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// Gmsh - Copyright (C) 1997-2020 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file for license information. Please report all
// issues on https://gitlab.onelab.info/gmsh/gmsh/issues.
#include "elasticityTerm.h"
#include "Numeric.h"
// The SElement (Solver element) that has been sent to the function
// contains 2 enrichments, that can enrich both shape and test functions
void elasticityTerm::createData(MElement *e) const
{
if(_data.find(e->getTypeForMSH()) != _data.end()) return;
elasticityDataAtGaussPoint d;
int nbSF = (int)e->getNumShapeFunctions();
int integrationOrder = 2 * (e->getPolynomialOrder() - 1);
int npts;
IntPt *GP;
double gs[100][3];
e->getIntegrationPoints(integrationOrder, &npts, &GP);
for(int i = 0; i < npts; i++) {
fullMatrix<double> a(nbSF, 3);
const double u = GP[i].pt[0];
const double v = GP[i].pt[1];
const double w = GP[i].pt[2];
const double weight = GP[i].weight;
e->getGradShapeFunctions(u, v, w, gs);
for(int j = 0; j < nbSF; j++) {
a(j, 0) = gs[j][0];
a(j, 1) = gs[j][1];
a(j, 2) = gs[j][2];
}
d.gradSF.push_back(a);
d.u.push_back(u);
d.v.push_back(v);
d.w.push_back(w);
d.weight.push_back(weight);
}
_data[e->getTypeForMSH()] = d;
}
void elasticityTerm::elementMatrix(SElement *se, fullMatrix<double> &m) const
{
MElement *e = se->getMeshElement();
createData(e);
int nbSF = (int)e->getNumShapeFunctions();
elasticityDataAtGaussPoint &d = _data[e->getTypeForMSH()];
int npts = d.u.size();
m.setAll(0.);
double FACT = _e / (1 + _nu);
double C11 = FACT * (1 - _nu) / (1 - 2 * _nu);
double C12 = FACT * _nu / (1 - 2 * _nu);
double C44 = (C11 - C12) / 2;
const double C[6][6] = {{C11, C12, C12, 0, 0, 0}, {C12, C11, C12, 0, 0, 0},
{C12, C12, C11, 0, 0, 0}, {0, 0, 0, C44, 0, 0},
{0, 0, 0, 0, C44, 0}, {0, 0, 0, 0, 0, C44}};
fullMatrix<double> H(6, 6);
fullMatrix<double> B(6, 3 * nbSF);
fullMatrix<double> BTH(3 * nbSF, 6);
fullMatrix<double> BT(3 * nbSF, 6);
for(int i = 0; i < 6; i++)
for(int j = 0; j < 6; j++) H(i, j) = C[i][j];
double jac[3][3], invjac[3][3], Grads[100][3];
for(int i = 0; i < npts; i++) {
const double weight = d.weight[i];
const fullMatrix<double> &grads = d.gradSF[i];
const double detJ = e->getJacobian(grads, jac);
inv3x3(jac, invjac);
for(int j = 0; j < nbSF; j++) {
Grads[j][0] = invjac[0][0] * grads(j, 0) + invjac[0][1] * grads(j, 1) +
invjac[0][2] * grads(j, 2);
Grads[j][1] = invjac[1][0] * grads(j, 0) + invjac[1][1] * grads(j, 1) +
invjac[1][2] * grads(j, 2);
Grads[j][2] = invjac[2][0] * grads(j, 0) + invjac[2][1] * grads(j, 1) +
invjac[2][2] * grads(j, 2);
}
B.setAll(0.);
BT.setAll(0.);
if(se->getShapeEnrichement() == se->getTestEnrichement()) {
for(int j = 0; j < nbSF; j++) {
BT(j, 0) = B(0, j) = Grads[j][0];
BT(j, 3) = B(3, j) = Grads[j][1];
BT(j, 5) = B(5, j) = Grads[j][2];
BT(j + nbSF, 1) = B(1, j + nbSF) = Grads[j][1];
BT(j + nbSF, 3) = B(3, j + nbSF) = Grads[j][0];
BT(j + nbSF, 4) = B(4, j + nbSF) = Grads[j][2];
BT(j + 2 * nbSF, 2) = B(2, j + 2 * nbSF) = Grads[j][2];
BT(j + 2 * nbSF, 4) = B(4, j + 2 * nbSF) = Grads[j][1];
BT(j + 2 * nbSF, 5) = B(5, j + 2 * nbSF) = Grads[j][0];
}
}
else {
/*
se->gradNodalTestFunctions (u, v, w, invjac,GradsT);
for (int j = 0; j < nbSF; j++){
BT(j, 0) = Grads[j][0]; B(0, j) = GradsT[j][0];
BT(j, 3) = Grads[j][1]; B(3, j) = GradsT[j][1];
BT(j, 5) = Grads[j][2]; B(5, j) = GradsT[j][2];
BT(j + nbSF, 1) = Grads[j][1]; B(1, j + nbSF) = GradsT[j][1];
BT(j + nbSF, 3) = Grads[j][0]; B(3, j + nbSF) = GradsT[j][0];
BT(j + nbSF, 4) = Grads[j][2]; B(4, j + nbSF) = GradsT[j][2];
BT(j + 2 * nbSF, 2) = Grads[j][2]; B(2, j + 2 * nbSF) = GradsT[j][2];
BT(j + 2 * nbSF, 4) = Grads[j][1]; B(4, j + 2 * nbSF) = GradsT[j][1];
BT(j + 2 * nbSF, 5) = Grads[j][0]; B(5, j + 2 * nbSF) = GradsT[j][0];
}
*/
}
BTH.setAll(0.);
BTH.gemm(BT, H);
m.gemm(BTH, B, weight * detJ, 1.);
}
}
void elasticityTerm::elementVector(SElement *se, fullVector<double> &m) const
{
MElement *e = se->getMeshElement();
int nbSF = (int)e->getNumShapeFunctions();
int integrationOrder = 2 * e->getPolynomialOrder();
int npts;
IntPt *GP;
double jac[3][3];
double ff[256];
e->getIntegrationPoints(integrationOrder, &npts, &GP);
m.scale(0.);
for(int i = 0; i < npts; i++) {
const double u = GP[i].pt[0];
const double v = GP[i].pt[1];
const double w = GP[i].pt[2];
const double weight = GP[i].weight;
const double detJ = e->getJacobian(u, v, w, jac);
se->nodalTestFunctions(u, v, w, ff);
for(int j = 0; j < nbSF; j++) {
m(j) += _volumeForce.x() * ff[j] * weight * detJ * .5;
m(j + nbSF) += _volumeForce.y() * ff[j] * weight * detJ * .5;
m(j + 2 * nbSF) += _volumeForce.z() * ff[j] * weight * detJ * .5;
}
}
}
/*
B_d is the deviatoric part of the FE strains
K_{uu} = \int_\Omega B^T_d H B_d dv
*/
void elasticityMixedTerm::elementMatrix(SElement *se,
fullMatrix<double> &m) const
{
setPolynomialBasis(se);
MElement *e = se->getMeshElement();
int integrationOrder = 4 * (e->getPolynomialOrder()) + 2;
int npts;
IntPt *GP;
double jac[3][3];
double invjac[3][3];
double Grads[100][3];
double SF[100];
e->getIntegrationPoints(integrationOrder, &npts, &GP);
m.setAll(0.);
fullMatrix<double> KUU(3 * _sizeN, 3 * _sizeN);
fullMatrix<double> KUP(3 * _sizeN, _sizeM);
fullMatrix<double> KUG(3 * _sizeN, _sizeM);
fullMatrix<double> KPG(_sizeM, _sizeM);
fullMatrix<double> KGG(_sizeM, _sizeM);
fullMatrix<double> KPP(_sizeM, _sizeM); // stabilization
double FACT = _e / ((1 + _nu) * (1. - 2 * _nu));
double C11 = FACT * (1 - _nu);
double C12 = FACT * _nu;
double C44 = FACT * (1 - 2. * _nu) * .5;
// double _k = 3*_e / (1 - 2 * _nu);
// FIXME : PLANE STRESS !!!
// FACT = _e / (1-_nu*_nu);
// C11 = FACT;
// C12 = _nu * FACT;
// C44 = (1.-_nu)*.5*FACT;
const double C[6][6] = {{C11, C12, C12, 0, 0, 0}, {C12, C11, C12, 0, 0, 0},
{C12, C12, C11, 0, 0, 0}, {0, 0, 0, C44, 0, 0},
{0, 0, 0, 0, C44, 0}, {0, 0, 0, 0, 0, C44}};
fullMatrix<double> H(6, 6);
fullMatrix<double> B(6, 3 * _sizeN);
fullMatrix<double> BDEV(6, 3 * _sizeN);
fullMatrix<double> BDIL(1, 3 * _sizeN);
fullMatrix<double> BDILT(3 * _sizeN, 1);
fullMatrix<double> BTH(3 * _sizeN, 6);
fullMatrix<double> BT(3 * _sizeN, 6);
fullMatrix<double> trBTH(3 * _sizeN, 1);
fullMatrix<double> MT(_sizeM, 1);
fullMatrix<double> M(1, _sizeM);
for(int i = 0; i < 6; i++)
for(int j = 0; j < 6; j++) H(i, j) = C[i][j];
double _dimension = 2.0;
for(int i = 0; i < npts; i++) {
const double u = GP[i].pt[0];
const double v = GP[i].pt[1];
const double w = GP[i].pt[2];
const double weight = GP[i].weight;
const double detJ = e->getJacobian(u, v, w, jac);
inv3x3(jac, invjac);
se->gradNodalShapeFunctions(u, v, w, invjac, Grads);
e->getShapeFunctions(u, v, w, SF, _polyOrderM);
B.setAll(0.);
BT.setAll(0.);
const double K =
.0000002 * weight * detJ *
pow(detJ, 2 / _dimension); // the second detJ is for stabilization
for(int j = 0; j < _sizeM; j++) {
for(int k = 0; k < _sizeM; k++) {
KPP(j, k) += (Grads[j][0] * Grads[k][0] + Grads[j][1] * Grads[k][1] +
Grads[j][2] * Grads[k][2]) *
K;
}
}
const double K2 = weight * detJ;
for(int j = 0; j < _sizeN; j++) {
for(int k = 0; k < _sizeM; k++) {
KUP(j + 0 * _sizeN, k) += Grads[j][0] * SF[k] * K2;
KUP(j + 1 * _sizeN, k) += Grads[j][1] * SF[k] * K2;
KUP(j + 2 * _sizeN, k) += Grads[j][2] * SF[k] * K2;
}
}
/*
const double K3 = weight * detJ * _e/(2*(1+_nu));
for (int j = 0; j < _sizeN; j++){
for (int k = 0; k < _sizeN; k++){
const double fa = (Grads[j][0] * Grads[k][0] +
Grads[j][1] * Grads[k][1] +
Grads[j][2] * Grads[k][2]) * K3;
KUU(j+0*_sizeN, k+0*_sizeN) += fa;
KUU(j+1*_sizeN, k+1*_sizeN) += fa;
KUU(j+2*_sizeN, k+2*_sizeN) += fa;
}
}
*/
for(int j = 0; j < _sizeN; j++) {
// printf("%g %g %g\n",Grads[j][0],Grads[j][1],Grads[j][2]);
BDILT(j, 0) = BDIL(0, j) = Grads[j][0] / _dimension;
BT(j, 0) = B(0, j) = Grads[j][0]; //-Grads[j][0]/_dimension;
// BT(j, 1) = B(1, j) = -Grads[j][1]/_dimension;
// BT(j, 2) = B(2, j) = -Grads[j][2]/_dimension;
BT(j, 3) = B(3, j) = Grads[j][1];
BT(j, 4) = B(4, j) = Grads[j][2];
BDILT(j + _sizeN, 0) = BDIL(0, j + _sizeN) = Grads[j][1] / _dimension;
// BT(j + _sizeN, 0) = B(0, j + _sizeN) = -Grads[j][0]/_dimension;
BT(j + _sizeN, 1) = B(1, j + _sizeN) =
Grads[j][1]; //-Grads[j][1]/_dimension;
// BT(j + _sizeN, 2) = B(2, j + _sizeN) = -Grads[j][2]/_dimension;
BT(j + _sizeN, 3) = B(3, j + _sizeN) = Grads[j][0];
BT(j + _sizeN, 5) = B(5, j + _sizeN) = Grads[j][2];
BDILT(j + 2 * _sizeN, 0) = BDIL(0, j + 2 * _sizeN) =
Grads[j][2] / _dimension;
// BT(j + 2 * _sizeN, 0) = B(0, j + 2 * _sizeN) =
// -Grads[j][0]/_dimension; BT(j + 2 * _sizeN, 1) = B(1, j + 2 *
// _sizeN) = -Grads[j][1]/_dimension;
BT(j + 2 * _sizeN, 2) = B(2, j + 2 * _sizeN) =
Grads[j][2]; //-Grads[j][2]/_dimension;
BT(j + 2 * _sizeN, 4) = B(4, j + 2 * _sizeN) = Grads[j][1];
BT(j + 2 * _sizeN, 5) = B(5, j + 2 * _sizeN) = Grads[j][0];
}
for(int j = 0; j < _sizeM; j++) {
MT(j, 0) = M(0, j) = SF[j];
}
// printf("BT (%d %d) x H (%d,%d) = BTH(%d,%d)\n",BT.size1(),BT.size2(),
// H.size1(),H.size2(),BTH.size1(),BTH.size2());
BTH.setAll(0.);
BTH.gemm(BT, H);
for(int j = 0; j < 3 * _sizeN; j++) {
trBTH(j, 0) = BTH(j, 0) + BTH(j, 1) + BTH(j, 2);
}
KUU.gemm(BTH, B, weight * detJ);
// KUP.gemm(BDILT, M, weight * detJ);
// KPG.gemm(MT, M, -weight * detJ);
// KUG.gemm(trBTH, M, weight * detJ/_dimension);
// KGG.gemm(MT, M, weight * detJ * (_k)/(_dimension*_dimension));
}
/*
3*_sizeN _sizeM _sizeM
KUU KUP KUG
m = KUP^t KPP KPG
KUG^T KPG^t KGG
*/
for(int i = 0; i < 3 * _sizeN; i++) {
for(int j = 0; j < 3 * _sizeN; j++) m(i, j) = KUU(i, j); // assemble KUU
for(int j = 0; j < _sizeM; j++) {
m(i, j + 3 * _sizeN) = KUP(i, j); // assemble KUP
m(j + 3 * _sizeN, i) = KUP(i, j); // assemble KUP^T
}
for(int j = 0; j < _sizeM; j++) {
m(i, j + 3 * _sizeN + _sizeM) = KUG(i, j); // assemble KUG
m(j + 3 * _sizeN + _sizeM, i) = KUG(i, j); // assemble KUG^t
}
}
for(int i = 0; i < _sizeM; i++) {
for(int j = 0; j < _sizeM; j++) {
m(i + 3 * _sizeN, j + 3 * _sizeN + _sizeM) = KPG(i, j); // assemble KPG
m(j + 3 * _sizeN + _sizeM, i + 3 * _sizeN) = KPG(i, j); // assemble KPG^t
m(i + 3 * _sizeN + _sizeM, j + 3 * _sizeN + _sizeM) =
KGG(i, j); // assemble KGG
m(i + 3 * _sizeN, j + 3 * _sizeN) = KPP(i, j); // assemble KPP
}
}
// m.print("Mixed");
return;
}
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