//send back the tangent
const XC::Matrix &XC::PlateFiberMaterial::getTangent(void) const
{
static XC::Matrix dd11(5,5);
static XC::Matrix dd12(5,1);
static XC::Matrix dd21(1,5);
static XC::Matrix dd22(1,1);
static XC::Matrix dd22invdd21(1,5);
static XC::Matrix threeDtangentCopy(6,6);
const XC::Matrix &threeDtangent = theMaterial->getTangent();
//swap matrix indices to sort out-of-plane components
int i,j, ii, jj;
for(i=0; i<6; i++) {
ii = this->indexMap(i);
for(j=0; j<6; j++) {
jj = this->indexMap(j);
threeDtangentCopy(ii,jj) = threeDtangent(i,j);
}//end for j
}//end for i
dd22(0,0) = threeDtangentCopy(5,5);
for(i=0; i<5; i++) {
dd12(i,0) = threeDtangentCopy(i,5);
dd21(0,i) = threeDtangentCopy(5,i);
for(int j=0; j<5; j++)
dd11(i,j) = threeDtangentCopy(i,j);
}//end for i
//int Solve(const XC::Vector &V, XC::Vector &res) const;
//int Solve(const XC::Matrix &M, XC::Matrix &res) const;
//condensation
dd22.Solve(dd21, dd22invdd21);
this->tangent = dd11;
this->tangent -= (dd12*dd22invdd21);
return this->tangent;
}
const Matrix&
BeamFiberMaterial::getInitialTangent()
{
const Matrix &threeDtangent = theMaterial->getInitialTangent();
static Matrix dd11(3,3);
dd11(0,0) = threeDtangent(0,0);
dd11(1,0) = threeDtangent(3,0);
dd11(2,0) = threeDtangent(5,0);
dd11(0,1) = threeDtangent(0,3);
dd11(1,1) = threeDtangent(3,3);
dd11(2,1) = threeDtangent(5,3);
dd11(0,2) = threeDtangent(0,5);
dd11(1,2) = threeDtangent(3,5);
dd11(2,2) = threeDtangent(5,5);
static Matrix dd12(3,3);
dd12(0,0) = threeDtangent(0,1);
dd12(1,0) = threeDtangent(3,1);
dd12(2,0) = threeDtangent(5,1);
dd12(0,1) = threeDtangent(0,2);
dd12(1,1) = threeDtangent(3,2);
dd12(2,1) = threeDtangent(5,2);
dd12(0,2) = threeDtangent(0,4);
dd12(1,2) = threeDtangent(3,4);
dd12(2,2) = threeDtangent(5,4);
static Matrix dd21(3,3);
dd21(0,0) = threeDtangent(1,0);
dd21(1,0) = threeDtangent(2,0);
dd21(2,0) = threeDtangent(4,0);
dd21(0,1) = threeDtangent(1,3);
dd21(1,1) = threeDtangent(2,3);
dd21(2,1) = threeDtangent(4,3);
dd21(0,2) = threeDtangent(1,5);
dd21(1,2) = threeDtangent(2,5);
dd21(2,2) = threeDtangent(4,5);
static Matrix dd22(3,3);
dd22(0,0) = threeDtangent(1,1);
dd22(1,0) = threeDtangent(2,1);
dd22(2,0) = threeDtangent(4,1);
dd22(0,1) = threeDtangent(1,2);
dd22(1,1) = threeDtangent(2,2);
dd22(2,1) = threeDtangent(4,2);
dd22(0,2) = threeDtangent(1,4);
dd22(1,2) = threeDtangent(2,4);
dd22(2,2) = threeDtangent(4,4);
//int Solve(const Vector &V, Vector &res) const;
//int Solve(const Matrix &M, Matrix &res) const;
//condensation
static Matrix dd22invdd21(3,3);
dd22.Solve(dd21, dd22invdd21);
//this->tangent = dd11;
//this->tangent -= (dd12*dd22invdd21);
dd11.addMatrixProduct(1.0, dd12, dd22invdd21, -1.0);
tangent = dd11;
return tangent;
}
const Vector&
BeamFiberMaterial::getStressSensitivity(int gradIndex,
bool conditional)
{
const Vector &threeDstress = theMaterial->getStressSensitivity(gradIndex, conditional);
stress(0) = threeDstress(0);
stress(1) = threeDstress(3);
stress(2) = threeDstress(5);
const Matrix &threeDtangent = theMaterial->getTangent();
static Matrix dd12(3,3);
dd12(0,0) = threeDtangent(0,1);
dd12(1,0) = threeDtangent(3,1);
dd12(2,0) = threeDtangent(5,1);
dd12(0,1) = threeDtangent(0,2);
dd12(1,1) = threeDtangent(3,2);
dd12(2,1) = threeDtangent(5,2);
dd12(0,2) = threeDtangent(0,4);
dd12(1,2) = threeDtangent(3,4);
dd12(2,2) = threeDtangent(5,4);
static Matrix dd22(3,3);
dd22(0,0) = threeDtangent(1,1);
dd22(1,0) = threeDtangent(2,1);
dd22(2,0) = threeDtangent(4,1);
dd22(0,1) = threeDtangent(1,2);
dd22(1,1) = threeDtangent(2,2);
dd22(2,1) = threeDtangent(4,2);
dd22(0,2) = threeDtangent(1,4);
dd22(1,2) = threeDtangent(2,4);
dd22(2,2) = threeDtangent(4,4);
static Vector sigma2(3);
sigma2(0) = threeDstress(1);
sigma2(1) = threeDstress(2);
sigma2(2) = threeDstress(4);
static Vector dd22sigma2(3);
dd22.Solve(sigma2,dd22sigma2);
stress.addMatrixVector(1.0, dd12, dd22sigma2, -1.0);
return stress;
}
//receive the strain
int
BeamFiberMaterial::setTrialStrain(const Vector &strainFromElement)
{
static const double tolerance = 1.0e-08;
strain(0) = strainFromElement(0);
strain(1) = strainFromElement(1);
strain(2) = strainFromElement(2);
//newton loop to solve for out-of-plane strains
double norm;
static Vector condensedStress(3);
static Vector strainIncrement(3);
static Vector threeDstrain(6);
static Matrix dd22(3,3);
int count = 0;
const int maxCount = 20;
double norm0;
do {
//set three dimensional strain
threeDstrain(0) = this->strain(0);
threeDstrain(1) = this->Tstrain22;
threeDstrain(2) = this->Tstrain33;
threeDstrain(3) = this->strain(1);
threeDstrain(4) = this->Tgamma23;
threeDstrain(5) = this->strain(2);
if (theMaterial->setTrialStrain(threeDstrain) < 0) {
opserr << "BeamFiberMaterial::setTrialStrain - setStrain failed in material with strain " << threeDstrain;
return -1;
}
//three dimensional stress
const Vector &threeDstress = theMaterial->getStress();
//three dimensional tangent
const Matrix &threeDtangent = theMaterial->getTangent();
//NDmaterial strain order = 11, 22, 33, 12, 23, 31
//BeamFiberMaterial strain order = 11, 12, 31, 22, 33, 23
condensedStress(0) = threeDstress(1);
condensedStress(1) = threeDstress(2);
condensedStress(2) = threeDstress(4);
dd22(0,0) = threeDtangent(1,1);
dd22(1,0) = threeDtangent(2,1);
dd22(2,0) = threeDtangent(4,1);
dd22(0,1) = threeDtangent(1,2);
dd22(1,1) = threeDtangent(2,2);
dd22(2,1) = threeDtangent(4,2);
dd22(0,2) = threeDtangent(1,4);
dd22(1,2) = threeDtangent(2,4);
dd22(2,2) = threeDtangent(4,4);
//set norm
norm = condensedStress.Norm();
if (count == 0)
norm0 = norm;
//condensation
dd22.Solve(condensedStress, strainIncrement);
//update out of plane strains
this->Tstrain22 -= strainIncrement(0);
this->Tstrain33 -= strainIncrement(1);
this->Tgamma23 -= strainIncrement(2);
} while (count++ < maxCount && norm > tolerance);
return 0;
}
const Matrix&
BeamFiberMaterial2d::getInitialTangent()
{
static Matrix dd11(2,2);
static Matrix dd12(2,4);
static Matrix dd21(4,2);
static Matrix dd22(4,4);
static Matrix dd22invdd21(4,4);
static Matrix threeDtangentCopy(6,6);
const Matrix &threeDtangent = theMaterial->getInitialTangent();
//swap matrix indices to sort out-of-plane components
int i, j , ii, jj;
for (i=0; i<6; i++) {
ii = this->indexMap(i);
for (j=0; j<6; j++) {
jj = this->indexMap(j);
threeDtangentCopy(ii,jj) = threeDtangent(i,j);
}//end for j
}//end for i
for (i=0; i<3; i++) {
for (j=0; j<3; j++) {
//dd11(i,j) = threeDtangentCopy(i, j );
//dd12(i,j) = threeDtangentCopy(i, j+3);
//dd21(i,j) = threeDtangentCopy(i+3,j );
//dd22(i,j) = threeDtangentCopy(i+3,j+3);
}
}
for (i = 0; i < 2; i++)
for (j = 0; j < 2; j++)
dd11(i,j) = threeDtangentCopy(i,j);
for (i = 0; i < 2; i++)
for (j = 0; j < 4; j++)
dd12(i,j) = threeDtangentCopy(i,j+2);
for (i = 0; i < 4; i++)
for (j = 0; j < 2; j++)
dd21(i,j) = threeDtangentCopy(i+2,j);
for (i = 0; i < 4; i++)
for (j = 0; j < 4; j++)
dd22(i,j) = threeDtangentCopy(i+2,j+2);
//int Solve(const Vector &V, Vector &res) const;
//int Solve(const Matrix &M, Matrix &res) const;
//condensation
dd22.Solve(dd21, dd22invdd21);
this->tangent = dd11;
this->tangent -= (dd12*dd22invdd21);
return this->tangent;
}
