinder shape.
  • finite_element_analysis_welsim_part_face: creates a plate shape.
  • finite_element_analysis_welsim_part_line: creates a line shape.
  • finite_element_analysis_welsim_part_union: consolidates the selected geometries into one part.
  • finite_element_analysis_welsim_part_intersec: creates geometry from the commonly shared field of multiple geometries.
  • finite_element_analysis_welsim_part_diff: creates geometry from the difference among multiple geometries.

finite_element_analysis_welsim_toolbar_geometry

FEM toolbar

The FEM toolbar contains finite element analysis commands as shown in Figure below. Each icon button and its description follows:

  • finite_element_analysis_welsim_gui_import: generates the mesh for the entire domain.
  • finite_element_analysis_welsim_gui_import: clear the generated mesh.
  • finite_element_analysis_welsim_gui_import: examines the mesh quality.
  • finite_element_analysis_welsim_gui_import: creates a mesh method object, which is used for the local mesh settings.
  • finite_element_analysis_welsim_gui_import: generates the mesh for the scoped geometries in mesh method object.
  • finite_element_analysis_welsim_gui_import: creates a new contact pair object.
  • finite_element_analysis_welsim_gui_import: solves the finite element model.
  • finite_element_analysis_welsim_gui_import: creates a new user-defined result object.
  • finite_element_analysis_welsim_gui_import: evaluates the selected result objects.
  • finite_element_analysis_welsim_gui_import: evaluates all result objects in current project.

finite_element_analysis_welsim_toolbar_fem

Structural toolbar

The Structural toolbar contains structural analysis commands as shown in Figure below. Each icon button and its description follows:

  • finite_element_analysis_welsim_bc_fixed: creates a fixed support boundary condition object.
  • finite_element_analysis_welsim_bc_displacement: creates a displacement boundary condition object.
  • finite_element_analysis_welsim_bc_force: creates a force boundary condition object.
  • finite_element_analysis_welsim_bc_pressure: creates a pressure boundary condition object.
  • finite_element_analysis_welsim_bc_fixed_rot: creates a fixed rotation boundary condition object.
  • finite_element_analysis_welsim_bc_velocity: creates a velocity boundary condition object. It is available for the transient structural analysis.
  • finite_element_analysis_welsim_bc_acceleration: creates a acceleration boundary condition object. It is available for the transient structural analysis.
  • finite_element_analysis_welsim_dc_bodyforce: creates a body force domain condition object.
  • finite_element_analysis_welsim_dc_acceleration: creates an acceleration domain condition object.
  • finite_element_analysis_welsim_dc_gravity: creates a standard earth gravity domain condition object.
  • finite_element_analysis_welsim_dc_rotvelocity: creates a rotational velocity domain condition object.
  • finite_element_analysis_welsim_result_disp: creates a displacement result object.
  • finite_element_analysis_welsim_result_stress: creates a stress result object.
  • finite_element_analysis_welsim_result_strain: creates a strain result object.
  • finite_element_analysis_welsim_rst_velocity: creates a velocity result object. It is available for the transient structural analysis.
  • finite_element_analysis_welsim_rst_acceleration: creates a velocity result object. It is available for the transient structural analysis.
  • finite_element_analysis_welsim_rst_reaction_force: creates a rotation result object. It is available for the shell model.
  • finite_element_analysis_welsim_rst_reaction_force: creates a force reaction probe object.
  • finite_element_analysis_welsim_rst_reaction_moment: creates a moment reaction probe object. It is available for the shell model.

finite_element_analysis_welsim_toolbar_structural

Thermal toolbar

The Thermal toolbar contains thermal analysis commands as shown in Figure below. Each icon button and its description follows:

  • finite_element_analysis_welsim_bc_temperature: creates a temperature boundary condition object.
  • finite_element_analysis_welsim_bc_heatflux: creates a heat flux boundary condition object.
  • finite_element_analysis_welsim_bc_heat_convection: creates a heat convection boundary condition object.
  • finite_element_analysis_welsim_bc_radiation: creates a heat radiation boundary condition object.
  • finite_element_analysis_welsim_initial_temperature: creates an initial temperature boundary condition object. It is available for the transient thermal analysis.
  • finite_element_analysis_welsim_result_temperature: creates a temperature result object.

finite_element_analysis_welsim_toolbar_thermal

Electromagnetic toolbar

The Electromagnetic toolbar contains electric and magnetic analyses commands as shown in Figure below. Each icon button and its description follows:

  • finite_element_analysis_welsim_bc_ground: creates a ground boundary condition object.
  • finite_element_analysis_welsim_bc_voltage: creates a velocity boundary condition object.
  • finite_element_analysis_welsim_bc_em_symmetry: creates a symmetry boundary condition object.
  • finite_element_analysis_welsim_bc_zero_charge: creates a zero charge boundary condition object.
  • finite_element_analysis_welsim_bc_surface_charge: creates a surface charge density boundary condition object.
  • finite_element_analysis_welsim_bc_electricdisp: creates an electric displacement boundary condition object.
  • finite_element_analysis_welsim_bc_em_insulting: creates an insulating boundary condition object.
  • finite_element_analysis_welsim_bc_magneticpotential: creates a magnetic potential boundary condition object.
  • finite_element_analysis_welsim_bc_magneticfluxdensity: creates a magnetic flux density boundary condition object.
  • finite_element_analysis_welsim_rst_voltage: creates a voltage result object.
  • finite_element_analysis_welsim_rst_efield: creates an electric field result object.
  • finite_element_analysis_welsim_rst_dfield: creates an electric displacement result object.
  • finite_element_analysis_welsim_rst_magneticpotential: creates a vector magnetic potential result object.
  • finite_element_analysis_welsim_rst_hfield: creates a magnetic field result object.
  • finite_element_analysis_welsim_rst_bfield: creates a magnetic induction field result object.
  • finite_element_analysis_welsim_rst_emenergydensity: creates an electromagnetic energy density result object.

finite_element_analysis_welsim_toolbar_em

Tool toolbar

The Tool toolbar contains assistance commands as shown in Figure below. Each icon button and its description follows:

To be added ...
-

Help toolbar

The Help toolbar contains assistance commands as shown in Figure below. Each icon button and its description follows:

  • finite_element_analysis_welsim_gui_onlinedoc: opens the default internet web browser, and visits online documentation.
  • finite_element_analysis_welsim_gui_website: opens the default internet web browser, and visits official website.
  • finite_element_analysis_welsim_gui_licmgr: opens WELSIM license manager interface. You can activate the application with the license key or update the license here.
  • finite_element_analysis_welsim_about: displays the copyrights and version information of WELSIM application.

finite_element_analysis_welsim_toolbar_help

Graphics toolbar

The Graphics toolbar contains graphical operation commands as shown in Figure below. Each icon button and its description follows:

  • finite_element_analysis_welsim_gui_zoomall: fits the entire model in the graphics window.
  • finite_element_analysis_welsim_gui_zoomin: displays a closer view of the geometries.
  • finite_element_analysis_welsim_gui_zoomout: displays a more distant view of the geometries.
  • finite_element_analysis_welsim_gui_zoombox: displays the selected area of a model in a box that you define.
  • finite_element_analysis_welsim_view_axo: displays the 3D model in an isometric view.
  • finite_element_analysis_welsim_view_xy: displays the 3D model in an XY-plane view.
  • finite_element_analysis_welsim_view_yz: displays the 3D model in a YZ-plane view.
  • finite_element_analysis_welsim_view_xz: displays the 3D model in an XZ-plane view.
  • finite_element_analysis_welsim_select_volume: set the volume selectable.
  • finite_element_analysis_welsim_select_face: set the face selectable.
  • finite_element_analysis_welsim_select_edge: set the edge selectable.
  • finite_element_analysis_welsim_select_vertex: set the vertex selectable.

finite_element_analysis_welsim_toolbar_graphics

Working with graphics

The following lists the tips for working with WELSIM graphics:

  • You can use the ruler, presented at the bottom of the graphics window, to estimate the scale of the geometry size.
  • You can rotate the view of geometries by holding and dragging the left mouse button.
  • You can select or deselect multiple topological entities by pressing CTRL or SHIFT key.
  • You can pan the view by dragging your right mouse button or arrow keys.
  • You can zoom in/out the view by scrolling the mouse wheel or using ± and CTRL keys.
  • You can rotate the view by using the left mouse button.
  • You can open a context menu of views by right-clicking on the graphics field.

PreSelecting geometry

This section discusses the pre-selection features in the Graphics window.

Highlighting

As you hover the cursor over a geometry entity, the graphics highlights the selection and shows the location of the pointer. The pre-selection is controlled by the selection filter, and only the allowed entity types can be pre-selected and highlighted.

As shown in Figure below, the face are highlighted in green color at pre-selection mode.

finite_element_analysis_welsim_graphics_presel

Selecting geometry

This section discusses how to select and pick geometry in the Graphics window.

Picking

You can pick visible geometries by left clicking on the entities. A valid picking sets the geometry selection property for specific objects, such as boundary conditions.

You can hold the Ctrl or Shift key down to add or remove multiple selections from the current selections. A pick in the free space clears the current selection.

Selection filters

The selection filters control the user selection mode and provide an easy interface for users to pick or select the geometry entities. A pressed button in the selection filter toolbar denotes a selectable geometry type. The following describes the filters.

  • Volumes: Allows selection of the entire body. Highlighted by body surfaces in green. Depressing this filter releases the Faces, Edges, and Vertices filters.
  • Faces: Allows selection of faces. Highlighted by surfaces in green. Depressing this filter releases the Volumes filters.
  • Edges: Allows selection of edges. Highlighted by lines in green. Depressing this filter releases the Volumes filters.
  • Vertices: Allows selection of vertices. Highlighted by points in green. Depressing this filter releases the Volumes filters.

Controlling graphical view

The section describes the controlling and manipulating the graphical view with mouse and keys.

  • Zoom: Middle scrolling.
  • Pan: Right clicking, or arrow keys.
  • Rotate: Left clicking and dragging.

View annotations

Graphics window may contain these types of annotations:

  • 2D annotation: statically locates at the left top of the graphics windows. This annotation shows texts about the object type and name and color indicator for specific objects such as boundary conditions.

  • 3D annotation: dynamically locates on the geometry area, the position can be changed as the user rotates, zooms or pans the view.

\ No newline at end of file + Application user interface - WelSim Documentation
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Application user interface

This section describes the fundamental components of the WELSIM application interface, their usage, and behaviors.

WELSIM application window

The functional components of the graphical user interface include the following as listed in Table below.

Window Component Description
Main Menus This menu includes all application level actions such as File and About
Standard Toolbar This toolbar contains commonly used actions such as Mesh and Solve
Graphics Toolbar This toolbar contains graphics related actions such as Zoom and Selection
Project Explorer (Tree) Window This window contains a list of simulation objects that represents the modeling settings. Since it contains the branches and trunk, this windows is also called tree outline. The context menu for each object could vary. The object can be renamed, deleted, duplicated, copied and pasted
Properties Window This window displays the properties of each object in the tree list. The user can view or edit the property values
Graphics View This window shows and manipulates the visual content of the simulation entities. This window can display: 3D geometry, mesh, annotation, coordinate system symbol, spreadsheet, etc
Output Window This window display the messages from the system or solvers
Tabular Data Window This window lists the data that is input from user or output from the solvers. The listed data is always consistent with the curves in the Chart window
Chart Window This window plots the graphics that is input from user or output from the solvers. The curves are always consistent with the table data in the Tabular Data window
Context Menu This menu shows up as user right mouse button click on objects, graphics, toolbars, etc. Different entities may show different context
Status Bar This widget shows the message and status on the bottom area of the application interface

Windows management

The WELSIM window owns panes that can carry project objects, properties, graphics, output, tabular data, and chart views.Window management functionalities enable you to dock, hide, show, move, and resize the windows.

Hiding and showing

The windows can be hidden or shown by setting the view controller. As shown in Figure [tab:ch3_guide_gui_windows], there are two ways to control the window views:

  1. Browse the View Menu > Windows, toggle the windows that you would show or hide.
  2. Right mouse button clicks on the Toolbar, you can toggle the windows.

You also can click the cross button on the title bar to hide the window.

finite_element_analysis_welsim_gui_window1 finite_element_analysis_welsim_gui_window2

Docking and undocking

You can drag a window's title bar to move a window pane. Once you start to drag the window, the activated window is moving with your mouse. You can release the button on the target area to settle the new docking area. You can double-click a window's title bar to move it around the screen. The size of the window can be adjusted easily by dragging the borders or corners. You also can click the undocking button on the title bar to undock the window.

Moving and resizing

You can drag a window's title bar to move and undock a window pane. Once you start to drag the window, the potential dock target area appears in the allowed space. At this moment, you can release the button to dock the window on the target area.

Main windows

Besides the menu and toolbar widgets of the user interface, some other widgets are available. Those windows appear by default or when specific options are activated. The availability of those windows is controlled by the VIEW > Windows menu. This section discusses the following windows:

  • Project Explorer (Tree list)
  • Properties View
  • Graphics Window
  • Output Window
  • Tabular Data Window
  • Chart Window
  • Spreadsheet Window

As the user selects a tree object in the Project Explorer window, all attributes for the selected object in Properties View, Tabular Data, and Chart Window are displayed or updated. The Properties window contains two tabs, and the Data tab shows the attributes about the object data, the Display tab lists the specifications about the graphics. The Graphics window shows the three-dimensional geometry model, depending on the tree object selection, shows information about the object details, highlighted areas, and annotations. The Output window displays the messages from the system or solvers. The Spreadsheet window shows the worksheet data for specific tree objects.

Those user interface components are described in the following sections:

Project explorer

The object Tree list represents the logical steps of the conducted simulation study. All branches relate to the parenting object. For instance, a key object called Study contains Study Settings and boundary condition objects. The user can right click on an object to activate a context menu that relates to the clicked object. The objects can be copied, pasted, duplicated, and renamed.

An example of the Project Explorer window is shown in Figure below.

finite_element_analysis_welsim_gui_tree1

Note

The tree outline contains all elements that applied in the simulation study. The root object displays the number of projects in the solution. The Material project node includes all material specification. The FEM project contains the analysis settings, multiple FEM projects are allowed in the solution.

Knowing the tree objects

The tree objects in the Project Explorer window have the following conventions:

  • Object Icon appears to the left of the object in the tree list. The icon is intended for users to identify the type of object. For example, icons for computational results always consist of three colors (red, green, and blue), which can help distinguish other objects.
  • A right-head arrow symbol to the left of the object indicates that this object contains child sub-objects. Clicking the arrow to expand the object and display the children.
  • A down-head arrow symbol to the left of the object indicates that the object expends all child objects. Clicking the arrow to collapse the sub-objects.
  • To delete an object from the tree list, you can right click on the target object and select Delete.

Object status symbols

The status icons are smaller than the tree object icon and located to the right bottom corner of the object icon. These symbols are intend to provide a quick visual reference to the status of the object. The details of the status symbols are described in Table below.

Status Name Symbol Icon Description
Underdefined finite_element_analysis_welsim_status_undefined A study object or its child objects requires user input values
Error finite_element_analysis_welsim_status_error A fixed supported object may stop the simulation due to the confliction with other settings, user needs to resolve the confliction to continue the modeling
OK finite_element_analysis_welsim_status_ok A mesh settings object is well defined or any action about this object is succeed
Suppressed finite_element_analysis_welsim_status_suppressed An object is suppressed, such object becomes deactivated and won't participate the simulation. User can unsuppress the object
Needs to be Updated finite_element_analysis_welsim_status_needtoupdate An answers object or its child objects are not evaluated. Waiting for user to update

Suppressing/Unsuppressing objects

Most of the objects in the Project Explorer window can be suppressed or unsuppressed by users. A suppressed object means that it is excluded from the further analysis. For example, suppressing a boundary condition excludes the boundary condition from the study and the further solutions. You also can unsuppress the object with the restored object attributes.

There are two ways to suppress/unsuppress an object:

  • Right-click the object, and then select Suppress from the context menu. Or
  • In the property view of the object, set the Suppressed option to True. Conversely, you can unsuppress objects by setting the Suppressed option to False.

Properties view

The Properties View is located in the bottom left corner of the main user interface by default, and the user can change the location by dragging the window pane. This view window provides the user with details and information that relate to the selected object in the Project Explorer. Some properties are read-only that cannot be changed by the users, and some properties allow users to input values. An example of Properties View of the object is shown in Figures below.

finite_element_analysis_welsim_properties_view1 finite_element_analysis_welsim_properties_view2

Features

The features of the Properties View include:

  • Resizable and movable.
  • Drop-down cells for Boolean or Enumeration list.
  • Buttons to display a dialog box (such as color picker).
  • OK/Cancel buttons for geometry selection.
  • Property cell can change background color according to the content.

Group property

The Group Property is a read-only and occupy the entire row of the Properties pane, as shown in Figure below.

finite_element_analysis_welsim_group_property

The group provides you better user experience by organizing the properties into distinct categories.

Undefined or invalid properties

In the Properties View, the undefined or invalid fields are highlighted in yellow as shown in Figure below.

finite_element_analysis_welsim_invalid_property

Once the property is well defined and becomes valid, highlight yellow color disappears.

The combo property shows the drop-down list as user clicks the attribute as shown in Figure below.

finite_element_analysis_welsim_dropdown_property

Note

You can adjust the width of the columns by dragging the separator between the columns.

Text entry

In the text entry field, you can input strings, numbers, or integers, depending on the type of the cell as shown in Figure below.

finite_element_analysis_welsim_text_property

The invalid value for the specific cell will be discarded, or the cell shows red background.

Geometry selection

Geometry Selection allows users to scope topological entities from the graphics window. An example of Geometry Selection property is shown in Figure below.

finite_element_analysis_welsim_property_sel2

After selecting appropriate geometry entities, you can click the OK button to set the current selection into the field. Clicking the Cancel button does not change the pre-existing selection.

Graphics window

The Graphics window displays the geometry, annotation, mesh, result, etc. The components in the graphics window could be:

  • 3D Graphics
  • A scale rule
  • A legend and a coutour controller (for result display)
  • 2D Annotations (for boundary conditions, result display)
  • 3D Annotations (for boundary conditions)
  • Global coordinate system symbol
  • Graphical toolbar
  • Multi-purpose tabs
  • WELSIM logo and version number

An example view of the Grpahics window is shown in Figure below.

finite_element_analysis_welsim_graphics_full

Tabular data window

Tabular Data window is designed in better reviewing the input and output data. When you select the following objects in the tree window, both Tabular Data and Chart windows display data on the interface.

  • Boundary conditions
  • Body conditions
  • Results
  • Probe Results

The listed data in Tabular Data window is consistent with the curves in the Chart window. As an example shown in Figure below, you can see the maximum and minimum values at all time steps are consistent between those two windows.

finite_element_analysis_welsim_tabular_data_view1

Chart window

The Chart window displays the curves for the selected tree object. The curves are consistent with the data in the Tabular Data window. An example of Chart window drawing the maximum and minimum values along time is shown in Figure below.

finite_element_analysis_welsim_chart_view1

Spreadsheet window

The spreadsheet window provides object data in the form of tables, charts, or text to you. This widget usually contains the summarized data for a collection of properties. Note that not all objects contain a spreadsheet window, only the object that has large data may own a spreadsheet window. The behaviors of the spreadsheet window are:

  1. A spreadsheet designed to show large data on one field does not automatically display the data. You can open the spreadsheet window by double-clicking specific objects, such as Material and Study Setting objects.
  2. A new tab shows up as the spreadsheet window is open. You can close the window by clicking the cross button on the tab, or by pressing the OK button on the spreadsheet.

An example of the spreadsheet window is shown in Figure below.

finite_element_analysis_welsim_spreadsheet_view1

Output window

The output window prompts you with feedback concerning the results of your actions in using WELSIM. In the current version, the output window mainly displays the message from the solvers. An example of output window displaying the solver messages is shown in Figure below.

finite_element_analysis_welsim_output_view1

The Output window pane contains several buttons, there are:

  • Save Output Text: saves the output text into an external file.
  • Clear Text: clears the text field.
  • Stop Interprocess: discontinues the solver process.

The main menus contain the following items as shown in Figure below.

finite_element_analysis_welsim_main_menu

File menu

The FILE menu includes the following actions:

  • New: Creates a new finite element analysis project.
  • Open: Resumes the WELSIM solution from an external “*.wsdb” file.
  • Save: stores the WELSIM solution to an external “.wsdb” file.
  • Save As: stores the WELSIM solution to another external “.wsdb” file.
  • Close Project: deletes the current finite element project.
  • Close All: deletes all projects in the solution.
  • Quit: Exit the application.

The items of the File menu is shown in Figure below.

finite_element_analysis_welsim_menu_file

View menu

The VIEW menu includes the following actions:

  • Zooms: adjusts display scale of the graphics field, contains sub-items: Zoom Extents, Zoom In, Zoom Out, Box Zoom.
  • Views: changes the viewpoint to the graphics display field. Includes sub-items: Isometric, Top, Right, Front.
  • Graphics Window: changes the mode of the graphics window. Includes sub-items: Docked, Undocked, and Full Screen.
  • Toolbars: determines to show the toolbars on the uesr interface. The available toolbars include File, Material, Geometry, FEM, Structural, Thermal, Electromagnetic, Tools, and Help.
  • Windows: controls the display of the windows. The options that can be toggled are Project Explorer, Properties, Output, Tabular Data, and Chart windows.
  • Status Bar: toggles the display of the status bar to the bottom of the main window.

The items of the View menu is shown in Figure below.

finite_element_analysis_welsim_menu_view

Material menu

The MATERIAL menu includes the following actions:

  • New Material Project: adds a new material project if the tree has no material project.
  • Add Material: defines a new material object.
  • Export Materials: outputs material data into an external file with JSON format.

The items of the Material Menu is shown in Figure below.

finite_element_analysis_welsim_menu_material

Geometry menu

The GEOMETRY menu includes the following actions:

  • Import: creates new geometries from the external files with STEP or IGES format.
  • Export: saves geometries into external STEP file.
  • Add Box: creates a new 3D box shape.
  • Add Cylinder: creates a new 3D cylinder shape.
  • Add Plate: creates a new 3D plate shape.
  • Add Line: creates a new 3D line shape.
  • Generate Solid: create a 3D solid shape according to the enclosed surface shape.
  • Union: consolidates multiple geometries into one geometry.
  • Intersection: creates a geometry that is the common area of multiple geometries.
  • Difference: creates a geometry that is differentiated between the selected geometries.
  • Show: displays the selected geometry objects.
  • Hide: hides the selected geometry objects.
  • Show All: displays all geometries.
  • Hide All: hides all geometries.

The items of the Geometry Menu is shown in Figure below.

finite_element_analysis_welsim_menu_geometry

FEM menu

The FEM Menu includes the following actions:

  • Mesh All: generates the mesh for the entire domain.
  • Clear Generated Mesh: removes all generated mesh.
  • Check Mesh: examines the quality of the generated mesh.
  • Add Mesh Settings: adds a global mesh settings object to the tree.
  • Add Mesh Method: adds a local mesh method object to the tree.
  • Mesh Method: generates the mesh for the geometries that are scoped in the mesh method object.
  • Connections: adds a Connections object if no connection object is presented.
  • Add Contact: adds a Contact Pair object to the tree.
  • Add Study Settings: adds a Study Settings object to the tree if no study settings object is presented.
  • Compute: solves the finite element model.
  • Clear Calculated Solution: remove the solved data in the current project.
  • User Defined Result: adds a user-defined result object to the tree.
  • Evaluate Result: evaluates the selected result objects.
  • Evaluate All: evaluate all result objects in current project.
  • Clear Result: remove the generated result data.
  • Export Result: export the result data into an external file in ASCII format.

The items of the FEM Menu is shown in Figure below.

finite_element_analysis_welsim_menu_fem

Structural menu

The STRUCTURAL menu includes the following actions:

  • Constraint: adds a fixed support boundary condition object. It essentially sets displacement to zero.
  • Displacement: adds a displacement boundary condition object.
  • Force: adds a force boundary condition object.
  • Pressure: adds a pressure boundary condition object.
  • Fixed Rotation: adds a fixed rotation boundary condition object, specifically for the shell model.
  • Velocity: adds a velocity boundary condition object, specifically for the transient structural analysis.
  • Acceleration: adds a velocity boundary condition object, specifically for the transient structural analysis.
  • Body Force: adds a body force condition object.
  • Acceleration: adds a body acceleration condition object.
  • Earth Gravity: adds a standard earth gravity condition object.
  • Rotational Velocity: adds a rotational velocity object.
  • Displacement Result: adds a displacement result object.
  • Stress Result: adds a stress result object.
  • Strain Result: adds a strain result object.
  • Velocity Result: adds a velocity result object. It is available for the transient structural analysis.
  • Acceleration Result: adds an acceleration result object. It is available for the transient structural analysis.
  • Rotation Result: adds a ratation result object. It is available for the shell structure.
  • Reaction Force Probe: adds a force reaction probe result.
  • Reaction Moment Probe: adds a moment reaction probe result. It is available for the shell structure.

The items of the Structural menu is shown in Figure below.

finite_element_analysis_welsim_menu_structural

Thermal menu

The THERMAL menu includes the following actions:

  • Temperature: adds a temperature boundary condition object.
  • Heat Flux: adds a heat flux boundary condition object.
  • Convection: adds a heat convection boundary condition object.
  • Radiation: adds a heat radiation boundary condition object.
  • Initial Temperature: adds a initial temperature condition object. It is available for transient thermal analysis.
  • Temperature Result: adds a temperature result object.

The items on the Thermal menu is shown in Figure below.

finite_element_analysis_welsim_menu_thermal

Electromagnetic menu

The ELECTROMAGNETIC menu includes the following actions:

  • Ground: adds a ground boundary condition object. It essentially sets the voltage to zero.
  • Voltage: adds a voltage boundary condition object.
  • Symmetry: adds a symmetry boundary condition object.
  • Zero Charge: adds a zero charge boundary condition object.
  • Surface Charge Density: adds a surface charge density boundary condition object.
  • Electric Displacement: adds an electric displacement boundary condition object.
  • Insulating: adds an insulating boundary condition object. It essentially sets zero magnetic potential.
  • Magnetic Potential: adds a magnetic potential boundary condition object.
  • Magnetic Flux Density: adds a magnetic flux density boundary condition object.
  • Voltage Result: adds a voltage result object.
  • Electric Field Result: adds an electric field result object.
  • Electric Displacement Result: adds an electric displacement result object.
  • Magnetic Potential Result: adds a magnetic potential result object.
  • Magnetic Field Result: adds a magnetic field result object.
  • Magnetic Induction Field Result: adds a magnetic induction field result object.
  • Energy Density Result: adds an energy density result object.

The items of the Electromagnetic menu is shown in Figure below.

finite_element_analysis_welsim_menu_em

Tools menu

The TOOLS menu includes the following actions:

  • Export Input Script: generates solver input scripts to the designated directory.
  • Reveal Files in Explorer: opens the local directory that contains project files.

The items of the Tools menu is shown in Figure below.

finite_element_analysis_welsim_menu_tools

Help menu

The HELP menu includes the following actions:

  • Documentation: opens the default internet web browser, and visits online documentation.
  • Website: opens the default internet web browser, and visits official website.
  • License Manager: opens WELSIM license manager interface. You can activate the application with the license key or update the license here.
  • About: provides copyright and application version information.

The items of the Help menu is shown in Figure below.

finite_element_analysis_welsim_menu_help

Toolbars

Toolbars are displayed across the top of the main user interface. Toolbars are dockable, and you can drag the toolbar to your preferred field.

File toolbar

The File toolbar contains application-level commands as shown in Figure below. Each icon button and its description follows:

  • finite_element_analysis_welsim_gui_newdoc: creates a new finite element analysis project.
  • finite_element_analysis_welsim_gui_save: saves solution into an external “*.wsdb” file.
  • finite_element_analysis_welsim_gui_opendoc: resumes solution from an external “*.wsdb” file.
  • finite_element_analysis_welsim_gui_closedoc: closes the current analysis project.

finite_element_analysis_welsim_toolbar_file

Material toolbar

The Material toolbar contains material-related simulation commands as shown in Figure below. Each icon button and its description follows:

  • finite_element_analysis_welsim_materialobject: creates a new material object.
  • finite_element_analysis_welsim_exportmaterial: exports all material data into an external JSON file.

finite_element_analysis_welsim_toolbar_material

Geometry toolbar

The Geometry toolbar contains geometry-related commands as shown in Figure below. Each icon button and its description follows:

  • finite_element_analysis_welsim_gui_import: imports the geometries from an external STEP or IGES file.
  • finite_element_analysis_welsim_gui_export_part: exports the geometries into an external STEP file.
  • finite_element_analysis_welsim_part_box: creates a box shape.
  • finite_element_analysis_welsim_part_cylinder: creates a cylinder shape.
  • finite_element_analysis_welsim_part_face: creates a plate shape.
  • finite_element_analysis_welsim_part_line: creates a line shape.
  • finite_element_analysis_welsim_part_union: consolidates the selected geometries into one part.
  • finite_element_analysis_welsim_part_intersec: creates geometry from the commonly shared field of multiple geometries.
  • finite_element_analysis_welsim_part_diff: creates geometry from the difference among multiple geometries.

finite_element_analysis_welsim_toolbar_geometry

FEM toolbar

The FEM toolbar contains finite element analysis commands as shown in Figure below. Each icon button and its description follows:

  • finite_element_analysis_welsim_gui_import: generates the mesh for the entire domain.
  • finite_element_analysis_welsim_gui_import: clear the generated mesh.
  • finite_element_analysis_welsim_gui_import: examines the mesh quality.
  • finite_element_analysis_welsim_gui_import: creates a mesh method object, which is used for the local mesh settings.
  • finite_element_analysis_welsim_gui_import: generates the mesh for the scoped geometries in mesh method object.
  • finite_element_analysis_welsim_gui_import: creates a new contact pair object.
  • finite_element_analysis_welsim_gui_import: solves the finite element model.
  • finite_element_analysis_welsim_gui_import: creates a new user-defined result object.
  • finite_element_analysis_welsim_gui_import: evaluates the selected result objects.
  • finite_element_analysis_welsim_gui_import: evaluates all result objects in current project.

finite_element_analysis_welsim_toolbar_fem

Structural toolbar

The Structural toolbar contains structural analysis commands as shown in Figure below. Each icon button and its description follows:

  • finite_element_analysis_welsim_bc_fixed: creates a fixed support boundary condition object.
  • finite_element_analysis_welsim_bc_displacement: creates a displacement boundary condition object.
  • finite_element_analysis_welsim_bc_force: creates a force boundary condition object.
  • finite_element_analysis_welsim_bc_pressure: creates a pressure boundary condition object.
  • finite_element_analysis_welsim_bc_fixed_rot: creates a fixed rotation boundary condition object.
  • finite_element_analysis_welsim_bc_velocity: creates a velocity boundary condition object. It is available for the transient structural analysis.
  • finite_element_analysis_welsim_bc_acceleration: creates a acceleration boundary condition object. It is available for the transient structural analysis.
  • finite_element_analysis_welsim_dc_bodyforce: creates a body force domain condition object.
  • finite_element_analysis_welsim_dc_acceleration: creates an acceleration domain condition object.
  • finite_element_analysis_welsim_dc_gravity: creates a standard earth gravity domain condition object.
  • finite_element_analysis_welsim_dc_rotvelocity: creates a rotational velocity domain condition object.
  • finite_element_analysis_welsim_result_disp: creates a displacement result object.
  • finite_element_analysis_welsim_result_stress: creates a stress result object.
  • finite_element_analysis_welsim_result_strain: creates a strain result object.
  • finite_element_analysis_welsim_rst_velocity: creates a velocity result object. It is available for the transient structural analysis.
  • finite_element_analysis_welsim_rst_acceleration: creates a velocity result object. It is available for the transient structural analysis.
  • finite_element_analysis_welsim_rst_reaction_force: creates a rotation result object. It is available for the shell model.
  • finite_element_analysis_welsim_rst_reaction_force: creates a force reaction probe object.
  • finite_element_analysis_welsim_rst_reaction_moment: creates a moment reaction probe object. It is available for the shell model.

finite_element_analysis_welsim_toolbar_structural

Thermal toolbar

The Thermal toolbar contains thermal analysis commands as shown in Figure below. Each icon button and its description follows:

  • finite_element_analysis_welsim_bc_temperature: creates a temperature boundary condition object.
  • finite_element_analysis_welsim_bc_heatflux: creates a heat flux boundary condition object.
  • finite_element_analysis_welsim_bc_heat_convection: creates a heat convection boundary condition object.
  • finite_element_analysis_welsim_bc_radiation: creates a heat radiation boundary condition object.
  • finite_element_analysis_welsim_initial_temperature: creates an initial temperature boundary condition object. It is available for the transient thermal analysis.
  • finite_element_analysis_welsim_result_temperature: creates a temperature result object.

finite_element_analysis_welsim_toolbar_thermal

Electromagnetic toolbar

The Electromagnetic toolbar contains electric and magnetic analyses commands as shown in Figure below. Each icon button and its description follows:

  • finite_element_analysis_welsim_bc_ground: creates a ground boundary condition object.
  • finite_element_analysis_welsim_bc_voltage: creates a velocity boundary condition object.
  • finite_element_analysis_welsim_bc_em_symmetry: creates a symmetry boundary condition object.
  • finite_element_analysis_welsim_bc_zero_charge: creates a zero charge boundary condition object.
  • finite_element_analysis_welsim_bc_surface_charge: creates a surface charge density boundary condition object.
  • finite_element_analysis_welsim_bc_electricdisp: creates an electric displacement boundary condition object.
  • finite_element_analysis_welsim_bc_em_insulting: creates an insulating boundary condition object.
  • finite_element_analysis_welsim_bc_magneticpotential: creates a magnetic potential boundary condition object.
  • finite_element_analysis_welsim_bc_magneticfluxdensity: creates a magnetic flux density boundary condition object.
  • finite_element_analysis_welsim_rst_voltage: creates a voltage result object.
  • finite_element_analysis_welsim_rst_efield: creates an electric field result object.
  • finite_element_analysis_welsim_rst_dfield: creates an electric displacement result object.
  • finite_element_analysis_welsim_rst_magneticpotential: creates a vector magnetic potential result object.
  • finite_element_analysis_welsim_rst_hfield: creates a magnetic field result object.
  • finite_element_analysis_welsim_rst_bfield: creates a magnetic induction field result object.
  • finite_element_analysis_welsim_rst_emenergydensity: creates an electromagnetic energy density result object.

finite_element_analysis_welsim_toolbar_em

Tool toolbar

The Tool toolbar contains assistance commands as shown in Figure below. Each icon button and its description follows:

To be added ...
+

Help toolbar

The Help toolbar contains assistance commands as shown in Figure below. Each icon button and its description follows:

  • finite_element_analysis_welsim_gui_onlinedoc: opens the default internet web browser, and visits online documentation.
  • finite_element_analysis_welsim_gui_website: opens the default internet web browser, and visits official website.
  • finite_element_analysis_welsim_gui_licmgr: opens WELSIM license manager interface. You can activate the application with the license key or update the license here.
  • finite_element_analysis_welsim_about: displays the copyrights and version information of WELSIM application.

finite_element_analysis_welsim_toolbar_help

Graphics toolbar

The Graphics toolbar contains graphical operation commands as shown in Figure below. Each icon button and its description follows:

  • finite_element_analysis_welsim_gui_zoomall: fits the entire model in the graphics window.
  • finite_element_analysis_welsim_gui_zoomin: displays a closer view of the geometries.
  • finite_element_analysis_welsim_gui_zoomout: displays a more distant view of the geometries.
  • finite_element_analysis_welsim_gui_zoombox: displays the selected area of a model in a box that you define.
  • finite_element_analysis_welsim_view_axo: displays the 3D model in an isometric view.
  • finite_element_analysis_welsim_view_xy: displays the 3D model in an XY-plane view.
  • finite_element_analysis_welsim_view_yz: displays the 3D model in a YZ-plane view.
  • finite_element_analysis_welsim_view_xz: displays the 3D model in an XZ-plane view.
  • finite_element_analysis_welsim_select_volume: set the volume selectable.
  • finite_element_analysis_welsim_select_face: set the face selectable.
  • finite_element_analysis_welsim_select_edge: set the edge selectable.
  • finite_element_analysis_welsim_select_vertex: set the vertex selectable.

finite_element_analysis_welsim_toolbar_graphics

Working with graphics

The following lists the tips for working with WELSIM graphics:

  • You can use the ruler, presented at the bottom of the graphics window, to estimate the scale of the geometry size.
  • You can rotate the view of geometries by holding and dragging the left mouse button.
  • You can select or deselect multiple topological entities by pressing CTRL or SHIFT key.
  • You can pan the view by dragging your right mouse button or arrow keys.
  • You can zoom in/out the view by scrolling the mouse wheel or using ± and CTRL keys.
  • You can rotate the view by using the left mouse button.
  • You can open a context menu of views by right-clicking on the graphics field.

PreSelecting geometry

This section discusses the pre-selection features in the Graphics window.

Highlighting

As you hover the cursor over a geometry entity, the graphics highlights the selection and shows the location of the pointer. The pre-selection is controlled by the selection filter, and only the allowed entity types can be pre-selected and highlighted.

As shown in Figure below, the face are highlighted in green color at pre-selection mode.

finite_element_analysis_welsim_graphics_presel

Selecting geometry

This section discusses how to select and pick geometry in the Graphics window.

Picking

You can pick visible geometries by left clicking on the entities. A valid picking sets the geometry selection property for specific objects, such as boundary conditions.

You can hold the Ctrl or Shift key down to add or remove multiple selections from the current selections. A pick in the free space clears the current selection.

Selection filters

The selection filters control the user selection mode and provide an easy interface for users to pick or select the geometry entities. A pressed button in the selection filter toolbar denotes a selectable geometry type. The following describes the filters.

  • Volumes: Allows selection of the entire body. Highlighted by body surfaces in green. Depressing this filter releases the Faces, Edges, and Vertices filters.
  • Faces: Allows selection of faces. Highlighted by surfaces in green. Depressing this filter releases the Volumes filters.
  • Edges: Allows selection of edges. Highlighted by lines in green. Depressing this filter releases the Volumes filters.
  • Vertices: Allows selection of vertices. Highlighted by points in green. Depressing this filter releases the Volumes filters.

Controlling graphical view

The section describes the controlling and manipulating the graphical view with mouse and keys.

  • Zoom: Middle scrolling.
  • Pan: Right clicking, or arrow keys.
  • Rotate: Left clicking and dragging.

View annotations

Graphics window may contain these types of annotations:

  • 2D annotation: statically locates at the left top of the graphics windows. This annotation shows texts about the object type and name and color indicator for specific objects such as boundary conditions.

  • 3D annotation: dynamically locates on the geometry area, the position can be changed as the user rotates, zooms or pans the view.

\ No newline at end of file diff --git a/welsim/users/objects/index.html b/welsim/users/objects/index.html index 884f87f..c893e5d 100755 --- a/welsim/users/objects/index.html +++ b/welsim/users/objects/index.html @@ -1 +1 @@ - Objects reference - WelSim Documentation
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Objects reference

This reference provides a specification for the objects in the tree.

Answers

The Answers object customizes the solution properties and contains all result-level objects. The Properties View of the Answers object is shown in Figure below.

finite_element_analysis_welsim_obj_answers

Tree dependencies

Insertion options

Appears by default when you create a new FEM project.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Solver Method A drop-down field allows you to select a solver from the options: CG(Conjugate Gradient), BiCGStab, GMRES, GPBiCG, MUMPS, Direct, DIRECTmkl, where MUMPS, Direct, and DIRECTmkl are direct solvers, and the rest are iterative solvers. The default solver is MUMPS
Number of Iterations A number field defines the maximum number of the linear algebra solver iterations. The default is 10000
Residual Threshold A number field defines the residual threshold for the linear algebra solver. The default is 1e-7
Output Time Log A Boolean field outputs the log for each time step. The default is False
Output Iteration Log A Boolean field outputs the log each iteration step. The default is False
Generate Result Files A Boolean field generates ASCII format result file. The default is False
Output Frequency A number field determines the frequency of the result data output. The default value is 1, which outputs result data every step.

Body conditions

Body condition type objects enable you to impose the body condition onto the geometry bodies.

Application objects

Body Force, Acceleration, Earth Gravity, Rotational Velocity

Tree dependencies

  • Valid Parent Tree Object: Study.
  • Valid Child Tree Objects: None.

Insertion options

You can use any of the following methods to insert body conditions:

  • Click the item from the standard Toolbar.
  • Click the item from the Menu.
  • Right click on the Study level objects, and choose the target object from the pop-up context menu.

Object properties

The properties may vary for different body conditions. See the Setting Up Boundary Conditions section for more information about body conditions.

Boundary conditions

Boundary condition type objects enable you to impose the boundary condition onto the geometry entities, such as faces, edges, and vertices.

Application objects

Displacement, Fixed Support, Fixed Rotation, Pressure, Force, Velocity, Acceleration, Temperature, Heat Flux, Convection, Radiation, Voltage, Ground, Symmetry, Zero Charge, Surface Charge Density, Electric Displacement, Insulating, Magnetic Potential, Magnetic Flux Density

Tree dependencies

  • Valid Parent Tree Object: Study.
  • Valid Child Tree Objects: None.

Insertion options

You can use any of the following methods to insert boundary condition:

  • Click the item from the standard Toolbar.
  • Click the item from the Menu.
  • Right click on the Study level objects, and choose the target object from the pop-up context menu.

Object properties

The properties may vary for different body conditions. See the Setting up Boundary Conditions section for more information about Boundary Conditions.

Box

The Box object defines a shape that is generated by the built-in modeler. An example of Box object and properties are illustrated in Figure below.

finite_element_analysis_welsim_obj_box_prop

Tree dependencies

  • Valid Parent Tree Object: Geometry Group.
  • Valid Child Tree Objects: None.

Insertion options

Appears when you create a box shape. You can use any of the following methods to insert a Box:

  • Click the Add Box item from the standard Toolbar.
  • Click the Add Box item from the Geometry Menu.
  • Right click on the Geometry level objects, and choose the Add Box from the pop-up context menu.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Suppressed Include (False - default) or exclude (True) the geometry from the analysis
Length A vector component field to determine the length, width, and height of the box. The default value is 10
Origin A vector component field to determine the location of origin. The default vector is 0
Material A drop-down field to assign the material for the selected part. The available material candidates are defined in the Material Project
Source A read-only field indicates the shape is generated internally

Connections

The Connections object is a group-type object that may contain the connection objects between two or more parts. The currently supported children object types are Contact Pair.

Tree dependencies

Insertion options

Connections object is automatically inserted as you add a contact pair object to the tree.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Suppressed A Boolean field to include (False - Default) or exclude (True) the object in the analysis

Contact pair

This object defines a contact pair between parts.

Tree dependencies

  • Valid Parent Tree Object: Connections.
  • Valid Child Tree Objects: None.

Insertion options

You can use any of the following methods to insert contact pairs:

  • Click the item from the standard Toolbar.
  • Click the item from the FEM Menu.
  • Right click on the Connections level objects, and select Add Contact command from the pop-up context menu.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Suppressed A Boolean field to include (False - Default) or exclude (True) the object in the analysis
Master Geometry A Geometry Selection field to scope geometry entities, such as faces, edges
Target Geometry A Geometry Selection field to scope geometry entities, such as faces, edges
Contact Type A drop-down enumeration field to select a type from three options: Bonded, Frictionless, and Frictional
Formulation A drop-down enumeration field to selection contact formulation from two options: Lagrange and Augmented Lagrange. This property is only available for Frictionless or Frictional contact type
Finite Sliding A Boolean field to turn on (True) or off (False - default) the finite sliding algorithm. This property is only available for Frictionless or Frictional contact type
Normal Direction Tolerance A number field to determine the distance tolerance in the normal direction. The default value is 1e-5
Tangential Direction Tolerance A number field to determine the distance tolerance in the tangential direction. The default value is 1e-5
Normal Direction Penalty A number field to determine the penalty value in the normal direction. The default value is 1e3
Tangential Direction Penalty A number field to determine the penalty value in the tangential direction. The default value is 1e3

Cylinder

The Cylinder object defines a shape that is generated by the built-in modeler. An example of Cylinder object and properties are illustrated in Figure below.

finite_element_analysis_welsim_obj_cylinder_prop

Tree dependencies

  • Valid Parent Tree Object: Geometry Group.
  • Valid Child Tree Objects: None.

Insertion options

Appears when you create a Cylinder shape. You can use any of the following methods to insert a Cylinder:

  • Click the Add Cylinder item from the standard Toolbar.
  • Click the Add Cylinder item from the Geometry Menu.
  • Right click on the Geometry level objects, and choose the Add Cylinder from the pop-up context menu.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Suppressed Include (False - default) or exclude (True) the geometry from the analysis
Normal A vector component field to determine the direction of the cylinder. The default value is (0,0,1)
Radius A number component field to determine the radius of the cylinder base. The default value is 10
Height A number component field to determine the height of the cylinder. The default value is 30
Angle A number component field to determine the sweeping angle of the cylinder circle. The default value 360 gives a full cylinder
Origin A vector component field to determine the location of origin. The default vector is 0
Material A drop-down field to assign the material for the selected part. The available material candidates are defined in the Material Project
Source A read-only field indicates the shape is generated internally

FEM project

The FEM Project object represents an independent analysis, which contains Geometry, Mesh, Study, and Answers objects. The Connections object is not created until you add a contact pair object. An example of FEM Project and properties are illustrated in Figure [fig:ch3_guide_obj_fem_proj].

finite_element_analysis_welsim_obj_fem_project

Tree dependencies

Insertion options

Appears by default when you create a new FEM project.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Numerical Method A read-only field to indicate the Finite Element Method applied in this project
Dimension A read-only field to indicate a 3D analysis of this project
Physics Type A drop-down enumeration field for you to select the physics type. The available options are Structural, Thermal, and Electromagnetic. The default is Structural. Note that change this property may change the validation of existing objects and display of object's properties
Analysis Type A drop-down enumeration field for you to select the analysis type. Depending on the Physics Type, the available options vary. For the Structural analysis, the options are Static, Transient, and Modal. For the Thermal analysis, the options are Steady-State and Transient. For the Electromagnetic analysis, the options are ElectroStatic and MagnetoStatic
Ambient Temperature A number field to determine the environment temperature for the analysis, the default value is 22.3

Geometry group

Geometry Group object contains the geometries in the form of a part or assembly. All imported and created geometries are included in this group-level object as shown in Figure below.

finite_element_analysis_welsim_obj_geometry_group

Tree dependencies

  • Valid Parent Tree Object: FEM Project.
  • Valid Child Tree Objects: Part, Box, Cylinder, Plane, Line.

Insertion options

Appears by default when you create a new FEM project.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name

Initial temperature

Initial Temperature defines the temperature status at the beginning of the simulation for transient thermal analysis. An example of Initial Temperature and its properties are shown in Figure below.

finite_element_analysis_welsim_obj_initial_temperature

Tree dependencies

  • Valid Parent Tree Object: Study.
  • Valid Child Tree Objects: None.

Insertion options

You can use any of the following methods to insert initial temperature:

  • Click the item from the standard Toolbar.
  • Click the item from the FEM Menu.
  • Right click on the Study level objects, and choose Insert Conditions... > Initial Temperature command from the pop-up context menu.

Note

Inserting initial condition command is only applicable when the Physics Type and Analysis Type properties of FEM Project object are Thermal and Transient, respectively.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Suppressed A Boolean field to include (False - Default) or exclude (True) the object in the analysis
Scoping Method A read-only field shows All
Initial Temperature A number field to define the temperature value. The default is 22.3

Line

The Line object defines a shape that is generated by the built-in modeler. An example of Line object and properties are illustrated in Figure below.

finite_element_analysis_welsim_obj_line

Tree dependencies

  • Valid Parent Tree Object: Geometry Group.
  • Valid Child Tree Objects: None.

Insertion options

Appears when you create a line shape. You can use any of the following methods to insert a Line:

  • Click the Add Line item from the standard Toolbar.
  • Click the Add Line item from the Geometry Menu.
  • Right click on the Geometry level objects, and choose the Add Line from the pop-up context menu.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Suppressed Include (False - default) or exclude (True) the geometry from the analysis
Start Point A vector component field to determine one point of a line. The default value is 0
End Point A vector component field to determine another point of a line. The default value is (10, 10, 0)
Material A drop-down field to assign the material for the selected part. The available material candidates are defined in the Material Project
Source A read-only field indicates the shape is generated internally

Material

A Material object defines a material data using the associated properties and spreadsheet data. You can define multiple material objects in the WELSIM application. An example of a Material object and its properties and spreadsheet are shown in Figure below.

finite_element_analysis_welsim_obj_mat

Tree dependencies

Insertion options

You can use any of the following methods to insert material:

  • Click the Add Material item from the standard Toolbar.
  • Click the Add Material item from the Material Menu.
  • Right click on the Material level objects, and choose Add Material command from the pop-up context menu.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Suppressed A Boolean field to include (False - Default) or exclude (True) the object in the analysis

Spreadsheet

The Material object is able to display the Spreadsheet window, which provides a friendly user interface for defining all material properties as shown in Figure below. You can double click or right click on the Material object and select the Edit command to display the spreadsheet window.

Material project

The Material Project object holds all material definition objects.

Tree dependencies

Insertion options

Appears by default when you create a new FEM project.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name

Mesh group

Mesh Group manages all meshing features and tools for the project. An example of mesh object and properties is shown in Figure below.

finite_element_analysis_welsim_obj_mesh_group

Tree dependencies

Insertion options

Appears by default when you create a new FEM project.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Number of Nodes A read-only output field to show the number of generated nodes. The value is automatically updated as the mesh is completed
Number of Elements A read-only output field to show the number of generated elements. The value is automatically updated as the mesh is completed
Number of Tetrahedrons A read-only output field to show the number of generated tetrahedrons. The value is automatically updated as the mesh is completed
Number of Triangles A read-only output field to show the number of generated triangles. The value is automatically updated as the mesh is completed

Mesh method

In the multi-body analysis, different parts may need different mesh density due to the various sizes of geometries. Mesh Method object helps you fine tuning the mesh for the specifically scoped geometries. An example of Mesh Method object is shown in Figure below.

finite_element_analysis_welsim_obj_mesh_method

Tree dependencies

  • Valid Parent Tree Object: Mesh Group.
  • Valid Child Tree Objects: None.

Insertion options

You can use any of the following methods to insert Mesh Method:

  • Click the item from the standard Toolbar.
  • Click the item from the FEM Menu.
  • Right click on the Mesh level objects, and choose Add Mesh Method command from the pop-up context menu.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Scoping Method A read-only field indicates the scoping method
Geometry A geometry selection field to scope the geometry entities (volume/body only)
Maximum Size A number field determines the maximum size of the generated finite element
Quadratic A read-only field to show the order of the generated element. This property is determined by the Quadratic property in the global Mesh Settings object
Mesh Density A drop-down enumeration field to determine the mesh density for the scoped geometries. The options are Very Coarse, Coarse, Regular, Fine, Very Fine, and User Defined. The default is Regular. If you select User Defined, additional properties Growth Rate, Segments per Edge, and Segments per Radius are shown
Growth Rate A number field determines the change of mesh density in spatial. The default value is 0.3
Segments per Edge A number field determines the number of element segments per edge. The default value is 1. The higher value, the more dense mesh
Segments per Radius A number field determines the number of element segments per radius. The default value is 2. The higher value, the more dense mesh
Number of Nodes A read-only output field to show the number of generated nodes. The value is updated as the mesh is completed
Number of Elements A read-only output field to show the number of generated elements. The value is updated as the mesh is completed
Number of Tetrahedrons A read-only output field to show the number of generated tetrahedrons. The value is updated as the mesh is completed
Number of Triangles A read-only output field to show the number of generated triangles. The value is updated as the mesh is completed

Mesh settings

The Mesh Settings object is a global setting for the meshing operations. You change the global mesh settings by tuning the properties of this object. An example of Mesh Settings object is shown in Figure [fig:ch3_guide_obj_mesh_settings].

finite_element_analysis_welsim_obj_mesh_settings

Tree dependencies

  • Valid Parent Tree Object: Mesh Group.
  • Valid Child Tree Objects: None.

Insertion options

Appears by default when you create a new FEM project.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Maximum Size A number field to determine the maximum size of the generated finite element
Quadratic A Boolean field to determine the linear element (False) or bilinear element (True)
Mesh Density A drop-down enumeration field to determine the mesh density for the scoped geometries. The options are Very Coarse, Coarse, Regular, Fine, Very Fine, and User Defined. The default is Regular. If you select User Defined, additional properties Growth Rate, Segments per Edge, and Segments per Radius are shown
Growth Rate A number field indicate the change of mesh density in spatial. The default value is 0.3
Segments per Edge A number field indicate the element segment per edge. The default value is 1. The higher value, the more dense mesh
Segments per Radius A number field indicate the element segment per radius. The default value is 2. The higher value, the more dense mesh

Part

The Part object defines a component of the geometry that is imported from an external CAD file. An example of Part object and properties are illustrated in Figure [fig:ch3_guide_obj_part].

finite_element_analysis_welsim_obj_part

Tree dependencies

  • Valid Parent Tree Object: Geometry Group.
  • Valid Child Tree Objects: None.

Insertion options

Appears when you import geometry from external files. You can use any of the following methods to insert Part:

  • Click the item from the standard Toolbar.
  • Click the Import item from the Menu.
  • Right click on the Geometry level objects, and choose the Insert... from the pop-up context menu.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Suppressed Include (False - default) or exclude (True) the part from the analysis
Scale A number field to manipulate the size of the imported geometry. The default value is 1
Origin A vector component field to determine the location of origin. The default vector is 0
Material A drop-down field to assign the material for the selected part. The available material candidates are defined in the Material Project
Structure Type A drop-down field to define the structure type. The available options are Solid, Shell, Beam, and Truss. The default is Solid
Source A read-only field indicates the name of the imported geometry file

Plate

The Plate object defines a shape that is generated by the built-in modeler. An example of Plate object and properties are illustrated in Figure [fig:ch3_guide_obj_part].

finite_element_analysis_welsim_obj_plate_prop

Tree dependencies

  • Valid Parent Tree Object: Geometry Group.
  • Valid Child Tree Objects: None.

Insertion options

Appears when you create a plate shape. You can use any of the following methods to insert a Plate:

  • Click the Add Plate item from the standard Toolbar.
  • Click the Add Plate item from the Geometry Menu.
  • Right click on on the Geometry level objects, and choose the Add Plate from the pop-up context menu.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Suppressed Include (False - default) or exclude (True) the geometry from the analysis
Length A vector component field to determine the length vector of the plate. The default value is (10, 0, 0)
Width A vector component field to determine the width vector from the origin. The default vector is (0, 5, 0)
Material A drop-down field to assign the material for the selected part. The available material candidates are defined in the Material Project
Thickness A number field to determine the thickness of the plate. The default value is 0.01
Source A read-only field indicates the shape is generated internally

Results

The Result objects define the simulation output for displaying and analyzing the results from a solution.

Application objects

Deformation, Stress, Strain, Acceleration, Velocity, Rotation, Reaction Force, Reaction Moment, Temperature, Voltage, Electric Field, Electric Displacement, Electromagnetic Energy Density, Magnetic Potential, Magnetic Flux Density, Magnetic Field, User-Defined Result.

Tree dependencies

  • Valid Parent Tree Object: Answers.
  • Valid Child Tree Objects: None.

Insertion options

Appears by default when you start the WELSIM application.

Object properties

The properties may vary for different result types. The following lists the properties that may be shown for the most of Result objects. See the Using results section for more information.

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Suppressed Include (False - default) or exclude (True) the result object from the analysis
Result By Determines the result loading type
Set Number Determines the set number to retrieve the result data
Maximum Value The maximum result value at the current step
Minimum Value The minimum result value at the current step

Solution

The Solution object acts as a root object in the WELSIM application. Only one Solution can exist per simulation session, and one solution can contain multiple FEM projects.

Tree dependencies

  • Valid Parent Tree Object: None - highest level in the tree.
  • Valid Child Tree Objects: FEM Project.

Insertion options

Appears by default when you create a new FEM project.

Study

The Study object holds all analysis related objects such as Study Settings, Boundary Conditions, Body Conditions, and Initial Conditions. An example of Study object is shown in Figure [fig:ch3_guide_obj_study].

finite_element_analysis_welsim_obj_study

Tree dependencies

Insertion options

Appears by default when you create a new FEM project.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Number of Steps A number field to determine the total number of steps. The default value is 1. The input value must be positive
Current Step A number field to determine the current step for the successive settings. The default value is 1. The input value must be less than or equal to the Number of Steps. Note that Current Step property of Study object is adjustable, and determines the Current Step properties in other objects such as Study Settings, and Boundary Conditions
Current End Time a number field to determine the end time of the current step. The value must be larger than that of the last step

Study Settings

The Study Settings object allows you to define analysis and solving settings to customize a specific simulation model. An example of Study Settings object is shown in Figure [fig:ch3_guide_obj_study_settings].

finite_element_analysis_welsim_obj_study_settings

Tree dependencies

  • Valid Parent Tree Object: Study.
  • Valid Child Tree Objects: None.

Insertion options

Appears by default when you create a new FEM project.

Object properties

The properties of Study Settings vary for different Physics and Analysis types. The following lists the available properties according to Analysis Type:

  • Static Structural and Thermal: Current Step (Read-Only), Number of SubSteps, Relative Tolerance, Absolute Tolerance, Maximum Iterations.
  • Transient Structural and Thermal: Current Step (Read-Only), Auto-Timing, Number of SubSteps, Time Incremental (Shown as Auto Timing is False), Relative Tolerance, Absolute Tolerance, Maximum Iterations.
  • Modal Structural: Number of Modes, Lancos Tolerance, Lancos Iterations.
  • ElectroStatic and MagnetoStatic: Current Step (Read-Only), Relative Tolerance, Absolute Tolerance, Maximum Iterations.

Spreadsheet

The Study Settings object can display the Spreadsheet window, which provides a friendly user interface to review properties at all steps as shown in Figure [fig:ch3_guide_obj_study_settings]. You can double click or right click on the Study Settings object and select the Edit command to display the Spreadsheet window.

\ No newline at end of file + Objects reference - WelSim Documentation
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Objects reference

This reference provides a specification for the objects in the tree.

Answers

The Answers object customizes the solution properties and contains all result-level objects. The Properties View of the Answers object is shown in Figure below.

finite_element_analysis_welsim_obj_answers

Tree dependencies

Insertion options

Appears by default when you create a new FEM project.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Solver Method A drop-down field allows you to select a solver from the options: CG(Conjugate Gradient), BiCGStab, GMRES, GPBiCG, MUMPS, Direct, DIRECTmkl, where MUMPS, Direct, and DIRECTmkl are direct solvers, and the rest are iterative solvers. The default solver is MUMPS
Number of Iterations A number field defines the maximum number of the linear algebra solver iterations. The default is 10000
Residual Threshold A number field defines the residual threshold for the linear algebra solver. The default is 1e-7
Output Time Log A Boolean field outputs the log for each time step. The default is False
Output Iteration Log A Boolean field outputs the log each iteration step. The default is False
Generate Result Files A Boolean field generates ASCII format result file. The default is False
Output Frequency A number field determines the frequency of the result data output. The default value is 1, which outputs result data every step.

Body conditions

Body condition type objects enable you to impose the body condition onto the geometry bodies.

Application objects

Body Force, Acceleration, Earth Gravity, Rotational Velocity

Tree dependencies

  • Valid Parent Tree Object: Study.
  • Valid Child Tree Objects: None.

Insertion options

You can use any of the following methods to insert body conditions:

  • Click the item from the standard Toolbar.
  • Click the item from the Menu.
  • Right click on the Study level objects, and choose the target object from the pop-up context menu.

Object properties

The properties may vary for different body conditions. See the Setting Up Boundary Conditions section for more information about body conditions.

Boundary conditions

Boundary condition type objects enable you to impose the boundary condition onto the geometry entities, such as faces, edges, and vertices.

Application objects

Displacement, Fixed Support, Fixed Rotation, Pressure, Force, Velocity, Acceleration, Temperature, Heat Flux, Convection, Radiation, Voltage, Ground, Symmetry, Zero Charge, Surface Charge Density, Electric Displacement, Insulating, Magnetic Potential, Magnetic Flux Density

Tree dependencies

  • Valid Parent Tree Object: Study.
  • Valid Child Tree Objects: None.

Insertion options

You can use any of the following methods to insert boundary condition:

  • Click the item from the standard Toolbar.
  • Click the item from the Menu.
  • Right click on the Study level objects, and choose the target object from the pop-up context menu.

Object properties

The properties may vary for different body conditions. See the Setting up Boundary Conditions section for more information about Boundary Conditions.

Box

The Box object defines a shape that is generated by the built-in modeler. An example of Box object and properties are illustrated in Figure below.

finite_element_analysis_welsim_obj_box_prop

Tree dependencies

  • Valid Parent Tree Object: Geometry Group.
  • Valid Child Tree Objects: None.

Insertion options

Appears when you create a box shape. You can use any of the following methods to insert a Box:

  • Click the Add Box item from the standard Toolbar.
  • Click the Add Box item from the Geometry Menu.
  • Right click on the Geometry level objects, and choose the Add Box from the pop-up context menu.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Suppressed Include (False - default) or exclude (True) the geometry from the analysis
Length A vector component field to determine the length, width, and height of the box. The default value is 10
Origin A vector component field to determine the location of origin. The default vector is 0
Material A drop-down field to assign the material for the selected part. The available material candidates are defined in the Material Project
Source A read-only field indicates the shape is generated internally

Connections

The Connections object is a group-type object that may contain the connection objects between two or more parts. The currently supported children object types are Contact Pair.

Tree dependencies

Insertion options

Connections object is automatically inserted as you add a contact pair object to the tree.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Suppressed A Boolean field to include (False - Default) or exclude (True) the object in the analysis

Contact pair

This object defines a contact pair between parts.

Tree dependencies

  • Valid Parent Tree Object: Connections.
  • Valid Child Tree Objects: None.

Insertion options

You can use any of the following methods to insert contact pairs:

  • Click the item from the standard Toolbar.
  • Click the item from the FEM Menu.
  • Right click on the Connections level objects, and select Add Contact command from the pop-up context menu.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Suppressed A Boolean field to include (False - Default) or exclude (True) the object in the analysis
Master Geometry A Geometry Selection field to scope geometry entities, such as faces, edges
Target Geometry A Geometry Selection field to scope geometry entities, such as faces, edges
Contact Type A drop-down enumeration field to select a type from three options: Bonded, Frictionless, and Frictional
Formulation A drop-down enumeration field to selection contact formulation from two options: Lagrange and Augmented Lagrange. This property is only available for Frictionless or Frictional contact type
Finite Sliding A Boolean field to turn on (True) or off (False - default) the finite sliding algorithm. This property is only available for Frictionless or Frictional contact type
Normal Direction Tolerance A number field to determine the distance tolerance in the normal direction. The default value is 1e-5
Tangential Direction Tolerance A number field to determine the distance tolerance in the tangential direction. The default value is 1e-5
Normal Direction Penalty A number field to determine the penalty value in the normal direction. The default value is 1e3
Tangential Direction Penalty A number field to determine the penalty value in the tangential direction. The default value is 1e3

Cylinder

The Cylinder object defines a shape that is generated by the built-in modeler. An example of Cylinder object and properties are illustrated in Figure below.

finite_element_analysis_welsim_obj_cylinder_prop

Tree dependencies

  • Valid Parent Tree Object: Geometry Group.
  • Valid Child Tree Objects: None.

Insertion options

Appears when you create a Cylinder shape. You can use any of the following methods to insert a Cylinder:

  • Click the Add Cylinder item from the standard Toolbar.
  • Click the Add Cylinder item from the Geometry Menu.
  • Right click on the Geometry level objects, and choose the Add Cylinder from the pop-up context menu.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Suppressed Include (False - default) or exclude (True) the geometry from the analysis
Normal A vector component field to determine the direction of the cylinder. The default value is (0,0,1)
Radius A number component field to determine the radius of the cylinder base. The default value is 10
Height A number component field to determine the height of the cylinder. The default value is 30
Angle A number component field to determine the sweeping angle of the cylinder circle. The default value 360 gives a full cylinder
Origin A vector component field to determine the location of origin. The default vector is 0
Material A drop-down field to assign the material for the selected part. The available material candidates are defined in the Material Project
Source A read-only field indicates the shape is generated internally

FEM project

The FEM Project object represents an independent analysis, which contains Geometry, Mesh, Study, and Answers objects. The Connections object is not created until you add a contact pair object. An example of FEM Project and properties are illustrated in Figure [fig:ch3_guide_obj_fem_proj].

finite_element_analysis_welsim_obj_fem_project

Tree dependencies

Insertion options

Appears by default when you create a new FEM project.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Numerical Method A read-only field to indicate the Finite Element Method applied in this project
Dimension A read-only field to indicate a 3D analysis of this project
Physics Type A drop-down enumeration field for you to select the physics type. The available options are Structural, Thermal, and Electromagnetic. The default is Structural. Note that change this property may change the validation of existing objects and display of object's properties
Analysis Type A drop-down enumeration field for you to select the analysis type. Depending on the Physics Type, the available options vary. For the Structural analysis, the options are Static, Transient, and Modal. For the Thermal analysis, the options are Steady-State and Transient. For the Electromagnetic analysis, the options are ElectroStatic and MagnetoStatic
Ambient Temperature A number field to determine the environment temperature for the analysis, the default value is 22.3

Geometry group

Geometry Group object contains the geometries in the form of a part or assembly. All imported and created geometries are included in this group-level object as shown in Figure below.

finite_element_analysis_welsim_obj_geometry_group

Tree dependencies

  • Valid Parent Tree Object: FEM Project.
  • Valid Child Tree Objects: Part, Box, Cylinder, Plane, Line.

Insertion options

Appears by default when you create a new FEM project.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name

Initial temperature

Initial Temperature defines the temperature status at the beginning of the simulation for transient thermal analysis. An example of Initial Temperature and its properties are shown in Figure below.

finite_element_analysis_welsim_obj_initial_temperature

Tree dependencies

  • Valid Parent Tree Object: Study.
  • Valid Child Tree Objects: None.

Insertion options

You can use any of the following methods to insert initial temperature:

  • Click the item from the standard Toolbar.
  • Click the item from the FEM Menu.
  • Right click on the Study level objects, and choose Insert Conditions... > Initial Temperature command from the pop-up context menu.

Note

Inserting initial condition command is only applicable when the Physics Type and Analysis Type properties of FEM Project object are Thermal and Transient, respectively.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Suppressed A Boolean field to include (False - Default) or exclude (True) the object in the analysis
Scoping Method A read-only field shows All
Initial Temperature A number field to define the temperature value. The default is 22.3

Line

The Line object defines a shape that is generated by the built-in modeler. An example of Line object and properties are illustrated in Figure below.

finite_element_analysis_welsim_obj_line

Tree dependencies

  • Valid Parent Tree Object: Geometry Group.
  • Valid Child Tree Objects: None.

Insertion options

Appears when you create a line shape. You can use any of the following methods to insert a Line:

  • Click the Add Line item from the standard Toolbar.
  • Click the Add Line item from the Geometry Menu.
  • Right click on the Geometry level objects, and choose the Add Line from the pop-up context menu.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Suppressed Include (False - default) or exclude (True) the geometry from the analysis
Start Point A vector component field to determine one point of a line. The default value is 0
End Point A vector component field to determine another point of a line. The default value is (10, 10, 0)
Material A drop-down field to assign the material for the selected part. The available material candidates are defined in the Material Project
Source A read-only field indicates the shape is generated internally

Material

A Material object defines a material data using the associated properties and spreadsheet data. You can define multiple material objects in the WELSIM application. An example of a Material object and its properties and spreadsheet are shown in Figure below.

finite_element_analysis_welsim_obj_mat

Tree dependencies

Insertion options

You can use any of the following methods to insert material:

  • Click the Add Material item from the standard Toolbar.
  • Click the Add Material item from the Material Menu.
  • Right click on the Material level objects, and choose Add Material command from the pop-up context menu.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Suppressed A Boolean field to include (False - Default) or exclude (True) the object in the analysis

Spreadsheet

The Material object is able to display the Spreadsheet window, which provides a friendly user interface for defining all material properties as shown in Figure below. You can double click or right click on the Material object and select the Edit command to display the spreadsheet window.

Material project

The Material Project object holds all material definition objects.

Tree dependencies

Insertion options

Appears by default when you create a new FEM project.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name

Mesh group

Mesh Group manages all meshing features and tools for the project. An example of mesh object and properties is shown in Figure below.

finite_element_analysis_welsim_obj_mesh_group

Tree dependencies

Insertion options

Appears by default when you create a new FEM project.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Number of Nodes A read-only output field to show the number of generated nodes. The value is automatically updated as the mesh is completed
Number of Elements A read-only output field to show the number of generated elements. The value is automatically updated as the mesh is completed
Number of Tetrahedrons A read-only output field to show the number of generated tetrahedrons. The value is automatically updated as the mesh is completed
Number of Triangles A read-only output field to show the number of generated triangles. The value is automatically updated as the mesh is completed

Mesh method

In the multi-body analysis, different parts may need different mesh density due to the various sizes of geometries. Mesh Method object helps you fine tuning the mesh for the specifically scoped geometries. An example of Mesh Method object is shown in Figure below.

finite_element_analysis_welsim_obj_mesh_method

Tree dependencies

  • Valid Parent Tree Object: Mesh Group.
  • Valid Child Tree Objects: None.

Insertion options

You can use any of the following methods to insert Mesh Method:

  • Click the item from the standard Toolbar.
  • Click the item from the FEM Menu.
  • Right click on the Mesh level objects, and choose Add Mesh Method command from the pop-up context menu.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Scoping Method A read-only field indicates the scoping method
Geometry A geometry selection field to scope the geometry entities (volume/body only)
Maximum Size A number field determines the maximum size of the generated finite element
Quadratic A read-only field to show the order of the generated element. This property is determined by the Quadratic property in the global Mesh Settings object
Mesh Density A drop-down enumeration field to determine the mesh density for the scoped geometries. The options are Very Coarse, Coarse, Regular, Fine, Very Fine, and User Defined. The default is Regular. If you select User Defined, additional properties Growth Rate, Segments per Edge, and Segments per Radius are shown
Growth Rate A number field determines the change of mesh density in spatial. The default value is 0.3
Segments per Edge A number field determines the number of element segments per edge. The default value is 1. The higher value, the more dense mesh
Segments per Radius A number field determines the number of element segments per radius. The default value is 2. The higher value, the more dense mesh
Number of Nodes A read-only output field to show the number of generated nodes. The value is updated as the mesh is completed
Number of Elements A read-only output field to show the number of generated elements. The value is updated as the mesh is completed
Number of Tetrahedrons A read-only output field to show the number of generated tetrahedrons. The value is updated as the mesh is completed
Number of Triangles A read-only output field to show the number of generated triangles. The value is updated as the mesh is completed

Mesh settings

The Mesh Settings object is a global setting for the meshing operations. You change the global mesh settings by tuning the properties of this object. An example of Mesh Settings object is shown in Figure [fig:ch3_guide_obj_mesh_settings].

finite_element_analysis_welsim_obj_mesh_settings

Tree dependencies

  • Valid Parent Tree Object: Mesh Group.
  • Valid Child Tree Objects: None.

Insertion options

Appears by default when you create a new FEM project.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Maximum Size A number field to determine the maximum size of the generated finite element
Quadratic A Boolean field to determine the linear element (False) or bilinear element (True)
Mesh Density A drop-down enumeration field to determine the mesh density for the scoped geometries. The options are Very Coarse, Coarse, Regular, Fine, Very Fine, and User Defined. The default is Regular. If you select User Defined, additional properties Growth Rate, Segments per Edge, and Segments per Radius are shown
Growth Rate A number field indicate the change of mesh density in spatial. The default value is 0.3
Segments per Edge A number field indicate the element segment per edge. The default value is 1. The higher value, the more dense mesh
Segments per Radius A number field indicate the element segment per radius. The default value is 2. The higher value, the more dense mesh

Part

The Part object defines a component of the geometry that is imported from an external CAD file. An example of Part object and properties are illustrated in Figure [fig:ch3_guide_obj_part].

finite_element_analysis_welsim_obj_part

Tree dependencies

  • Valid Parent Tree Object: Geometry Group.
  • Valid Child Tree Objects: None.

Insertion options

Appears when you import geometry from external files. You can use any of the following methods to insert Part:

  • Click the item from the standard Toolbar.
  • Click the Import item from the Menu.
  • Right click on the Geometry level objects, and choose the Insert... from the pop-up context menu.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Suppressed Include (False - default) or exclude (True) the part from the analysis
Scale A number field to manipulate the size of the imported geometry. The default value is 1
Origin A vector component field to determine the location of origin. The default vector is 0
Material A drop-down field to assign the material for the selected part. The available material candidates are defined in the Material Project
Structure Type A drop-down field to define the structure type. The available options are Solid, Shell, Beam, and Truss. The default is Solid
Source A read-only field indicates the name of the imported geometry file

Plate

The Plate object defines a shape that is generated by the built-in modeler. An example of Plate object and properties are illustrated in Figure [fig:ch3_guide_obj_part].

finite_element_analysis_welsim_obj_plate_prop

Tree dependencies

  • Valid Parent Tree Object: Geometry Group.
  • Valid Child Tree Objects: None.

Insertion options

Appears when you create a plate shape. You can use any of the following methods to insert a Plate:

  • Click the Add Plate item from the standard Toolbar.
  • Click the Add Plate item from the Geometry Menu.
  • Right click on on the Geometry level objects, and choose the Add Plate from the pop-up context menu.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Suppressed Include (False - default) or exclude (True) the geometry from the analysis
Length A vector component field to determine the length vector of the plate. The default value is (10, 0, 0)
Width A vector component field to determine the width vector from the origin. The default vector is (0, 5, 0)
Material A drop-down field to assign the material for the selected part. The available material candidates are defined in the Material Project
Thickness A number field to determine the thickness of the plate. The default value is 0.01
Source A read-only field indicates the shape is generated internally

Results

The Result objects define the simulation output for displaying and analyzing the results from a solution.

Application objects

Deformation, Stress, Strain, Acceleration, Velocity, Rotation, Reaction Force, Reaction Moment, Temperature, Voltage, Electric Field, Electric Displacement, Electromagnetic Energy Density, Magnetic Potential, Magnetic Flux Density, Magnetic Field, User-Defined Result.

Tree dependencies

  • Valid Parent Tree Object: Answers.
  • Valid Child Tree Objects: None.

Insertion options

Appears by default when you start the WELSIM application.

Object properties

The properties may vary for different result types. The following lists the properties that may be shown for the most of Result objects. See the Using results section for more information.

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Suppressed Include (False - default) or exclude (True) the result object from the analysis
Result By Determines the result loading type
Set Number Determines the set number to retrieve the result data
Maximum Value The maximum result value at the current step
Minimum Value The minimum result value at the current step

Solution

The Solution object acts as a root object in the WELSIM application. Only one Solution can exist per simulation session, and one solution can contain multiple FEM projects.

Tree dependencies

  • Valid Parent Tree Object: None - highest level in the tree.
  • Valid Child Tree Objects: FEM Project.

Insertion options

Appears by default when you create a new FEM project.

Study

The Study object holds all analysis related objects such as Study Settings, Boundary Conditions, Body Conditions, and Initial Conditions. An example of Study object is shown in Figure [fig:ch3_guide_obj_study].

finite_element_analysis_welsim_obj_study

Tree dependencies

Insertion options

Appears by default when you create a new FEM project.

Object properties

The Properties View for this object include the following:

Property Name Description
ID A read-only field denotes the ID of this object
Class Label A read-only field denotes the class name
Number of Steps A number field to determine the total number of steps. The default value is 1. The input value must be positive
Current Step A number field to determine the current step for the successive settings. The default value is 1. The input value must be less than or equal to the Number of Steps. Note that Current Step property of Study object is adjustable, and determines the Current Step properties in other objects such as Study Settings, and Boundary Conditions
Current End Time a number field to determine the end time of the current step. The value must be larger than that of the last step

Study Settings

The Study Settings object allows you to define analysis and solving settings to customize a specific simulation model. An example of Study Settings object is shown in Figure [fig:ch3_guide_obj_study_settings].

finite_element_analysis_welsim_obj_study_settings

Tree dependencies

  • Valid Parent Tree Object: Study.
  • Valid Child Tree Objects: None.

Insertion options

Appears by default when you create a new FEM project.

Object properties

The properties of Study Settings vary for different Physics and Analysis types. The following lists the available properties according to Analysis Type:

  • Static Structural and Thermal: Current Step (Read-Only), Number of SubSteps, Relative Tolerance, Absolute Tolerance, Maximum Iterations.
  • Transient Structural and Thermal: Current Step (Read-Only), Auto-Timing, Number of SubSteps, Time Incremental (Shown as Auto Timing is False), Relative Tolerance, Absolute Tolerance, Maximum Iterations.
  • Modal Structural: Number of Modes, Lancos Tolerance, Lancos Iterations.
  • ElectroStatic and MagnetoStatic: Current Step (Read-Only), Relative Tolerance, Absolute Tolerance, Maximum Iterations.

Spreadsheet

The Study Settings object can display the Spreadsheet window, which provides a friendly user interface to review properties at all steps as shown in Figure [fig:ch3_guide_obj_study_settings]. You can double click or right click on the Study Settings object and select the Edit command to display the Spreadsheet window.

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This chapter is the user guide for working with WELSIM application, which is used to perform various types of structural, thermal, and electromagnetic analyses. The entire simulation process is tied together by a unified graphical user interface.

Overview

WELSIM application enables you to investigate design alternative efficiently. You can modify any aspect of analysis or vary parameters, then update the project to the see results of the change in the modeling. A typical modeling process is composed of defining the model, and boundary conditions applied to it, computing for the simulation's response to the conditions, then evaluating the solutions with a variety of tools.

The WELSIM software application has a tree structure that consists of “objects” that enable you to define simulation conditions. By clicking the objects, you activate the associated properties in the property window, and you can use the corresponding command and tools to conduct the simulation study. The following sections describe in details to use the WELSIM to set up and implement simulation studies.

\ No newline at end of file + Overview - WelSim Documentation
Skip to content

This chapter is the user guide for working with WELSIM application, which is used to perform various types of structural, thermal, and electromagnetic analyses. The entire simulation process is tied together by a unified graphical user interface.

Overview

WELSIM application enables you to investigate design alternative efficiently. You can modify any aspect of analysis or vary parameters, then update the project to the see results of the change in the modeling. A typical modeling process is composed of defining the model, and boundary conditions applied to it, computing for the simulation's response to the conditions, then evaluating the solutions with a variety of tools.

The WELSIM software application has a tree structure that consists of “objects” that enable you to define simulation conditions. By clicking the objects, you activate the associated properties in the property window, and you can use the corresponding command and tools to conduct the simulation study. The following sections describe in details to use the WELSIM to set up and implement simulation studies.

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Using results

This section describes the details of a result. The help for Results is classified by the physics and analysis types.

Introduction to the results

You can generate results to understand the behaviors of the analyzed model. The advantages of using results in WELSIM application are:

  • Illustrates result contour over the simulation domain for various solution quantities, such as stress, deformation, temperature, voltage, etc.
  • Probe results to calculate the abstract engineering quantities, such as reaction forces.
  • Displays the minimum and maximum values over time in Chart and Tabular Data windows.
  • Allows customized results using User-Defined Results.
  • Export result data to external files.

Result application

Applying results can be achieved by

  • Right-click on the Answer object or its children objects in the tree, select Insert Results from the pop-up context menu and then choose from the result options.
  • Click the result object from the Menu or Toolbar.

Result definitions

This section describes the fundamental features in result definitions.

Result controller

In the multi-step or transient analysis, the solution contains result data at various steps. Result By property provides a controller to select the desired step data to display. You can determine to show the result by Set Number or Time/Frequency. The default is by Set Number. Additional properties such as Set Number, Time, or Frequency shows up as you define the Result By property.

Clear generated data

You can clear results data from the database using the Clear Result command from the Toolbar, Menu, or the right-click context menu on a result object.

You also can clear entire solution data from the database using the Clear Calculated Data command from the Toolbar, Menu, or the right-click context menu on an Answers object. These two commands from the context menu are shown in Figure [fig:ch3_guide_rst_clear_data].

finite_element_analysis_welsim_rst_clear_result_menu finite_element_analysis_welsim_rst_clear_solution_menu

Display controller

You can select the Graphics tab on the result Properties View pane. As shown in Figure [fig:ch3_guide_rst_display_prop], the following properties are available to adjust the contour display:

  • Line Width: determines the line width of the mesh frame.
  • Show Mesh: Show (True) or hide (False - default) the mesh frames on the result contour.
  • Show Backface: Show (True - default) result contour on the back face.
  • Show Deformation: Show (True) or ignore (False - default) the structural deformation on the result contour. This option is only valid for the structural analysis.
  • Deformation Scale: Determines the scale of the deformation, the default value 1 denotes the true deformation. This option is only valid as Show Deformation is True.

finite_element_analysis_welsim_rst_display_prop

Structural results

The following structural results are described in this section.

Deformation

Physical deformation of the modeling geometries can be calculated and plotted in the form of contour. This result is available for all structural analysis. The following gives the properties of result object:

  • Type: The available options are Deformation X, Deformation Y, Deformation Z, and Total Deformation. The default is Total Deformation, which essentially shows the magnitude of the deformation vector.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Stress

The stress quantities provide mechanical insights to the given model and material of a part or an assembly under a specific structural loading environment. A general 3D stress state contains three normal and three shear stresses. The stress quantities in WELSIM application are the nodal values and available for all structural analysis. The equivalent stress (also called von-Mises stress) is related to the principal stresses by the equation:

\[ \sigma_{VM}=\left[\dfrac{(\sigma_{11}-\sigma_{22})^{2}+(\sigma_{22}-\sigma_{33})^{2}+(\sigma_{33}-\sigma_{11})^{2}+6(\sigma_{12}^{2}+\sigma_{23}^{2}+\sigma_{31}^{2})}{2}\right]^{1/2} \]

The following gives the properties of result object:

  • Type: The available options are Normal Stress X, Normal Stress Y, Normal Stress Z, Shear Stress XY, Shear Stress YZ, Shear Stress XZ, and von-Mises Stress. The default is von-Mises Stress.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Strain

The strain quantities provide deformation insights to the given model and material of a part or an assembly under a specific structural loading environment. This result is available for all structural analysis.

The available properties for strain result are:

  • Type: The available options are Normal Strain X, Normal Strain Y, Normal Strain Z, Shear Strain XY, Shear Strain YZ, and Shear Strain XZ. The default is Normal Strain X.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Acceleration

The acceleration quantities demonstrate the acceleration of the given model and material of a part or an assembly under a specific structural loading environment. This result is available for transient structural analysis.

The available properties for acceleration result are:

  • Type: The available options are Acceleration X, Acceleration Y, Acceleration Z, and Total Acceleration. The default is Total Acceleration.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Note

Acceleration result is only available for the transient structural analysis.

Velocity

The velocity quantities demonstrate the velocity of the given model and material of a part or an assembly under a specific structural loading environment. This result is available for transient structural analysis.

The available properties for velocity result are:

  • Type: The available options are Velocity X, Velocity Y, Velocity Z, and Total Velocity. The default is Total Velocity.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Note

Velocity result is only available for the transient structural analysis.

Rotation

The rotation quantities demonstrate the rotation of the given model and material of a part or an assembly under a specific structural loading environment. This result is available for only shell structure.

The available properties for rotation result are:

  • Type: The available options are Rotation XY, Rotation YZ, Rotation XZ, and Total Rotation. The default is Total Rotation.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Note

Rotation result is only available for the shell structural analysis.

Reaction Force Probe

The reaction force provides an insight to abstract reaction force of the given model and material of a part or an assembly under a specific structural loading environment. This result is available for structural analysis.

The available properties for a reaction force probe are:

  • Type: The available options are Reaction Force X, Reaction Force Y, Reaction Force Z, and Total Reaction Force. The default is Total Reaction Force.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Note

This probe result does not show contour on the geometry. The primary output data is the Maximum Value and Minimum Value displayed in the Properties View window.

Reaction Moment Probe

The reaction moment provides an insight to abstract quantities of the given model and material of a part or an assembly under a specific structural loading environment. This result is available for only shell structure.

The available properties for reaction moment probe are:

  • Type: The available options are Reaction Moment X, Reaction Moment Y, Reaction Moment Z, and Total Reaction Moment. The default is Total Reaction Moment.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Note

Reaction moment probe result is only available for the shell structural analysis.

Reaction moment probe result does not show contour on the geometry. The primary output data is the Maximum Value and Minimum Value displayed in the Properties View window.

Thermal results

The following thermal results are described in this section:

Temperature

The temperature, a scalar quantity, provides an insight to the temperature distribution throughout the structure. Temperature results can be displayed as a contour plot.

The available properties for temperature are:

  • Type: The sole available option is Temperature. This field is read-only.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Electric results

Voltage

The voltage, a scalar quantity, provides an insight to the electric potential distribution throughout the conductor bodies.

The available properties for voltage are:

  • Type: The sole available option is Voltage. This is a read-only field.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Electric Field

The electric field, a vector component quantity, provides an insight to the electric field intensity distribution throughout the bodies.

The available properties for Electric Field are:

  • Type: The available options are Electric Field X, Electric Field Y, Electric Field Z, Total Electric Field. The default Total Electric Field option displays the total magnitude of the vectors as a contour.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Current Density

Electric Displacement

The electric displacement, a vector component quantity, provides an insight to the electric displacement intensity distribution throughout the bodies. This quantity has the constitutive relation with Electric Field as shown in equation below:

\[ D=\epsilon E \]

where D is the electric displacement, E is the electric field, and \(\epsilon\) is the electric permittivity. The available properties for Electric Displacement are:

  • Type: The available options are Electric Displacement X, Electric Displacement Y, Electric Displacement Z, Total Electric Displacement. The default Total Electric Displacement option displays the total magnitude of the vectors as a contour.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Energy Density

The energy density, a scalar quantity, provides an insight to the electromagnetic energy throughout the simulation bodies.

The available properties for energy density are:

  • Type: The sole available option is Energy Density. This is a read-only field.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Magnetic results

The magnetostatic analysis provides fundamental result quantities for you to investigate the field.

Electric Potential

Magnetic Potential

Magnetic Potential vector components are computed throughout the simulation domain. The available properties for Magnetic Potential are:

  • Type: The available options are Magnetic Potential X, Magnetic Potential Y, Magnetic Potential Z, Total Magnetic Potential. The default Total Magnetic Potential option displays the total magnitude of the vectors as a contour.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Magnetic Flux Density

Magnetic Flux Density vector components are computed throughout the simulation domain. The available properties for Magnetic Flux Density are:

  • Type: The available options are Magnetic Flux Density X, Magnetic Flux Density Y, Magnetic Flux Density Z, Total Magnetic Flux Density. The default Total Magnetic Flux Density option displays the total magnitude of the vectors as a contour.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Magnetic Field

Magnetic Field vector components are computed throughout the simulation domain. The available properties for Magnetic Field are:

  • Type: The available options are Magnetic Field X, Magnetic Field Y, Magnetic Field Z, Total Magnetic Field. The default Total Magnetic Field option displays the total magnitude of the vectors as a contour.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

User-Defined Results

This section describes the use of the User-Defined Result feature in WELSIM application. The user-defined result provides you with more flexible result evaluation methods. In addition to the system-provided result types, the User-Defined Result allows you to plot more broad kinds of results with the given expression.

Like other result types that display contours, chart, and data, the User-Defined results:

  • Need you to input a supported Expression to retrieve the result data.
  • Need you to specify a set, time, or frequency in the Properties View window.
  • Display Maximum and Minimum values in the Properties View window.
  • Display Maximum and Minimum data over time in Tabular Data and Chart windows.

Applying a User-Defined Result can be done using one of the following methods:

  • Select the User-Defined Result item from the Menu of FEM.
  • Select the User-Defined Result button from the standard Toolbar.
  • Right-click the Solution or Result object, and select the User-Defined Result item.

An example of User Defined Result properties view is shown in Figure [fig:ch3_guide_user_defined_rst_prop].

finite_element_analysis_welsim_rst_user_defined

User Defined Result expressions

The property Expression accepts the capital string values, and the lower case letters are converted automatically to the capital letters. The following lists the supported Expressions used in the WELSIM application:

Expression Result description
UVW Total deformation for structural analysis
U Directional deformation X for structural analysis
V Directional deformation Y for structural analysis
W Directional deformation Z for structural analysis
SIGVM von-Mises stress for the structural analysis
SIG00 Normal stress X for the structural analysis
SIG11 Normal stress Y for the structural analysis
SIG22 Normal stress Z for the structural analysis
SIG01 Shear stress XY for the structural analysis
SIG12 Shear stress YZ for the structural analysis
SIG02 Shear stress XZ for the structural analysis
EPS00 Normal strain X for the structural analysis
EPS11 Normal strain Y for the structural analysis
EPS22 Normal strain Z for the structural analysis
EPS01 Shear strain XY for the structural analysis
EPS12 Shear strain YZ for the structural analysis
EPS02 Shear strain XZ for the structural analysis
RFT Total reaction force for the structural analysis
RFX Directional reaction force X for the structural analysis
RFY Directional reaction force Y for the structural analysis
RFZ Directional reaction force Z for the structural analysis
RMT Total reaction moment for the shell structural analysis
RMX Directional reaction moment X for the shell structural analysis
RMY Directional reaction moment Y for the shell structural analysis
RMZ Directional reaction moment Z for the shell structural analysis
ENEEL Total energy for the structural analysis
V123 Total velocity for the transient structural analysis
V1 Directional velocity X for the transient structural analysis
V2 Directional velocity Y for the transient structural analysis
V3 Directional velocity Z for the transient structural analysis
A123 Total acceleration for the transient structural analysis
A1 Directional acceleration X for the transient structural analysis
A2 Directional acceleration Y for the transient structural analysis
A3 Directional acceleration Z for the transient structural analysis
ROTT Total rotation for shell structural analysis
ROTX Directional rotation X for shell structural analysis
ROTY Directional rotation Y for shell structural analysis
ROTZ Directional rotation Z for shell structural analysis
TEMP Temperature for thermal analysis
EM_U Voltage for electromagnetic analysis
EM_ET Total electric field intensity for electromagnetic analysis
EM_EX Directional electric field intensity X for electromagnetic analysis
EM_EY Directional electric field intensity Y for electromagnetic analysis
EM_EZ Directional electric field intensity Z for electromagnetic analysis
EM_DT Total electric displacement for electromagnetic analysis
EM_DX Directional electric displacement X for electromagnetic analysis
EM_DY Directional electric displacement Y for electromagnetic analysis
EM_DZ Directional electric displacement Z for electromagnetic analysis
EM_EN Energy density for electromagnetic analysis
EM_HT Total magnetic field intensity for electromagnetic analysis
EM_HX Directional magnetic field intensity X for electromagnetic analysis
EM_HY Directional magnetic field intensity Y for electromagnetic analysis
EM_HZ Directional magnetic field intensity Z for electromagnetic analysis
EM_BT Total magnetic flux density for electromagnetic analysis
EM_BX Directional magnetic flux density X for electromagnetic analysis
EM_BY Directional magnetic flux density Y for electromagnetic analysis
EM_BZ Directional magnetic flux density Z for electromagnetic analysis
EM_AT Magnitude of a magnetic potential vector for electromagnetic analysis
EM_A_x Magnetic potential vector component X for electromagnetic analysis
EM_A_y Magnetic potential vector component Y for electromagnetic analysis
EM_A_z Magnetic potential vector component Z for electromagnetic analysis
WelSim/docs

Using results

This section describes the details of a result. The help for Results is classified by the physics and analysis types.

Introduction to the results

You can generate results to understand the behaviors of the analyzed model. The advantages of using results in WELSIM application are:

  • Illustrates result contour over the simulation domain for various solution quantities, such as stress, deformation, temperature, voltage, etc.
  • Probe results to calculate the abstract engineering quantities, such as reaction forces.
  • Displays the minimum and maximum values over time in Chart and Tabular Data windows.
  • Allows customized results using User-Defined Results.
  • Export result data to external files.

Result application

Applying results can be achieved by

  • Right-click on the Answer object or its children objects in the tree, select Insert Results from the pop-up context menu and then choose from the result options.
  • Click the result object from the Menu or Toolbar.

Result definitions

This section describes the fundamental features in result definitions.

Result controller

In the multi-step or transient analysis, the solution contains result data at various steps. Result By property provides a controller to select the desired step data to display. You can determine to show the result by Set Number or Time/Frequency. The default is by Set Number. Additional properties such as Set Number, Time, or Frequency shows up as you define the Result By property.

Clear generated data

You can clear results data from the database using the Clear Result command from the Toolbar, Menu, or the right-click context menu on a result object.

You also can clear entire solution data from the database using the Clear Calculated Data command from the Toolbar, Menu, or the right-click context menu on an Answers object. These two commands from the context menu are shown in Figure [fig:ch3_guide_rst_clear_data].

finite_element_analysis_welsim_rst_clear_result_menu finite_element_analysis_welsim_rst_clear_solution_menu

Display controller

You can select the Graphics tab on the result Properties View pane. As shown in Figure [fig:ch3_guide_rst_display_prop], the following properties are available to adjust the contour display:

  • Line Width: determines the line width of the mesh frame.
  • Show Mesh: Show (True) or hide (False - default) the mesh frames on the result contour.
  • Show Backface: Show (True - default) result contour on the back face.
  • Show Deformation: Show (True) or ignore (False - default) the structural deformation on the result contour. This option is only valid for the structural analysis.
  • Deformation Scale: Determines the scale of the deformation, the default value 1 denotes the true deformation. This option is only valid as Show Deformation is True.

finite_element_analysis_welsim_rst_display_prop

Structural results

The following structural results are described in this section.

Deformation

Physical deformation of the modeling geometries can be calculated and plotted in the form of contour. This result is available for all structural analysis. The following gives the properties of result object:

  • Type: The available options are Deformation X, Deformation Y, Deformation Z, and Total Deformation. The default is Total Deformation, which essentially shows the magnitude of the deformation vector.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Stress

The stress quantities provide mechanical insights to the given model and material of a part or an assembly under a specific structural loading environment. A general 3D stress state contains three normal and three shear stresses. The stress quantities in WELSIM application are the nodal values and available for all structural analysis. The equivalent stress (also called von-Mises stress) is related to the principal stresses by the equation:

\[ \sigma_{VM}=\left[\dfrac{(\sigma_{11}-\sigma_{22})^{2}+(\sigma_{22}-\sigma_{33})^{2}+(\sigma_{33}-\sigma_{11})^{2}+6(\sigma_{12}^{2}+\sigma_{23}^{2}+\sigma_{31}^{2})}{2}\right]^{1/2} \]

The following gives the properties of result object:

  • Type: The available options are Normal Stress X, Normal Stress Y, Normal Stress Z, Shear Stress XY, Shear Stress YZ, Shear Stress XZ, and von-Mises Stress. The default is von-Mises Stress.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Strain

The strain quantities provide deformation insights to the given model and material of a part or an assembly under a specific structural loading environment. This result is available for all structural analysis.

The available properties for strain result are:

  • Type: The available options are Normal Strain X, Normal Strain Y, Normal Strain Z, Shear Strain XY, Shear Strain YZ, and Shear Strain XZ. The default is Normal Strain X.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Acceleration

The acceleration quantities demonstrate the acceleration of the given model and material of a part or an assembly under a specific structural loading environment. This result is available for transient structural analysis.

The available properties for acceleration result are:

  • Type: The available options are Acceleration X, Acceleration Y, Acceleration Z, and Total Acceleration. The default is Total Acceleration.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Note

Acceleration result is only available for the transient structural analysis.

Velocity

The velocity quantities demonstrate the velocity of the given model and material of a part or an assembly under a specific structural loading environment. This result is available for transient structural analysis.

The available properties for velocity result are:

  • Type: The available options are Velocity X, Velocity Y, Velocity Z, and Total Velocity. The default is Total Velocity.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Note

Velocity result is only available for the transient structural analysis.

Rotation

The rotation quantities demonstrate the rotation of the given model and material of a part or an assembly under a specific structural loading environment. This result is available for only shell structure.

The available properties for rotation result are:

  • Type: The available options are Rotation XY, Rotation YZ, Rotation XZ, and Total Rotation. The default is Total Rotation.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Note

Rotation result is only available for the shell structural analysis.

Reaction Force Probe

The reaction force provides an insight to abstract reaction force of the given model and material of a part or an assembly under a specific structural loading environment. This result is available for structural analysis.

The available properties for a reaction force probe are:

  • Type: The available options are Reaction Force X, Reaction Force Y, Reaction Force Z, and Total Reaction Force. The default is Total Reaction Force.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Note

This probe result does not show contour on the geometry. The primary output data is the Maximum Value and Minimum Value displayed in the Properties View window.

Reaction Moment Probe

The reaction moment provides an insight to abstract quantities of the given model and material of a part or an assembly under a specific structural loading environment. This result is available for only shell structure.

The available properties for reaction moment probe are:

  • Type: The available options are Reaction Moment X, Reaction Moment Y, Reaction Moment Z, and Total Reaction Moment. The default is Total Reaction Moment.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Note

Reaction moment probe result is only available for the shell structural analysis.

Reaction moment probe result does not show contour on the geometry. The primary output data is the Maximum Value and Minimum Value displayed in the Properties View window.

Thermal results

The following thermal results are described in this section:

Temperature

The temperature, a scalar quantity, provides an insight to the temperature distribution throughout the structure. Temperature results can be displayed as a contour plot.

The available properties for temperature are:

  • Type: The sole available option is Temperature. This field is read-only.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Electric results

Voltage

The voltage, a scalar quantity, provides an insight to the electric potential distribution throughout the conductor bodies.

The available properties for voltage are:

  • Type: The sole available option is Voltage. This is a read-only field.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Electric Field

The electric field, a vector component quantity, provides an insight to the electric field intensity distribution throughout the bodies.

The available properties for Electric Field are:

  • Type: The available options are Electric Field X, Electric Field Y, Electric Field Z, Total Electric Field. The default Total Electric Field option displays the total magnitude of the vectors as a contour.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Current Density

Electric Displacement

The electric displacement, a vector component quantity, provides an insight to the electric displacement intensity distribution throughout the bodies. This quantity has the constitutive relation with Electric Field as shown in equation below:

\[ D=\epsilon E \]

where D is the electric displacement, E is the electric field, and \(\epsilon\) is the electric permittivity. The available properties for Electric Displacement are:

  • Type: The available options are Electric Displacement X, Electric Displacement Y, Electric Displacement Z, Total Electric Displacement. The default Total Electric Displacement option displays the total magnitude of the vectors as a contour.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Energy Density

The energy density, a scalar quantity, provides an insight to the electromagnetic energy throughout the simulation bodies.

The available properties for energy density are:

  • Type: The sole available option is Energy Density. This is a read-only field.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Magnetic results

The magnetostatic analysis provides fundamental result quantities for you to investigate the field.

Electric Potential

Magnetic Potential

Magnetic Potential vector components are computed throughout the simulation domain. The available properties for Magnetic Potential are:

  • Type: The available options are Magnetic Potential X, Magnetic Potential Y, Magnetic Potential Z, Total Magnetic Potential. The default Total Magnetic Potential option displays the total magnitude of the vectors as a contour.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Magnetic Flux Density

Magnetic Flux Density vector components are computed throughout the simulation domain. The available properties for Magnetic Flux Density are:

  • Type: The available options are Magnetic Flux Density X, Magnetic Flux Density Y, Magnetic Flux Density Z, Total Magnetic Flux Density. The default Total Magnetic Flux Density option displays the total magnitude of the vectors as a contour.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

Magnetic Field

Magnetic Field vector components are computed throughout the simulation domain. The available properties for Magnetic Field are:

  • Type: The available options are Magnetic Field X, Magnetic Field Y, Magnetic Field Z, Total Magnetic Field. The default Total Magnetic Field option displays the total magnitude of the vectors as a contour.
  • Result By: Determines the result loading type.
  • Set Number: Determines the set number to retrieve the result data.
  • Maximum Value: The maximum result value at the current step.
  • Minimum Value: The minimum result value at the current step.
  • Suppressed: Include (False - default) or exclude (True) the result object.

User-Defined Results

This section describes the use of the User-Defined Result feature in WELSIM application. The user-defined result provides you with more flexible result evaluation methods. In addition to the system-provided result types, the User-Defined Result allows you to plot more broad kinds of results with the given expression.

Like other result types that display contours, chart, and data, the User-Defined results:

  • Need you to input a supported Expression to retrieve the result data.
  • Need you to specify a set, time, or frequency in the Properties View window.
  • Display Maximum and Minimum values in the Properties View window.
  • Display Maximum and Minimum data over time in Tabular Data and Chart windows.

Applying a User-Defined Result can be done using one of the following methods:

  • Select the User-Defined Result item from the Menu of FEM.
  • Select the User-Defined Result button from the standard Toolbar.
  • Right-click the Solution or Result object, and select the User-Defined Result item.

An example of User Defined Result properties view is shown in Figure [fig:ch3_guide_user_defined_rst_prop].

finite_element_analysis_welsim_rst_user_defined

User Defined Result expressions

The property Expression accepts the capital string values, and the lower case letters are converted automatically to the capital letters. The following lists the supported Expressions used in the WELSIM application:

Expression Result description
UVW Total deformation for structural analysis
U Directional deformation X for structural analysis
V Directional deformation Y for structural analysis
W Directional deformation Z for structural analysis
SIGVM von-Mises stress for the structural analysis
SIG00 Normal stress X for the structural analysis
SIG11 Normal stress Y for the structural analysis
SIG22 Normal stress Z for the structural analysis
SIG01 Shear stress XY for the structural analysis
SIG12 Shear stress YZ for the structural analysis
SIG02 Shear stress XZ for the structural analysis
EPS00 Normal strain X for the structural analysis
EPS11 Normal strain Y for the structural analysis
EPS22 Normal strain Z for the structural analysis
EPS01 Shear strain XY for the structural analysis
EPS12 Shear strain YZ for the structural analysis
EPS02 Shear strain XZ for the structural analysis
RFT Total reaction force for the structural analysis
RFX Directional reaction force X for the structural analysis
RFY Directional reaction force Y for the structural analysis
RFZ Directional reaction force Z for the structural analysis
RMT Total reaction moment for the shell structural analysis
RMX Directional reaction moment X for the shell structural analysis
RMY Directional reaction moment Y for the shell structural analysis
RMZ Directional reaction moment Z for the shell structural analysis
ENEEL Total energy for the structural analysis
V123 Total velocity for the transient structural analysis
V1 Directional velocity X for the transient structural analysis
V2 Directional velocity Y for the transient structural analysis
V3 Directional velocity Z for the transient structural analysis
A123 Total acceleration for the transient structural analysis
A1 Directional acceleration X for the transient structural analysis
A2 Directional acceleration Y for the transient structural analysis
A3 Directional acceleration Z for the transient structural analysis
ROTT Total rotation for shell structural analysis
ROTX Directional rotation X for shell structural analysis
ROTY Directional rotation Y for shell structural analysis
ROTZ Directional rotation Z for shell structural analysis
TEMP Temperature for thermal analysis
EM_U Voltage for electromagnetic analysis
EM_ET Total electric field intensity for electromagnetic analysis
EM_EX Directional electric field intensity X for electromagnetic analysis
EM_EY Directional electric field intensity Y for electromagnetic analysis
EM_EZ Directional electric field intensity Z for electromagnetic analysis
EM_DT Total electric displacement for electromagnetic analysis
EM_DX Directional electric displacement X for electromagnetic analysis
EM_DY Directional electric displacement Y for electromagnetic analysis
EM_DZ Directional electric displacement Z for electromagnetic analysis
EM_EN Energy density for electromagnetic analysis
EM_HT Total magnetic field intensity for electromagnetic analysis
EM_HX Directional magnetic field intensity X for electromagnetic analysis
EM_HY Directional magnetic field intensity Y for electromagnetic analysis
EM_HZ Directional magnetic field intensity Z for electromagnetic analysis
EM_BT Total magnetic flux density for electromagnetic analysis
EM_BX Directional magnetic flux density X for electromagnetic analysis
EM_BY Directional magnetic flux density Y for electromagnetic analysis
EM_BZ Directional magnetic flux density Z for electromagnetic analysis
EM_AT Magnitude of a magnetic potential vector for electromagnetic analysis
EM_A_x Magnetic potential vector component X for electromagnetic analysis
EM_A_y Magnetic potential vector component Y for electromagnetic analysis
EM_A_z Magnetic potential vector component Z for electromagnetic analysis

Result tools

Result legend

The result legend feature helps you display the result range and contour colors in a specific design. The legend component is shown in the left of the Graphics window. As shown in Figure below, the legend displays the following information:

  • Project Name
  • Result Object Name
  • Result Type
  • Unit
  • Time
  • Current Date and Time

finite_element_analysis_welsim_rst_legend

The Legend style can be adjusted by right-clicking on the Legend field. As shown in Figure below, the Context Menu contains items:

  • Banded: Displays the contour in banded colors. It is mutually exclusive to the Smooth option. The default is toggled Off.
  • Smooth: Displays the contour in smooth colors. It is mutually exclusive to the Banded option. The default is toggled On.
  • User-Defined Max/Min: Allows you to manually set the Minimum and Maximum values on the result legend, the contour on the bodies can be updated accordingly. Once this option is toggled, a popped-up dialog lets you input the specific minimum and maximum values. You can revert the manual minimum and maximum values by toggling off this option. The min/max input dialog is shown below.
  • Logarithmic Scale: Set legend markers in a logarithmic scale order. The default is toggled Off.
  • Scientific Notation: Use the scientific notation. The default is On.
  • Digits: Determines the number of digits after the decimal symbol, the range is between 1 and 7. The default value is 3.
  • Labels: Determines the number of legend markers, the range is between 6 and 14. The default value is 11.
  • Color Scheme: Provides you four color options: Rainbow, Reverse Rainbow, Grayscale, Reverse Grayscale. The default is Rainbow.
  • Reset All: Resets all settings to the default.

finite_element_analysis_welsim_rst_legend_context_menu

finite_element_analysis_welsim_rst_legend_minmax_input

Note

For the option of user-defined max/min settings, the input maximum value must be greater than the minimum value.

Exporting results

The data associated with result objects can be exported in ASCII (.txt or .dat) file format by right-clicking on the desired result object and selecting the Export Result option. Once executed, you are asked to define a filename and select the directory to save the file.

Note

The desired result object must have been successfully evaluated before exporting the result data.

\ No newline at end of file +### Probe results -->

Result tools

Result legend

The result legend feature helps you display the result range and contour colors in a specific design. The legend component is shown in the left of the Graphics window. As shown in Figure below, the legend displays the following information:

finite_element_analysis_welsim_rst_legend

The Legend style can be adjusted by right-clicking on the Legend field. As shown in Figure below, the Context Menu contains items:

finite_element_analysis_welsim_rst_legend_context_menu

finite_element_analysis_welsim_rst_legend_minmax_input

Note

For the option of user-defined max/min settings, the input maximum value must be greater than the minimum value.

Exporting results

The data associated with result objects can be exported in ASCII (.txt or .dat) file format by right-clicking on the desired result object and selecting the Export Result option. Once executed, you are asked to define a filename and select the directory to save the file.

Note

The desired result object must have been successfully evaluated before exporting the result data.

\ No newline at end of file diff --git a/welsim/users/steps/index.html b/welsim/users/steps/index.html index c0604ea..4eacf3e 100755 --- a/welsim/users/steps/index.html +++ b/welsim/users/steps/index.html @@ -1,2 +1,2 @@ - Steps for using the application - WelSim Documentation
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Steps for using the application

This section discusses the workflow in performing simulation analysis in the WELSIM application.

Creating analysis environment

All analyses in WELSIM are represented by one independent analysis environment. After creating a new project environment, you can choose the analysis type and define the parameters to conduct the simulation study.

Unit system behavior

The WELSIM provides eight types of unit systems for you to chose. You can select the preferred unit system from File > Preferences > General > Units. Once the unit system is chosen, quantity units of FEM objects are fixed. However, user still can select different unit for the quantity defined in material module. The material quantity will be converted to the system units at solve.

Defining materials

In simulation analysis, a geometry's attribute is influenced by the material properties that are assigned to the body. When you create a new FEM project, a material project and a structural steel material object are created automatically. This material project can include multiple material objects, which contains the material properties for the successive analysis. The system-generated structural steel can be used directly.

You can add new materials by either one of the methods below:

  • Click the Add Material button from Toolbar.
  • Click the Add Material item from the Material Menu.
  • Right click on the Material Project tree object, and choose Add Material item from the pop-up context menu.

Editing material properties

To manage material properties, you can

  • double click on the material object in the tree, or
  • right click on the material object and select Edit item from the pop-up context menu as shown in Figure below.

finite_element_analysis_welsim_mat_context_menu

Defining material properties

In the material definition panel, two tabs display on the left sub-window as shown in Figure below. The Library tab gives you a quick method to add a bundle of properties for the specific type of material. The Build allows you to add each preferred property one by one.

finite_element_analysis_welsim_mat_lib

Defining analysis type

There are several analysis types are supported in WELSIM. You can define the analysis type while performing an analysis. For example, if the temperature is to be calculated, you would choose a thermal analysis. In the FEM project object, you can set the Physics Type and Analysis Type from the Properties View window as shown in Figure below. The currently available physics and analysis types are:

  • Structural: Static, Transient, Modal
  • Thermal: Steady-State, Transient
  • Electromagnetics: Electostatic, Magnetostatic

finite_element_analysis_welsim_fem_project_prop

Generating geometries

There are two ways of generating geometries in the WELSIM application. You can either create primitive shapes using built-in tools or import an existing STEP/IGES file. Since the built-in tool only can create primitive shapes such as box and cylinder, it is recommended to create your complex geometry in an external application and import the CAD file into WELSIM.

Create primitive shapes

The following lists the primitive shapes that WELSIM build-in tool can create:

  • 3D box
  • 3D cylinder
  • 3D plate
  • 3D line

Import geometry files

For the complex geometry or practical designs, you can create your geometry in an external CAD application, and import to WELSIM application via STEP or IGES file. The properties view of the imported geometry allows you to define the geometry attributes, as shown in Figure below.

finite_element_analysis_welsim_fem_part_prop

Defining part behaviors

The primitive and imported parts have slightly different behaviors, but the primary attributes are the same. This section describes the behaviors of the imported part.

Geometry scale

The Scale determines the size change of the imported geometry, and the current geometry size is the original size multiplied by the scale value. The default value is 1. Increasing the scale value enlarges the geometry, reducing this value causes the geometry smaller. The scale ruler on the bottom of the Graphics Window provides a reference for users to recognize the current size of the geometry.

Spatial parameters

For the imported geometry, the Spatial Parameters allows the user to adjust the origin of geometries. The default value is the origin of global coordinates (0, 0, 0).

Material assignment

Once you have defined the material objects and created the geometry, you can assign the specific material to the selected geometry object. Click Material property, and the cell displays all candidate materials in the drop-down list as shown in Figure below. Each entry includes the material object name and ID.

finite_element_analysis_welsim_fem_mat_assign

Structure type

The Structure Type provides a topological reference for you to differentiate the solid, shell, and beam geometries. The default structural type is Solid.

Source file name

The read-only Source property shows the information of the imported geometry file name. It provides a reference for you to identify the specific imported CAD file.

Applying mesh

Meshing is the process that your geometry is spatially discretized into finite elements and nodes. The quality of the mesh directly influences the final solutions. You can automatically mesh the geometry domains, and generate 3D tetrahedral elements (Tet10 and Tet4), or 3D triangle elements (Tri6 and Tri3).

If your model does not mesh, the system applies the default settings and automatically meshes the domains at solve time. However, it is recommended to mesh the domain before solving since the system provides a reference for you to examine the mesh. Mesh Settings controls are available to assist you in adjusting the mesh density and quality.

In the multi-body analysis, you can apply local Mesh Method object and scope the target bodies to achieve a finer or coarser mesh comparing to other bodies.

Defining connections

In some analyses, you may need to set up the connections such as contact. The available connection features are:

  • Contact Pair: defines two parts are bonded or may contact during the motion. It is supported for both structural and thermal analyses.

Defining study settings

The Study and Study Settings objects are inserted automatically when you started a new FEM project in the step of Creating Analysis Environment. These two objects define the necessary conditions for the solving, such as steps, substeps, end time, convergence tolerance, etc.

You can create multiple steps in the properties of the Study object. As shown in Figure below, the property Number of Steps determines the total steps in the analysis. The Current Step property of determines the current step that other properties are defining on.

The spreadsheet for the Study Settings object displays the related properties for all steps.

finite_element_analysis_welsim_study_prop

Defining initial conditions

Based on the chosen analysis type, you can define the initial conditions to the analysis. The following initial conditions are supported:

  • Initial Temperature: For a transient thermal analysis, you can specify an initial temperature object. The properties view of initial temperature is shown in Figure below.

finite_element_analysis_welsim_initial_temp_prop

Applying boundary conditions

You can impose various boundary conditions based on the types of analysis. For instance, the structural analysis allows you to impose pressure, force, displacement, and other boundary conditions. The thermal analysis enable you to impose thermal flux and temperature boundary conditions.

The body conditions are imposed on the volumes instead of surfaces or edges. For example, the standard earth gravity, acceleration, and rotational velocity act on the bodies.

The boundary and body conditions act according to the steps. For the multi-step analysis, the magnitude of those conditions can vary. The Tabular Data and Chart windows show related data and curves to represent the input values along time/steps.

For the transient analysis, the Initial Status property provides options for the user to define the boundary value at the beginning of the simulation. As shown in Figure below, you can choose the initial value to be None or Equal to Step 1.

finite_element_analysis_welsim_prop_initial_status

Solving

The WELSIM application contains the integrated solvers. These solvers are essentially executable applications and can be instantiated by the front-end using inter-processing scheme. During the solving process, the front-end program generates the input scripts, mesh data file and feeds these files to the solvers. After calculation, the front-end interface can consume the generated result files and displays the resulting contour on the GUI.

Depended on the analysis type, the following solvers are available in WELSIM:

  • WelSimFemSolver1: solves the structural and thermal problems.
  • WelSimFemSolver2: solves the electromagnetic problems.

Solution progress

The overall solution progress can be indicated by the Output window, where you can view the output information from the solvers. If an calculation is completed successfully, you can see the similar message below in the Output window: 

WelSimFemSolver2 Completed !!
-

Evaluating results

The WELSIM application provides fully integrated result review module, and you can evaluate simulation results with no need of other software tools. Depends on the analysis type, various results are available for you to examine solutions. The Using Results section lists all available results that may be used in the post-processing.

The following lists the methods to add result objects:

  • Right click a Answers or Result object in the tree, and choose the target result item from the context menu.
  • Click the result button from the Menu or Toolbar.

The following steps are to evaluate results:

  • Select the target result object in the tree.
  • If the solution is calculated, you can review the result by clicking the Evaluate button from the toolbar, menu, or the right-clicking context menu.

The following result types are available:

  • Contour results: Displays a contour plot of result over geometry surface.
  • Probe results: Displays an annotation of the target area, and shows results in the Properties view.

See the Using Results section for more details on results.

Saving analysis project

You can save the solution with all settings into an external file, and open this file later or on a different computer that has WELSIM installed. The persisted data include two parts:

  • WELSIM database file (*.wsdb).
  • Associated data folder, the folder name is consistent with the database file.

Note

The saved database file (*.wsdb) contains the information of objects and their properties. The geometry data is saved as external STEP files. The mesh and result object settings are saved. However, the mesh and result data are not included yet. You need to perform meshing and solving to obtain those data in a resumed project.

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Steps for using the application

This section discusses the workflow in performing simulation analysis in the WELSIM application.

Creating analysis environment

All analyses in WELSIM are represented by one independent analysis environment. After creating a new project environment, you can choose the analysis type and define the parameters to conduct the simulation study.

Unit system behavior

The WELSIM provides eight types of unit systems for you to chose. You can select the preferred unit system from File > Preferences > General > Units. Once the unit system is chosen, quantity units of FEM objects are fixed. However, user still can select different unit for the quantity defined in material module. The material quantity will be converted to the system units at solve.

Defining materials

In simulation analysis, a geometry's attribute is influenced by the material properties that are assigned to the body. When you create a new FEM project, a material project and a structural steel material object are created automatically. This material project can include multiple material objects, which contains the material properties for the successive analysis. The system-generated structural steel can be used directly.

You can add new materials by either one of the methods below:

  • Click the Add Material button from Toolbar.
  • Click the Add Material item from the Material Menu.
  • Right click on the Material Project tree object, and choose Add Material item from the pop-up context menu.

Editing material properties

To manage material properties, you can

  • double click on the material object in the tree, or
  • right click on the material object and select Edit item from the pop-up context menu as shown in Figure below.

finite_element_analysis_welsim_mat_context_menu

Defining material properties

In the material definition panel, two tabs display on the left sub-window as shown in Figure below. The Library tab gives you a quick method to add a bundle of properties for the specific type of material. The Build allows you to add each preferred property one by one.

finite_element_analysis_welsim_mat_lib

Defining analysis type

There are several analysis types are supported in WELSIM. You can define the analysis type while performing an analysis. For example, if the temperature is to be calculated, you would choose a thermal analysis. In the FEM project object, you can set the Physics Type and Analysis Type from the Properties View window as shown in Figure below. The currently available physics and analysis types are:

  • Structural: Static, Transient, Modal
  • Thermal: Steady-State, Transient
  • Electromagnetics: Electostatic, Magnetostatic

finite_element_analysis_welsim_fem_project_prop

Generating geometries

There are two ways of generating geometries in the WELSIM application. You can either create primitive shapes using built-in tools or import an existing STEP/IGES file. Since the built-in tool only can create primitive shapes such as box and cylinder, it is recommended to create your complex geometry in an external application and import the CAD file into WELSIM.

Create primitive shapes

The following lists the primitive shapes that WELSIM build-in tool can create:

  • 3D box
  • 3D cylinder
  • 3D plate
  • 3D line

Import geometry files

For the complex geometry or practical designs, you can create your geometry in an external CAD application, and import to WELSIM application via STEP or IGES file. The properties view of the imported geometry allows you to define the geometry attributes, as shown in Figure below.

finite_element_analysis_welsim_fem_part_prop

Defining part behaviors

The primitive and imported parts have slightly different behaviors, but the primary attributes are the same. This section describes the behaviors of the imported part.

Geometry scale

The Scale determines the size change of the imported geometry, and the current geometry size is the original size multiplied by the scale value. The default value is 1. Increasing the scale value enlarges the geometry, reducing this value causes the geometry smaller. The scale ruler on the bottom of the Graphics Window provides a reference for users to recognize the current size of the geometry.

Spatial parameters

For the imported geometry, the Spatial Parameters allows the user to adjust the origin of geometries. The default value is the origin of global coordinates (0, 0, 0).

Material assignment

Once you have defined the material objects and created the geometry, you can assign the specific material to the selected geometry object. Click Material property, and the cell displays all candidate materials in the drop-down list as shown in Figure below. Each entry includes the material object name and ID.

finite_element_analysis_welsim_fem_mat_assign

Structure type

The Structure Type provides a topological reference for you to differentiate the solid, shell, and beam geometries. The default structural type is Solid.

Source file name

The read-only Source property shows the information of the imported geometry file name. It provides a reference for you to identify the specific imported CAD file.

Applying mesh

Meshing is the process that your geometry is spatially discretized into finite elements and nodes. The quality of the mesh directly influences the final solutions. You can automatically mesh the geometry domains, and generate 3D tetrahedral elements (Tet10 and Tet4), or 3D triangle elements (Tri6 and Tri3).

If your model does not mesh, the system applies the default settings and automatically meshes the domains at solve time. However, it is recommended to mesh the domain before solving since the system provides a reference for you to examine the mesh. Mesh Settings controls are available to assist you in adjusting the mesh density and quality.

In the multi-body analysis, you can apply local Mesh Method object and scope the target bodies to achieve a finer or coarser mesh comparing to other bodies.

Defining connections

In some analyses, you may need to set up the connections such as contact. The available connection features are:

  • Contact Pair: defines two parts are bonded or may contact during the motion. It is supported for both structural and thermal analyses.

Defining study settings

The Study and Study Settings objects are inserted automatically when you started a new FEM project in the step of Creating Analysis Environment. These two objects define the necessary conditions for the solving, such as steps, substeps, end time, convergence tolerance, etc.

You can create multiple steps in the properties of the Study object. As shown in Figure below, the property Number of Steps determines the total steps in the analysis. The Current Step property of determines the current step that other properties are defining on.

The spreadsheet for the Study Settings object displays the related properties for all steps.

finite_element_analysis_welsim_study_prop

Defining initial conditions

Based on the chosen analysis type, you can define the initial conditions to the analysis. The following initial conditions are supported:

  • Initial Temperature: For a transient thermal analysis, you can specify an initial temperature object. The properties view of initial temperature is shown in Figure below.

finite_element_analysis_welsim_initial_temp_prop

Applying boundary conditions

You can impose various boundary conditions based on the types of analysis. For instance, the structural analysis allows you to impose pressure, force, displacement, and other boundary conditions. The thermal analysis enable you to impose thermal flux and temperature boundary conditions.

The body conditions are imposed on the volumes instead of surfaces or edges. For example, the standard earth gravity, acceleration, and rotational velocity act on the bodies.

The boundary and body conditions act according to the steps. For the multi-step analysis, the magnitude of those conditions can vary. The Tabular Data and Chart windows show related data and curves to represent the input values along time/steps.

For the transient analysis, the Initial Status property provides options for the user to define the boundary value at the beginning of the simulation. As shown in Figure below, you can choose the initial value to be None or Equal to Step 1.

finite_element_analysis_welsim_prop_initial_status

Solving

The WELSIM application contains the integrated solvers. These solvers are essentially executable applications and can be instantiated by the front-end using inter-processing scheme. During the solving process, the front-end program generates the input scripts, mesh data file and feeds these files to the solvers. After calculation, the front-end interface can consume the generated result files and displays the resulting contour on the GUI.

Depended on the analysis type, the following solvers are available in WELSIM:

  • WelSimFemSolver1: solves the structural and thermal problems.
  • WelSimFemSolver2: solves the electromagnetic problems.

Solution progress

The overall solution progress can be indicated by the Output window, where you can view the output information from the solvers. If an calculation is completed successfully, you can see the similar message below in the Output window: 

WelSimFemSolver2 Completed !!
+

Evaluating results

The WELSIM application provides fully integrated result review module, and you can evaluate simulation results with no need of other software tools. Depends on the analysis type, various results are available for you to examine solutions. The Using Results section lists all available results that may be used in the post-processing.

The following lists the methods to add result objects:

  • Right click a Answers or Result object in the tree, and choose the target result item from the context menu.
  • Click the result button from the Menu or Toolbar.

The following steps are to evaluate results:

  • Select the target result object in the tree.
  • If the solution is calculated, you can review the result by clicking the Evaluate button from the toolbar, menu, or the right-clicking context menu.

The following result types are available:

  • Contour results: Displays a contour plot of result over geometry surface.
  • Probe results: Displays an annotation of the target area, and shows results in the Properties view.

See the Using Results section for more details on results.

Saving analysis project

You can save the solution with all settings into an external file, and open this file later or on a different computer that has WELSIM installed. The persisted data include two parts:

  • WELSIM database file (*.wsdb).
  • Associated data folder, the folder name is consistent with the database file.

Note

The saved database file (*.wsdb) contains the information of objects and their properties. The geometry data is saved as external STEP files. The mesh and result object settings are saved. However, the mesh and result data are not included yet. You need to perform meshing and solving to obtain those data in a resumed project.

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Configuring study settings

This section describes the Study and Study Settings configuration.

General settings

When you start a new FEM Project, the Study and Study Settings objects are inserted in the tree automatically. With these objects selected, you can define many solving options in the Properties View window. For example, you can define the properties of Steps, Substeps, Solver, etc.

Step controls

Step Controls define the analysis steps for both static and transient analysis. These properties in the Study object has such characteristics:

  • Number of Steps must be positive.
  • Current Step must be less than or equal to the Number of Steps. Note that Current Step property of Study object is adjustable, and determines the Current Step properties in other objects such as Study Settings, and boundary conditions.
  • Current End Time must be greater than the Current End Time in the last step.

Nonlinear controls

For the nonlinear analysis, the properties of the Nonlinear Settings Controls determine the convergence of the solution. Those properties are mainly related to the Newton-Raphson algorithm.

  • Relative Tolerance: The default value is 1e-4.
  • Absolute Tolerance: The default value is 1e-5.
  • Maximum Iterations: The default value is 40.

Solver controls

Solver Controls determines the attributes of the linear algebra solvers. The following lists the related properties:

  • Solver Method: provides user to select a solver from the options Conjugate Gradient, BiCGStab, GMRES, GPBiCG, MUMPS, Direct, DIRECTmkl, where MUMPS, Direct, and DIRECTmkl are the direct solver, and the rest are iterative solver. The default solver is MUMPS.
  • Number of Iterations: defines the maximum number of the linear algebra solver iterations.
  • Residual Threshold: defines the residual threshold for the linear algebra solver.

Output controls

The Output Controls determines the output rules of solving and results. The available options are:

  • Output Time Log: outputs the log for each time step. The default is false.
  • Output Iteration Log: outputs the log each iteration step. The default is false.
  • Generate Result Files: generates ASCII format result file. The default is false.
  • Output Frequency: determines the frequency of the result data output. The default value is 1, which outputs result data every step.
  • Reorder Result Element: changes the higher order elements to the linear elements in the mesh data of the result file. The deatil is false.
\ No newline at end of file + Configuring study settings - WelSim Documentation
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Configuring study settings

This section describes the Study and Study Settings configuration.

General settings

When you start a new FEM Project, the Study and Study Settings objects are inserted in the tree automatically. With these objects selected, you can define many solving options in the Properties View window. For example, you can define the properties of Steps, Substeps, Solver, etc.

Step controls

Step Controls define the analysis steps for both static and transient analysis. These properties in the Study object has such characteristics:

  • Number of Steps must be positive.
  • Current Step must be less than or equal to the Number of Steps. Note that Current Step property of Study object is adjustable, and determines the Current Step properties in other objects such as Study Settings, and boundary conditions.
  • Current End Time must be greater than the Current End Time in the last step.

Nonlinear controls

For the nonlinear analysis, the properties of the Nonlinear Settings Controls determine the convergence of the solution. Those properties are mainly related to the Newton-Raphson algorithm.

  • Relative Tolerance: The default value is 1e-4.
  • Absolute Tolerance: The default value is 1e-5.
  • Maximum Iterations: The default value is 40.

Solver controls

Solver Controls determines the attributes of the linear algebra solvers. The following lists the related properties:

  • Solver Method: provides user to select a solver from the options Conjugate Gradient, BiCGStab, GMRES, GPBiCG, MUMPS, Direct, DIRECTmkl, where MUMPS, Direct, and DIRECTmkl are the direct solver, and the rest are iterative solver. The default solver is MUMPS.
  • Number of Iterations: defines the maximum number of the linear algebra solver iterations.
  • Residual Threshold: defines the residual threshold for the linear algebra solver.

Output controls

The Output Controls determines the output rules of solving and results. The available options are:

  • Output Time Log: outputs the log for each time step. The default is false.
  • Output Iteration Log: outputs the log each iteration step. The default is false.
  • Generate Result Files: generates ASCII format result file. The default is false.
  • Output Frequency: determines the frequency of the result data output. The default value is 1, which outputs result data every step.
  • Reorder Result Element: changes the higher order elements to the linear elements in the mesh data of the result file. The deatil is false.
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Electromagnetic

To be added...

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Electromagnetic

To be added...

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WELSIM Verification Manual presents a collection of test cases that demonstrate a number of the capabilities of the WELSIM analysis environment. The available tests are engineering problems that provide independent verification, usually a closed form equation. Many of them are classical engineering problems.

Introduction

Index of test cases

The following lists all verification cases tested with WELSIM application. Each case entry describes the test case number, element type, analysis type, and solution options.

  • VM001: Solid Element, Static Structural, Linear.
  • VM002: Solid Element, Static Structural, Linear.
  • VM003: Solid Element, Steady-State Thermal, Linear.
\ No newline at end of file + Introduction - WelSim Documentation
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WELSIM Verification Manual presents a collection of test cases that demonstrate a number of the capabilities of the WELSIM analysis environment. The available tests are engineering problems that provide independent verification, usually a closed form equation. Many of them are classical engineering problems.

Introduction

Index of test cases

The following lists all verification cases tested with WELSIM application. Each case entry describes the test case number, element type, analysis type, and solution options.

  • VM001: Solid Element, Static Structural, Linear.
  • VM002: Solid Element, Static Structural, Linear.
  • VM003: Solid Element, Steady-State Thermal, Linear.
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Structural

Statically inteterminate reaction force analysis VM001

An assembly of three cylinder bars is supported at both end surfaces. Forces \(F_{1}\) and \(F_{2}\) is applied on the middle of the assembly as shown in Figure [fig:ch5_vm_001_schematic].

finite_element_analysis_welsim_verification_1_schematic

The input data about material, geometry, and loads are given in Table [tab:ch5_vm_001_parameters].

Material Properties Geometric Properties Boundary Conditions
Young's Modulus E=2e11 h=10 \(F_{1}\)=2000
Mass Density \(\rho\)=7850 a=3 \(F_{2}\)=1000
Poission's Ratio v=0.3 b=3

The geometries and imposed boundary conditions are shown in Figure [fig:ch5_vm_001_bc].

finite_element_analysis_welsim_verification_1_geometry

The result comparison is given in Table [tab:ch5_vm_001_result].

Results Theory WELSIM Error (%)
Z Reaction Force at Top Fixed Support 1800 1810 0.556
Z Reaction Force at Bottom Fixed Support 1200 1202 0.167

This test case project file is located at [vm/VM_WELSIM_001.wsdb].

Rectangular plate with circular hole subjected to tensile pressure VM002

A rectangular plate with a circular hole is fixed along one of the end faces. A tensile pressure load is imposed on another end face as shown in Figure [fig:ch5_vm_002_schematic].

finite_element_analysis_welsim_verification_2_schematic

The input data about material, geometry, and loads are given in Table [tab:ch5_vm_002_parameters].

Material Properties Geometric Properties Boundary Conditions
Young's Modulus E=2e11 a=15 Pressure P=1e4
Poission's Ratio v=0.3 b=7.5
c=2.5
d=5
thickness=1

The geometries and imposed boundary conditions are shown in Figure [fig:ch5_vm_002_bc].

finite_element_analysis_welsim_verification_2_geometry

The result comparison is given in Table [tab:ch5_vm_002_result].

Results Theory WELSIM Error (%)
Maximum Normal X Stress 3.125e4 3.156e4 0.992

This test case project file is located at %Installation Directory%/vm/VM_WELSIM_002.wsdb.

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Structural

Statically inteterminate reaction force analysis VM001

An assembly of three cylinder bars is supported at both end surfaces. Forces \(F_{1}\) and \(F_{2}\) is applied on the middle of the assembly as shown in Figure [fig:ch5_vm_001_schematic].

finite_element_analysis_welsim_verification_1_schematic

The input data about material, geometry, and loads are given in Table [tab:ch5_vm_001_parameters].

Material Properties Geometric Properties Boundary Conditions
Young's Modulus E=2e11 h=10 \(F_{1}\)=2000
Mass Density \(\rho\)=7850 a=3 \(F_{2}\)=1000
Poission's Ratio v=0.3 b=3

The geometries and imposed boundary conditions are shown in Figure [fig:ch5_vm_001_bc].

finite_element_analysis_welsim_verification_1_geometry

The result comparison is given in Table [tab:ch5_vm_001_result].

Results Theory WELSIM Error (%)
Z Reaction Force at Top Fixed Support 1800 1810 0.556
Z Reaction Force at Bottom Fixed Support 1200 1202 0.167

This test case project file is located at [vm/VM_WELSIM_001.wsdb].

Rectangular plate with circular hole subjected to tensile pressure VM002

A rectangular plate with a circular hole is fixed along one of the end faces. A tensile pressure load is imposed on another end face as shown in Figure [fig:ch5_vm_002_schematic].

finite_element_analysis_welsim_verification_2_schematic

The input data about material, geometry, and loads are given in Table [tab:ch5_vm_002_parameters].

Material Properties Geometric Properties Boundary Conditions
Young's Modulus E=2e11 a=15 Pressure P=1e4
Poission's Ratio v=0.3 b=7.5
c=2.5
d=5
thickness=1

The geometries and imposed boundary conditions are shown in Figure [fig:ch5_vm_002_bc].

finite_element_analysis_welsim_verification_2_geometry

The result comparison is given in Table [tab:ch5_vm_002_result].

Results Theory WELSIM Error (%)
Maximum Normal X Stress 3.125e4 3.156e4 0.992

This test case project file is located at %Installation Directory%/vm/VM_WELSIM_002.wsdb.

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Thermal

Heat transfer in a composite wall VM003

An assembly wall consists of fire brick and insulating brick. The temperature and surface convection coefficient are given for both end surfaces. The simulation tries to find the temperature distribution of the assembly. The schematic view of the model is shown in Figure [fig:ch5_vm_003_schematic].

finite_element_analysis_welsim_verification_3_schematic

The input data about material, geometry, and loads are given in Table [tab:ch5_vm_003_parameters].

Material Properties Geometric Properties Boundary Conditions
Thermal conductivity of fire brick wall: \(k_{F}\) = 1.852e-5 a=14 Convection coefficient \(h_{F}\)=2.315e-5
Thermal conductivity of insulating wall: \(k_{A}\)=2.315e-6 b=9 Ambient temperature \(T_{F}\)=3000
cross-section=1x1 Convection coefficient \(h_{A}\)=3.858e-6
Ambient temperature \(T_{A}\)=80

The geometries and imposed boundary conditions are shown in Figure [fig:ch5_vm_003_bc].

finite_element_analysis_welsim_verification_3_geometry

The result comparison is given in Table [tab:ch5_vm_003_result].

Results Theory WELSIM Error (%)
Minimum Temperature 336 336.724 0.215
Maximum Temperature 2957 2957.216 0.007

Info

This test case file is located at vm/VM_WELSIM_003.wsdb.

\ No newline at end of file + Thermal - WelSim Documentation
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Thermal

Heat transfer in a composite wall VM003

An assembly wall consists of fire brick and insulating brick. The temperature and surface convection coefficient are given for both end surfaces. The simulation tries to find the temperature distribution of the assembly. The schematic view of the model is shown in Figure [fig:ch5_vm_003_schematic].

finite_element_analysis_welsim_verification_3_schematic

The input data about material, geometry, and loads are given in Table [tab:ch5_vm_003_parameters].

Material Properties Geometric Properties Boundary Conditions
Thermal conductivity of fire brick wall: \(k_{F}\) = 1.852e-5 a=14 Convection coefficient \(h_{F}\)=2.315e-5
Thermal conductivity of insulating wall: \(k_{A}\)=2.315e-6 b=9 Ambient temperature \(T_{F}\)=3000
cross-section=1x1 Convection coefficient \(h_{A}\)=3.858e-6
Ambient temperature \(T_{A}\)=80

The geometries and imposed boundary conditions are shown in Figure [fig:ch5_vm_003_bc].

finite_element_analysis_welsim_verification_3_geometry

The result comparison is given in Table [tab:ch5_vm_003_result].

Results Theory WELSIM Error (%)
Minimum Temperature 336 336.724 0.215
Maximum Temperature 2957 2957.216 0.007

Info

This test case file is located at vm/VM_WELSIM_003.wsdb.

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