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emat_cst.cpp
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emat_cst.cpp
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/*
* emat_cst.cpp
* sensitive couture
*
* Created by Nobuyuki Umetani on 8/2/10.
* Copyright 2010 The University of Tokyo and Colubmia University. All rights reserved.
*
*/
#include <math.h>
#include <iostream>
#include "delfem/vector3d.h"
#include "emat_cst.h"
void MakePositiveDefinite_Sim22(const double s2[3],double s3[3])
{
const double b = (s2[0]+s2[1])*0.5;
// const double c = s2[0]*s2[1]-s2[2]*s2[2];
const double d = (s2[0]-s2[1])*(s2[0]-s2[1])*0.25 + s2[2]*s2[2];
const double e = sqrt(d);
if( b-e > 1.0e-20 ){
s3[0] = s2[0];
s3[1] = s2[1];
s3[2] = s2[2];
return;
}
if( b+e < 0 ){
s3[0] = 0;
s3[1] = 0;
s3[2] = 0;
return;
}
const double l = b+e;
double t0[2] = { s2[0]-l, s2[2] };
double t1[2] = { s2[2], s2[1]-l };
// std::cout << t0[0]*t1[1]-t0[1]*t1[0] << std::endl;
const double sqlen_t0 = t0[0]*t0[0]+t0[1]*t0[1];
const double sqlen_t1 = t1[0]*t1[0]+t1[1]*t1[1];
if( sqlen_t0 > sqlen_t1 ){
if( sqlen_t0 < 1.0e-20 ){
s3[0] = 0;
s3[1] = 0;
s3[2] = 0;
return;
}
const double invlen_t0 = 1.0/sqrt(sqlen_t0);
t0[0] *= invlen_t0;
t0[1] *= invlen_t0;
s3[0] = l*t0[0]*t0[0];
s3[1] = l*t0[1]*t0[1];
s3[2] = l*t0[0]*t0[1];
}
else{
if( sqlen_t1 < 1.0e-20 ){
s3[0] = 0;
s3[1] = 0;
s3[2] = 0;
return;
}
const double invlen_t1 = 1.0/sqrt(sqlen_t1);
t1[0] *= invlen_t1;
t1[1] *= invlen_t1;
s3[0] = l*t1[0]*t1[0];
s3[1] = l*t1[1]*t1[1];
s3[2] = l*t1[0]*t1[1];
}
return;
}
void GetMatRes_CST_BackwardEular
(double Kmat[3][3][3][3], double Res[3][3],
const double C[3][3],
const double u[3][3], const double v[3][3],
double lambda, double myu,
double dt, double damp_coeff,
double& strain_energy)
{
double Kmat0[3][3][3][3];
const double c[3][3] = {
{ C[0][0]+u[0][0], C[0][1]+u[0][1], C[0][2]+u[0][2] },
{ C[1][0]+u[1][0], C[1][1]+u[1][1], C[1][2]+u[1][2] },
{ C[2][0]+u[2][0], C[2][1]+u[2][1], C[2][2]+u[2][2] } };
GetKmatRes_CST(Kmat0,Res, C,c, lambda,myu, strain_energy);
for(unsigned int i=0;i<3*3*3*3;i++){ (&Kmat[0][0][0][0])[i] = dt*(dt+damp_coeff)*(&Kmat0[0][0][0][0])[i]; }
for(unsigned int ino=0;ino<3;ino++){
for(unsigned int idim=0;idim<3;idim++){
Res[ino][idim] *= dt;
for(unsigned int jno=0;jno<3;jno++){
for(unsigned int jdim=0;jdim<3;jdim++){
Res[ino][idim] += damp_coeff*Kmat0[ino][jno][idim][jdim]*v[jno][jdim]*dt;
Res[ino][idim] += Kmat0[ino][jno][idim][jdim]*v[jno][jdim]*dt*dt;
}
}
}
}
}
void GetMatRes_CST_NewmarkBeta
(double Kmat[3][3][3][3], double Res[3][3],
const double C[3][3],
const double u[3][3], const double v[3][3], const double a[3][3],
double lambda, double myu,
double dt, double gamma_n, double beta_n, bool isinit)
{
double Kmat0[3][3][3][3];
const double c[3][3] = {
{ C[0][0]+u[0][0], C[0][1]+u[0][1], C[0][2]+u[0][2] },
{ C[1][0]+u[1][0], C[1][1]+u[1][1], C[1][2]+u[1][2] },
{ C[2][0]+u[2][0], C[2][1]+u[2][1], C[2][2]+u[2][2] } };
double se = 0;
GetKmatRes_CST(Kmat0,Res, C,c, lambda,myu,se);
for(unsigned int i=0;i<3*3*3*3;i++){ (&Kmat[0][0][0][0])[i] = dt*dt*beta_n*(&Kmat0[0][0][0][0])[i]; }
if( isinit ){
for(unsigned int ino=0;ino<3;ino++){
for(unsigned int idim=0;idim<3;idim++){
for(unsigned int jno=0;jno<3;jno++){
for(unsigned int jdim=0;jdim<3;jdim++){
Res[ino][idim] += Kmat0[ino][jno][idim][jdim]*v[jno][jdim]*dt;
Res[ino][idim] += Kmat0[ino][jno][idim][jdim]*a[jno][jdim]*dt*dt*0.5;
}
}
}
}
}
}
void GetKmatResdRdC_CST
(double Kmat[3][3][3][3], double Res[3][3], double dRdC[3][3][3][3],
const double C[3][3], const double c[3][3],
double lambda, double myu)
{
double Gd[3][3] = {
{ C[1][0]-C[0][0], C[1][1]-C[0][1], C[1][2]-C[0][2] },
{ C[2][0]-C[0][0], C[2][1]-C[0][1], C[2][2]-C[0][2] }, { 0,0,0 } };
double Area;
Com::UnitNormalAreaTri3D(Gd[2], Area, C[0], C[1], C[2]);
double Gu[2][3];
{
double invArea = 0.5/Area;
Com::Cross3D(Gu[0], Gd[1], Gd[2]);
Gu[0][0] *= invArea; Gu[0][1] *= invArea; Gu[0][2] *= invArea;
////
Com::Cross3D(Gu[1], Gd[2], Gd[0]);
Gu[1][0] *= invArea ; Gu[1][1] *= invArea; Gu[1][2] *= invArea;
}
const double gd[2][3] = {
{ c[1][0]-c[0][0], c[1][1]-c[0][1], c[1][2]-c[0][2] },
{ c[2][0]-c[0][0], c[2][1]-c[0][1], c[2][2]-c[0][2] } };
const double E2[3] = { // engineering strain
0.5*( Com::Dot3D(gd[0],gd[0]) - Com::Dot3D(Gd[0],Gd[0]) ),
0.5*( Com::Dot3D(gd[1],gd[1]) - Com::Dot3D(Gd[1],Gd[1]) ),
1.0*( Com::Dot3D(gd[0],gd[1]) - Com::Dot3D(Gd[0],Gd[1]) ) };
const double E2dC[3][3][3] = { // E2dC[a][i][k] : derivative of E2[k] w.r.t. C[a][i]
{ {+Gd[0][0],+Gd[1][0],+Gd[0][0]+Gd[1][0]},
{+Gd[0][1],+Gd[1][1],+Gd[0][1]+Gd[1][1]},
{+Gd[0][2],+Gd[1][2],+Gd[0][2]+Gd[1][2]} },
{ {-Gd[0][0],0, -Gd[1][0]},
{-Gd[0][1],0, -Gd[1][1]},
{-Gd[0][2],0, -Gd[1][2]} },
{ {0, -Gd[1][0],-Gd[0][0]},
{0, -Gd[1][1],-Gd[0][1]},
{0, -Gd[1][2],-Gd[0][2]} } };
double DAdC[3][3];
{
const double D[3][3] = {
{ C[2][0]-C[1][0], C[2][1]-C[1][1], C[2][2]-C[1][2] },
{ C[0][0]-C[2][0], C[0][1]-C[2][1], C[0][2]-C[2][2] },
{ C[1][0]-C[0][0], C[1][1]-C[0][1], C[1][2]-C[0][2] } };
Com::Cross3D(DAdC[0], Gd[2], D[0]);
Com::Cross3D(DAdC[1], Gd[2], D[1]);
Com::Cross3D(DAdC[2], Gd[2], D[2]);
}
double GuDC[3][3][2][3]; // GuDC[a][i][b][j] : derivative of Gu[b][j] w.r.t. C[a][i]
{
const double invSqDArea = 0.25/(Area*Area);
double G101[3]; Com::Cross3D(G101, Gd[1], Gd[2]);
double G010[3]; Com::Cross3D(G010, Gd[2], Gd[0]);
for(unsigned int idim=0;idim<3;idim++){
for(unsigned int jdim=0;jdim<3;jdim++){
GuDC[0][idim][0][jdim] = invSqDArea*( -2.0*G101[jdim]*DAdC[0][idim] - 2.0*Gd[1][idim]*Gd[0][jdim] + (Gd[0][idim]+Gd[1][idim])*Gd[1][jdim] );
GuDC[1][idim][0][jdim] = invSqDArea*( -2.0*G101[jdim]*DAdC[1][idim] - Gd[1][idim]*Gd[1][jdim] );
GuDC[2][idim][0][jdim] = invSqDArea*( -2.0*G101[jdim]*DAdC[2][idim] + 2.0*Gd[1][idim]*Gd[0][jdim] - Gd[0][idim]*Gd[1][jdim] );
GuDC[0][idim][1][jdim] = invSqDArea*( -2.0*G010[jdim]*DAdC[0][idim] - 2.0*Gd[0][idim]*Gd[1][jdim] + (Gd[0][idim]+Gd[1][idim])*Gd[0][jdim] );
GuDC[1][idim][1][jdim] = invSqDArea*( -2.0*G010[jdim]*DAdC[1][idim] + 2.0*Gd[0][idim]*Gd[1][jdim] - Gd[1][idim]*Gd[0][jdim] );
GuDC[2][idim][1][jdim] = invSqDArea*( -2.0*G010[jdim]*DAdC[2][idim] - Gd[0][idim]*Gd[0][jdim] );
}
GuDC[0][idim][0][idim] += invSqDArea*( -Com::Dot3D(Gd[1],Gd[1]) + Com::Dot3D(Gd[0],Gd[1]) );
GuDC[1][idim][0][idim] += invSqDArea*( +Com::Dot3D(Gd[1],Gd[1]) );
GuDC[2][idim][0][idim] += invSqDArea*( -Com::Dot3D(Gd[1],Gd[0]) );
GuDC[0][idim][1][idim] += invSqDArea*( -Com::Dot3D(Gd[0],Gd[0]) + Com::Dot3D(Gd[0],Gd[1]) );
GuDC[1][idim][1][idim] += invSqDArea*( -Com::Dot3D(Gd[1],Gd[0]) );
GuDC[2][idim][1][idim] += invSqDArea*( +Com::Dot3D(Gd[0],Gd[0]) );
}
}
double GuGu2dC[3][3][3]; // GuDC[a][i][k] : derivative of GuGu[k] w.r.t. C[a][i]
for(unsigned int jno=0;jno<3;jno++){
for(unsigned int jdim=0;jdim<3;jdim++){
GuGu2dC[jno][jdim][0] = 2.0*Com::Dot3D(GuDC[jno][jdim][0],Gu[0]);
GuGu2dC[jno][jdim][1] = 2.0*Com::Dot3D(GuDC[jno][jdim][1],Gu[1]);
GuGu2dC[jno][jdim][2] = Com::Dot3D(GuDC[jno][jdim][0],Gu[1]) + Com::Dot3D(GuDC[jno][jdim][1],Gu[0]);
}
}
const double GuGu2[3] = { Com::Dot3D(Gu[0],Gu[0]), Com::Dot3D(Gu[1],Gu[1]), Com::Dot3D(Gu[1],Gu[0]) };
const double Cons2[6] = {
(lambda+2*myu)*GuGu2[0]*GuGu2[0],
(lambda+2*myu)*GuGu2[1]*GuGu2[1],
(lambda+ myu)*GuGu2[2]*GuGu2[2] + myu*GuGu2[0]*GuGu2[1],
(lambda+2*myu)*GuGu2[1]*GuGu2[2],
(lambda+2*myu)*GuGu2[0]*GuGu2[2],
lambda*GuGu2[0]*GuGu2[1] + 2*myu*(GuGu2[2]*GuGu2[2]) };
double Cons2dC[3][3][6];
{
for(unsigned int jno=0;jno<3;jno++){
for(unsigned int jdim=0;jdim<3;jdim++){
Cons2dC[jno][jdim][0] = 2*(lambda+2*myu)*GuGu2[0]*GuGu2dC[jno][jdim][0];
Cons2dC[jno][jdim][1] = 2*(lambda+2*myu)*GuGu2[1]*GuGu2dC[jno][jdim][1];
Cons2dC[jno][jdim][2] = 2*(lambda+ myu)*GuGu2[2]*GuGu2dC[jno][jdim][2] + myu*( GuGu2[1]*GuGu2dC[jno][jdim][0] + GuGu2[0]*GuGu2dC[jno][jdim][1] );
Cons2dC[jno][jdim][3] = (lambda+2*myu)*( GuGu2[1]*GuGu2dC[jno][jdim][2] + GuGu2[2]*GuGu2dC[jno][jdim][1] );
Cons2dC[jno][jdim][4] = (lambda+2*myu)*( GuGu2[0]*GuGu2dC[jno][jdim][2] + GuGu2[2]*GuGu2dC[jno][jdim][0] );
Cons2dC[jno][jdim][5] = lambda*( GuGu2[1]*GuGu2dC[jno][jdim][0] + GuGu2[0]*GuGu2dC[jno][jdim][1] ) + 4*myu*GuGu2[2]*GuGu2dC[jno][jdim][2];
}
}
}
const double S2[3] = { // stress
Cons2[0]*E2[0] + Cons2[5]*E2[1] + Cons2[4]*E2[2],
Cons2[5]*E2[0] + Cons2[1]*E2[1] + Cons2[3]*E2[2],
Cons2[4]*E2[0] + Cons2[3]*E2[1] + Cons2[2]*E2[2] };
const double dNdr[3][2] = { {-1.0, -1.0}, {+1.0, +0.0}, {+0.0, +1.0} };
for(unsigned int ino=0;ino<3;ino++){
for(unsigned int idim=0;idim<3;idim++){
Res[ino][idim] = Area*
(+S2[0]*gd[0][idim]*dNdr[ino][0]
+S2[2]*gd[0][idim]*dNdr[ino][1]
+S2[2]*gd[1][idim]*dNdr[ino][0]
+S2[1]*gd[1][idim]*dNdr[ino][1]);
}
}
double S2dC[3][3][3];
for(unsigned int jno=0;jno<3;jno++){
for(unsigned int jdim=0;jdim<3;jdim++){
S2dC[jno][jdim][0]
= Cons2[0]*E2dC[jno][jdim][0] + Cons2dC[jno][jdim][0]*E2[0]
+ Cons2[5]*E2dC[jno][jdim][1] + Cons2dC[jno][jdim][5]*E2[1]
+ Cons2[4]*E2dC[jno][jdim][2] + Cons2dC[jno][jdim][4]*E2[2];
S2dC[jno][jdim][1]
= Cons2[5]*E2dC[jno][jdim][0] + Cons2dC[jno][jdim][5]*E2[0]
+ Cons2[1]*E2dC[jno][jdim][1] + Cons2dC[jno][jdim][1]*E2[1]
+ Cons2[3]*E2dC[jno][jdim][2] + Cons2dC[jno][jdim][3]*E2[2];
S2dC[jno][jdim][2]
= Cons2[4]*E2dC[jno][jdim][0] + Cons2dC[jno][jdim][4]*E2[0]
+ Cons2[3]*E2dC[jno][jdim][1] + Cons2dC[jno][jdim][3]*E2[1]
+ Cons2[2]*E2dC[jno][jdim][2] + Cons2dC[jno][jdim][2]*E2[2];
}
}
for(unsigned int ino=0;ino<3;ino++){
for(unsigned int idim=0;idim<3;idim++){
for(unsigned int jno=0;jno<3;jno++){
for(unsigned int jdim=0;jdim<3;jdim++){
dRdC[ino][jno][idim][jdim] =
+(Area*S2dC[jno][jdim][0]+0.5*DAdC[jno][jdim]*S2[0])*gd[0][idim]*dNdr[ino][0]
+(Area*S2dC[jno][jdim][2]+0.5*DAdC[jno][jdim]*S2[2])*gd[0][idim]*dNdr[ino][1]
+(Area*S2dC[jno][jdim][2]+0.5*DAdC[jno][jdim]*S2[2])*gd[1][idim]*dNdr[ino][0]
+(Area*S2dC[jno][jdim][1]+0.5*DAdC[jno][jdim]*S2[1])*gd[1][idim]*dNdr[ino][1];
}
}
}
}
//////////////////////////
// Calc stiffness matrix
double S3[3] = { S2[0], S2[1], S2[2] };
MakePositiveDefinite_Sim22(S2,S3);
for(unsigned int ino=0;ino<3;ino++){
for(unsigned int jno=0;jno<ino+1;jno++){
for(unsigned int idim=0;idim<3;idim++){
for(unsigned int jdim=0;jdim<3;jdim++){
double dtmp0 = 0;
dtmp0 += gd[0][idim]*(dNdr[ino][0]*Cons2[0]+dNdr[ino][1]*Cons2[4])*gd[0][jdim]*dNdr[jno][0];
dtmp0 += gd[0][idim]*(dNdr[ino][0]*Cons2[5]+dNdr[ino][1]*Cons2[3])*gd[1][jdim]*dNdr[jno][1];
dtmp0 += gd[0][idim]*(dNdr[ino][0]*Cons2[4]+dNdr[ino][1]*Cons2[2])*gd[0][jdim]*dNdr[jno][1];
dtmp0 += gd[0][idim]*(dNdr[ino][0]*Cons2[4]+dNdr[ino][1]*Cons2[2])*gd[1][jdim]*dNdr[jno][0];
dtmp0 += gd[1][idim]*(dNdr[ino][0]*Cons2[4]+dNdr[ino][1]*Cons2[5])*gd[0][jdim]*dNdr[jno][0];
dtmp0 += gd[1][idim]*(dNdr[ino][0]*Cons2[3]+dNdr[ino][1]*Cons2[1])*gd[1][jdim]*dNdr[jno][1];
dtmp0 += gd[1][idim]*(dNdr[ino][0]*Cons2[2]+dNdr[ino][1]*Cons2[3])*gd[0][jdim]*dNdr[jno][1];
dtmp0 += gd[1][idim]*(dNdr[ino][0]*Cons2[2]+dNdr[ino][1]*Cons2[3])*gd[1][jdim]*dNdr[jno][0];
Kmat[ino][jno][idim][jdim] = dtmp0*Area;
}
}
const double dtmp1 = Area*
(+S3[0]*dNdr[ino][0]*dNdr[jno][0]
+S3[2]*dNdr[ino][0]*dNdr[jno][1]
+S3[2]*dNdr[ino][1]*dNdr[jno][0]
+S3[1]*dNdr[ino][1]*dNdr[jno][1]);
Kmat[ino][jno][0][0] += dtmp1;
Kmat[ino][jno][1][1] += dtmp1;
Kmat[ino][jno][2][2] += dtmp1;
}
}
for(unsigned int ino=0;ino<3;ino++){
for(unsigned int jno=ino+1;jno<3;jno++){
for(unsigned int idim=0;idim<3;idim++){
for(unsigned int jdim=0;jdim<3;jdim++){
Kmat[ino][jno][idim][jdim] = Kmat[jno][ino][jdim][idim];
}
}
}
}
}
static double TriArea2D(const double v1[2], const double v2[2], const double v3[2]){
double z = ( v2[0] - v1[0] )*( v3[1] - v1[1] ) - ( v3[0] - v1[0] )*( v2[1] - v1[1] );
return z*0.5;
}
void GetKmatRes_CST
(double Kmat[3][3][3][3], double res[3][3],
const double C[3][3], const double c[3][3],
const double lambda, const double myu,
double& strain_energy)
{
double Gd[3][3] = {
{ C[1][0]-C[0][0], C[1][1]-C[0][1], C[1][2]-C[0][2] },
{ C[2][0]-C[0][0], C[2][1]-C[0][1], C[2][2]-C[0][2] }, { 0,0,0 } };
double Area;
Com::UnitNormalAreaTri3D(Gd[2], Area, C[0], C[1], C[2]);
double Gu[2][3];
{
const double invDArea = 0.5/Area;
Com::Cross3D(Gu[0], Gd[1], Gd[2]);
Gu[0][0] *= invDArea; Gu[0][1] *= invDArea; Gu[0][2] *= invDArea;
////
Com::Cross3D(Gu[1], Gd[2], Gd[0]);
Gu[1][0] *= invDArea; Gu[1][1] *= invDArea; Gu[1][2] *= invDArea;
}
const double gd[2][3] = {
{ c[1][0]-c[0][0], c[1][1]-c[0][1], c[1][2]-c[0][2] },
{ c[2][0]-c[0][0], c[2][1]-c[0][1], c[2][2]-c[0][2] } };
const double dNdr[3][2] = { {-1.0, -1.0}, {+1.0, +0.0}, {+0.0, +1.0} };
const double E2[3] = { // engineering strain
0.5*( Com::Dot3D(gd[0],gd[0]) - Com::Dot3D(Gd[0],Gd[0]) ),
0.5*( Com::Dot3D(gd[1],gd[1]) - Com::Dot3D(Gd[1],Gd[1]) ),
1.0*( Com::Dot3D(gd[0],gd[1]) - Com::Dot3D(Gd[0],Gd[1]) ) };
const double GuGu2[3] = { Com::Dot3D(Gu[0],Gu[0]), Com::Dot3D(Gu[1],Gu[1]), Com::Dot3D(Gu[1],Gu[0]) };
const double Cons2[6] = {
(lambda+2*myu)*GuGu2[0]*GuGu2[0],
(lambda+2*myu)*GuGu2[1]*GuGu2[1],
(lambda+ myu)*GuGu2[2]*GuGu2[2] + myu*GuGu2[0]*GuGu2[1],
(lambda+2*myu)*GuGu2[1]*GuGu2[2],
(lambda+2*myu)*GuGu2[0]*GuGu2[2],
lambda*GuGu2[0]*GuGu2[1] + 2*myu*(GuGu2[2]*GuGu2[2]) };
const double S2[3] = { // stress
Cons2[0]*E2[0] + Cons2[5]*E2[1] + Cons2[4]*E2[2],
Cons2[5]*E2[0] + Cons2[1]*E2[1] + Cons2[3]*E2[2],
Cons2[4]*E2[0] + Cons2[3]*E2[1] + Cons2[2]*E2[2] };
strain_energy += 0.5*Area*(E2[0]*S2[0] + E2[1]*S2[1] + E2[2]*S2[2]);
////
for(unsigned int ino=0;ino<3;ino++){
for(unsigned int idim=0;idim<3;idim++){
res[ino][idim] = Area*
(+S2[0]*gd[0][idim]*dNdr[ino][0]
+S2[2]*gd[0][idim]*dNdr[ino][1]
+S2[2]*gd[1][idim]*dNdr[ino][0]
+S2[1]*gd[1][idim]*dNdr[ino][1]);
}
}
double S3[3] = { S2[0], S2[1], S2[2] };
MakePositiveDefinite_Sim22(S2,S3);
for(unsigned int ino=0;ino<3;ino++){
for(unsigned int jno=0;jno<ino+1;jno++){
for(unsigned int idim=0;idim<3;idim++){
for(unsigned int jdim=0;jdim<3;jdim++){
double dtmp0 = 0;
dtmp0 += gd[0][idim]*(dNdr[ino][0]*Cons2[0]+dNdr[ino][1]*Cons2[4])*gd[0][jdim]*dNdr[jno][0];
dtmp0 += gd[0][idim]*(dNdr[ino][0]*Cons2[5]+dNdr[ino][1]*Cons2[3])*gd[1][jdim]*dNdr[jno][1];
dtmp0 += gd[0][idim]*(dNdr[ino][0]*Cons2[4]+dNdr[ino][1]*Cons2[2])*gd[0][jdim]*dNdr[jno][1];
dtmp0 += gd[0][idim]*(dNdr[ino][0]*Cons2[4]+dNdr[ino][1]*Cons2[2])*gd[1][jdim]*dNdr[jno][0];
dtmp0 += gd[1][idim]*(dNdr[ino][0]*Cons2[4]+dNdr[ino][1]*Cons2[5])*gd[0][jdim]*dNdr[jno][0];
dtmp0 += gd[1][idim]*(dNdr[ino][0]*Cons2[3]+dNdr[ino][1]*Cons2[1])*gd[1][jdim]*dNdr[jno][1];
dtmp0 += gd[1][idim]*(dNdr[ino][0]*Cons2[2]+dNdr[ino][1]*Cons2[3])*gd[0][jdim]*dNdr[jno][1];
dtmp0 += gd[1][idim]*(dNdr[ino][0]*Cons2[2]+dNdr[ino][1]*Cons2[3])*gd[1][jdim]*dNdr[jno][0];
Kmat[ino][jno][idim][jdim] = dtmp0*Area;
}
}
const double dtmp1 = Area*
(+S3[0]*dNdr[ino][0]*dNdr[jno][0]
+S3[2]*dNdr[ino][0]*dNdr[jno][1]
+S3[2]*dNdr[ino][1]*dNdr[jno][0]
+S3[1]*dNdr[ino][1]*dNdr[jno][1]);
Kmat[ino][jno][0][0] += dtmp1;
Kmat[ino][jno][1][1] += dtmp1;
Kmat[ino][jno][2][2] += dtmp1;
}
}
for(unsigned int ino=0;ino<3;ino++){
for(unsigned int jno=ino+1;jno<3;jno++){
for(unsigned int idim=0;idim<3;idim++){
for(unsigned int jdim=0;jdim<3;jdim++){
Kmat[ino][jno][idim][jdim] = Kmat[jno][ino][jdim][idim];
}
}
}
}
}
/*
void GetKmatRes_CST
(double Kmat[3][3][3][3], double res[3][3],
const double C[3][3], const double c[3][3],
const double lambda, const double myu,
double& strain_energy)
{
double Gd[3][3] = {
{ C[1][0]-C[0][0], C[1][1]-C[0][1], C[1][2]-C[0][2] },
{ C[2][0]-C[0][0], C[2][1]-C[0][1], C[2][2]-C[0][2] }, { 0,0,0 } };
double Area;
UnitNormalAreaTri3D(Gd[2], Area, C[0], C[1], C[2]);
double Gu[3][2];
{
Cross3D(Gu[0], Gd[1], Gd[2]);
const double invtmp1 = 1.0/Dot3D(Gu[0],Gd[0]);
Gu[0][0] *= invtmp1; Gu[0][1] *= invtmp1; Gu[0][2] *= invtmp1;
////
Cross3D(Gu[1], Gd[2], Gd[0]);
const double invtmp2 = 1.0/Dot3D(Gu[1],Gd[1]);
Gu[1][0] *= invtmp2; Gu[1][1] *= invtmp2; Gu[1][2] *= invtmp2;
}
const double gd[2][3] = {
{ c[1][0]-c[0][0], c[1][1]-c[0][1], c[1][2]-c[0][2] },
{ c[2][0]-c[0][0], c[2][1]-c[0][1], c[2][2]-c[0][2] } };
const double dNdr[3][2] = { {-1.0, -1.0}, {+1.0, +0.0}, {+0.0, +1.0} };
const double E2[3] = { // engineering strain
0.5*( Dot3D(gd[0],gd[0]) - Dot3D(Gd[0],Gd[0]) ),
0.5*( Dot3D(gd[1],gd[1]) - Dot3D(Gd[1],Gd[1]) ),
1.0*( Dot3D(gd[0],gd[1]) - Dot3D(Gd[0],Gd[1]) ) };
const double GuGu2[3] = { Dot3D(Gu[0],Gu[0]), Dot3D(Gu[1],Gu[1]), Dot3D(Gu[1],Gu[0]) };
const double Cons2[3][3] = {
{ lambda*GuGu2[0]*GuGu2[0] + 2*myu*(GuGu2[0]*GuGu2[0]),
lambda*GuGu2[0]*GuGu2[1] + 2*myu*(GuGu2[2]*GuGu2[2]),
lambda*GuGu2[0]*GuGu2[2] + 2*myu*(GuGu2[0]*GuGu2[2]) },
{ lambda*GuGu2[1]*GuGu2[0] + 2*myu*(GuGu2[2]*GuGu2[2]),
lambda*GuGu2[1]*GuGu2[1] + 2*myu*(GuGu2[1]*GuGu2[1]),
lambda*GuGu2[1]*GuGu2[2] + 2*myu*(GuGu2[2]*GuGu2[1]) },
{ lambda*GuGu2[2]*GuGu2[0] + 2*myu*(GuGu2[0]*GuGu2[2]),
lambda*GuGu2[2]*GuGu2[1] + 2*myu*(GuGu2[2]*GuGu2[1]),
lambda*GuGu2[2]*GuGu2[2] + 1*myu*(GuGu2[0]*GuGu2[1] + GuGu2[2]*GuGu2[2]) } };
const double S2[3] = { // stress
Cons2[0][0]*E2[0] + Cons2[0][1]*E2[1] + Cons2[0][2]*E2[2],
Cons2[1][0]*E2[0] + Cons2[1][1]*E2[1] + Cons2[1][2]*E2[2],
Cons2[2][0]*E2[0] + Cons2[2][1]*E2[1] + Cons2[2][2]*E2[2] };
strain_energy += 0.5*Area*(E2[0]*S2[0] + E2[1]*S2[1] + E2[2]*S2[2]);
for(unsigned int ino=0;ino<3;ino++){
for(unsigned int idim=0;idim<3;idim++){
res[ino][idim] = Area*
(+S2[0]*gd[0][idim]*dNdr[ino][0]
+S2[2]*gd[0][idim]*dNdr[ino][1]
+S2[2]*gd[1][idim]*dNdr[ino][0]
+S2[1]*gd[1][idim]*dNdr[ino][1]);
}
}
for(unsigned int ino=0;ino<3;ino++){
for(unsigned int jno=0;jno<ino+1;jno++){
for(unsigned int idim=0;idim<3;idim++){
for(unsigned int jdim=0;jdim<3;jdim++){
double dtmp0 = 0;
dtmp0 += gd[0][idim]*dNdr[ino][0]*Cons2[0][0]*gd[0][jdim]*dNdr[jno][0];
dtmp0 += gd[0][idim]*dNdr[ino][0]*Cons2[0][1]*gd[1][jdim]*dNdr[jno][1];
dtmp0 += gd[0][idim]*dNdr[ino][0]*Cons2[0][2]*gd[0][jdim]*dNdr[jno][1];
dtmp0 += gd[0][idim]*dNdr[ino][0]*Cons2[0][2]*gd[1][jdim]*dNdr[jno][0];
dtmp0 += gd[1][idim]*dNdr[ino][1]*Cons2[1][0]*gd[0][jdim]*dNdr[jno][0];
dtmp0 += gd[1][idim]*dNdr[ino][1]*Cons2[1][1]*gd[1][jdim]*dNdr[jno][1];
dtmp0 += gd[1][idim]*dNdr[ino][1]*Cons2[1][2]*gd[0][jdim]*dNdr[jno][1];
dtmp0 += gd[1][idim]*dNdr[ino][1]*Cons2[1][2]*gd[1][jdim]*dNdr[jno][0];
dtmp0 += gd[0][idim]*dNdr[ino][1]*Cons2[2][0]*gd[0][jdim]*dNdr[jno][0];
dtmp0 += gd[0][idim]*dNdr[ino][1]*Cons2[2][1]*gd[1][jdim]*dNdr[jno][1];
dtmp0 += gd[0][idim]*dNdr[ino][1]*Cons2[2][2]*gd[0][jdim]*dNdr[jno][1];
dtmp0 += gd[0][idim]*dNdr[ino][1]*Cons2[2][2]*gd[1][jdim]*dNdr[jno][0];
dtmp0 += gd[1][idim]*dNdr[ino][0]*Cons2[2][0]*gd[0][jdim]*dNdr[jno][0];
dtmp0 += gd[1][idim]*dNdr[ino][0]*Cons2[2][1]*gd[1][jdim]*dNdr[jno][1];
dtmp0 += gd[1][idim]*dNdr[ino][0]*Cons2[2][2]*gd[0][jdim]*dNdr[jno][1];
dtmp0 += gd[1][idim]*dNdr[ino][0]*Cons2[2][2]*gd[1][jdim]*dNdr[jno][0];
Kmat[ino][jno][idim][jdim] = dtmp0*Area;
}
}
const double dtmp1 = Area*
(+S2[0]*dNdr[ino][0]*dNdr[jno][0]
+S2[2]*dNdr[ino][0]*dNdr[jno][1]
+S2[2]*dNdr[ino][1]*dNdr[jno][0]
+S2[1]*dNdr[ino][1]*dNdr[jno][1]);
Kmat[ino][jno][0][0] += dtmp1;
Kmat[ino][jno][1][1] += dtmp1;
Kmat[ino][jno][2][2] += dtmp1;
}
}
for(unsigned int ino=0;ino<3;ino++){
for(unsigned int jno=ino+1;jno<3;jno++){
for(unsigned int idim=0;idim<3;idim++){
for(unsigned int jdim=0;jdim<3;jdim++){
Kmat[ino][jno][idim][jdim] = Kmat[jno][ino][jdim][idim];
}
}
}
}
}
*/
void GetMatRes_MassCST_BackwardEular
(double Kmat[3][3][3][3], double Res[3][3],
const double C[3][3], const double u[3][3], const double v[3][3],
const double lambda, const double myu,
const double rho, double gx, double gy, double gz,
const double dt, const double damp_coeff,
double& kinetic_energy,
double& strain_energy,
double& potential_energy )
{
double c[3][3] = {
{ C[0][0]+u[0][0], C[0][1]+u[0][1], C[0][2]+u[0][2] },
{ C[1][0]+u[1][0], C[1][1]+u[1][1], C[1][2]+u[1][2] },
{ C[2][0]+u[2][0], C[2][1]+u[2][1], C[2][2]+u[2][2] } };
GetKmatRes_CST(Kmat,Res, C,c, lambda, myu,strain_energy);
for(unsigned int i=0;i<3*3; i++){ (&Res[0][0])[i] *= dt; }
for(unsigned int ino=0;ino<3;ino++){
for(unsigned int idim=0;idim<3;idim++){
for(unsigned int jno=0;jno<3;jno++){
for(unsigned int jdim=0;jdim<3;jdim++){
Res[ino][idim] += Kmat[ino][jno][idim][jdim]*v[jno][jdim]*dt*dt;
}
}
}
}
for(unsigned int i=0;i<3*3*3*3;i++){ (&Kmat[0][0][0][0])[i] *= dt*(dt+damp_coeff); }
////
const double Area = Com::TriArea3D(C[0], C[1], C[2]);
const double tmp_r = Area/3.0*rho*dt;
Res[0][0] -= gx*tmp_r;
Res[0][1] -= gy*tmp_r;
Res[0][2] -= gz*tmp_r;
Res[1][0] -= gx*tmp_r;
Res[1][1] -= gy*tmp_r;
Res[1][2] -= gz*tmp_r;
Res[2][0] -= gx*tmp_r;
Res[2][1] -= gy*tmp_r;
Res[2][2] -= gz*tmp_r;
const double tmp_m = Area/3.0*rho;
for(unsigned int ino=0;ino<3;ino++){
Kmat[ino][ino][0][0] += tmp_m;
Kmat[ino][ino][1][1] += tmp_m;
Kmat[ino][ino][2][2] += tmp_m;
}
const double sqv0 = v[0][0]*v[0][0] + v[0][1]*v[0][1] + v[0][2]*v[0][2];
const double sqv1 = v[1][0]*v[1][0] + v[1][1]*v[1][1] + v[1][2]*v[1][2];
const double sqv2 = v[2][0]*v[2][0] + v[2][1]*v[2][1] + v[2][2]*v[2][2];
kinetic_energy += 0.5*tmp_m*(sqv0+sqv1+sqv2);
potential_energy -= tmp_m*( gx*(u[0][0]+u[1][0]+u[2][0]) + gy*(u[0][1]+u[1][1]+u[2][1]) + gz*(u[0][2]+u[1][2]+u[2][2]) );
}