Stress linearization in an infinite pipe

This study shows many things

1. How the error of computing ASME linearized stresses depends on the number of elements through the thickness of a pipe. Two second-order elements are enough.
2. The error with respect to the analytical solution vs. CPU and memory usage. It is shown that, even the stresses are basically normal, second-order elements are more efficient that first-order elements.
3. The rate of convergence with respect to mesh size.

Show a single tet4 vs tet10 with nodes. Show a full mesh of tet4 vs tet10 with nodes. Derive the factor of 6 between the number of DOFs. Show the difference between straight and curved tet10s. Negative jacobians! Figure from Christophe's paper.

This case uses displacement-based FEM formulation for linear isotropic elasticity. Note the denominator $r$ in the solution. The iso-parametric displacement-based formulation with polynomial shape functions fail for small $r$ because it is hard for a line and a parabola to approximate $1/r$ when $r \rightarrow 0$.

Wall time and memory are computed only for the solver, not for the mesher. Wall time excludes computation of $L_2$ error.

• hex20?

• hex27?

• mumps?

• plane strain

• axisymmetric

• compare straight-curved

• penalty/lagrange

• the sigmas are not interpolated right, they need to use the constants from the nafems challenge

• unstructured tet4/tet10: ustet10/uctet10

• structured tet4/10: sstet10/sctet10

• structured hex8/hex20 sshex20/schex20

• strucutred hex8/hex27 sshex27/schex27

• for each shape above, draw the wheel with the difference between 1st and 2nd order