const Vector&
ElasticIsotropicBeamFiber2d::getStressSensitivity(int gradIndex,
bool conditional)
{
sigma(0) = 0.0;
sigma(1) = 0.0;
if (parameterID == 1) { // E
//double mu = 0.5*E/(1.0+v);
double dmudE = 0.5/(1.0+v);
sigma(0) = Tepsilon(0);
sigma(1) = dmudE*Tepsilon(1);
}
if (parameterID == 2) { // nu
//double mu = 0.5*E/(1.0+v);
double dmudnu = -0.5*E/(1.0 + 2*v + v*v);
sigma(0) = 0.0;
sigma(1) = dmudnu*Tepsilon(1);
}
return sigma;
}
const Vector&
ElasticIsotropicBeamFiber2d::getStress (void)
{
double mu = 0.50*E/(1.0+v);
sigma(0) = E*Tepsilon(0);
sigma(1) = mu*Tepsilon(1);
return sigma;
}
const Vector&
ElasticIsotropicBeamFiber::getStressSensitivity(int gradIndex,
bool conditional)
{
sigma.Zero();
if (parameterID == 1) { // E
//double mu = 0.5*E/(1.0+v);
double dmudE = 0.5/(1.0+v);
sigma(0) = Tepsilon(0);
sigma(1) = dmudE*Tepsilon(1);
sigma(2) = dmudE*Tepsilon(2);
}
return sigma;
}
int
J2BeamFiber2d::commitSensitivity(const Vector &depsdh, int gradIndex, int numGrads)
{
if (SHVs == 0) {
SHVs = new Matrix(3,numGrads);
}
if (gradIndex >= SHVs->noCols()) {
//opserr << gradIndex << ' ' << SHVs->noCols() << endln;
return 0;
}
//return 0;
double dEdh = 0.0;
double dsigmaYdh = 0.0;
double dHkindh = 0.0;
double dHisodh = 0.0;
double dGdh = 0.0;
if (parameterID == 1) { // E
dEdh = 1.0;
dGdh = 0.5/(1.0+nu);
}
if (parameterID == 2) { // nu
dGdh = -0.5*E/(1.0 + 2.0*nu + nu*nu);
}
if (parameterID == 5) {
dsigmaYdh = 1.0;
}
if (parameterID == 6) {
dHkindh = 1.0;
}
if (parameterID == 7) {
dHisodh = 1.0;
}
double G = 0.5*E/(1.0+nu);
double depsPdh[2]; depsPdh[0] = 0.0; depsPdh[1] = 0.0;
double dalphadh = 0.0;
if (SHVs != 0) {
depsPdh[0] = (*SHVs)(0,gradIndex);
depsPdh[1] = (*SHVs)(1,gradIndex);
dalphadh = (*SHVs)(2,gradIndex);
}
static const double one3 = 1.0/3;
static const double two3 = 2.0*one3;
static const double root23 = sqrt(two3);
double xsi[2];
xsi[0] = E*(Tepsilon(0)-epsPn1[0]) - Hkin*epsPn1[0];
xsi[1] = G*(Tepsilon(1)-epsPn1[1]) - one3*Hkin*epsPn1[1];
double q = sqrt(two3*xsi[0]*xsi[0] + 2.0*xsi[1]*xsi[1]);
double F = q - root23*(sigmaY + Hiso*alphan1);
if (F <= -100*DBL_EPSILON) {
// Do nothing
}
else {
static Matrix J(3,3);
static Vector b(3);
static Vector dx(3);
double dg = dg_n1;
J(0,0) = 1.0 + dg*two3*(E+Hkin); J(0,1) = 0.0;
J(1,0) = 0.0; J(1,1) = 1.0 + dg*(2.0*G+two3*Hkin);
J(0,2) = two3*(E+Hkin)*xsi[0];
J(1,2) = (2.0*G+two3*Hkin)*xsi[1];
//J(2,0) = xsi[0]*two3/q; J(2,1) = xsi[1]*2.0/q;
J(2,0) = (1.0-two3*Hiso*dg)*xsi[0]*two3/q;
J(2,1) = (1.0-two3*Hiso*dg)*xsi[1]*2.0/q;
//J(2,2) = -root23*Hiso;
J(2,2) = -two3*Hiso*q;
b(0) = E*depsdh(0) + dEdh*Tepsilon(0) - (E+ Hkin)*depsPdh[0] - (dEdh+ dHkindh)*epsPn1[0];
b(1) = G*depsdh(1) + dGdh*Tepsilon(1) - (G+one3*Hkin)*depsPdh[1] - (dGdh+one3*dHkindh)*epsPn1[1];
b(2) = root23*(dsigmaYdh + dHisodh*alphan1 + Hiso*dalphadh);
J.Solve(b, dx);
dalphadh += dx(2)*root23*q + dg*root23*(xsi[0]*two3*dx(0)+xsi[1]*2.0*dx(1))/q;
depsPdh[0] += dx(2)*two3*xsi[0] + dg*two3*dx(0);
depsPdh[1] += dx(2)* 2.0*xsi[1] + dg* 2.0*dx(1);
(*SHVs)(0,gradIndex) = depsPdh[0];
(*SHVs)(1,gradIndex) = depsPdh[1];
(*SHVs)(2,gradIndex) = dalphadh;
}
return 0;
}
const Vector&
J2BeamFiber2d::getStressSensitivity(int gradIndex, bool conditional)
{
static Vector sigma(2);
sigma(0) = 0.0;
sigma(1) = 0.0;
double dEdh = 0.0;
double dsigmaYdh = 0.0;
double dHkindh = 0.0;
double dHisodh = 0.0;
double dGdh = 0.0;
if (parameterID == 1) { // E
dEdh = 1.0;
dGdh = 0.5/(1.0+nu);
}
if (parameterID == 2) { // nu
dGdh = -0.5*E/(1.0 + 2.0*nu + nu*nu);
}
if (parameterID == 5) {
dsigmaYdh = 1.0;
}
if (parameterID == 6) {
dHkindh = 1.0;
}
if (parameterID == 7) {
dHisodh = 1.0;
}
double G = 0.5*E/(1.0+nu);
double depsPdh[2]; depsPdh[0] = 0.0; depsPdh[1] = 0.0;
double dalphadh = 0.0;
if (SHVs != 0) {
depsPdh[0] = (*SHVs)(0,gradIndex);
depsPdh[1] = (*SHVs)(1,gradIndex);
dalphadh = (*SHVs)(2,gradIndex);
}
static const double one3 = 1.0/3;
static const double two3 = 2.0*one3;
static const double root23 = sqrt(two3);
double xsi[2];
xsi[0] = E*(Tepsilon(0)-epsPn1[0]) - Hkin*epsPn1[0];
xsi[1] = G*(Tepsilon(1)-epsPn1[1]) - one3*Hkin*epsPn1[1];
double q = sqrt(two3*xsi[0]*xsi[0] + 2.0*xsi[1]*xsi[1]);
double F = q - root23*(sigmaY + Hiso*alphan1);
if (F <= -100*DBL_EPSILON) {
sigma(0) = dEdh*(Tepsilon(0)-epsPn1[0]) - E*depsPdh[0];
sigma(1) = dGdh*(Tepsilon(1)-epsPn1[1]) - G*depsPdh[1];
}
else {
static Matrix J(3,3);
static Vector b(3);
static Vector dx(3);
double dg = dg_n1;
J(0,0) = 1.0 + dg*two3*(E+Hkin); J(0,1) = 0.0;
J(1,0) = 0.0; J(1,1) = 1.0 + dg*(2.0*G+two3*Hkin);
J(0,2) = two3*(E+Hkin)*xsi[0];
J(1,2) = (2.0*G+two3*Hkin)*xsi[1];
//J(2,0) = xsi[0]*two3/q; J(2,1) = xsi[1]*2.0/q;
J(2,0) = (1.0-two3*Hiso*dg)*xsi[0]*two3/q;
J(2,1) = (1.0-two3*Hiso*dg)*xsi[1]*2.0/q;
//J(2,2) = -root23*Hiso;
J(2,2) = -two3*Hiso*q;
b(0) = dEdh*Tepsilon(0) - (E+ Hkin)*depsPdh[0] - (dEdh+ dHkindh)*epsPn1[0];
b(1) = dGdh*Tepsilon(1) - (G+one3*Hkin)*depsPdh[1] - (dGdh+one3*dHkindh)*epsPn1[1];
b(2) = root23*(dsigmaYdh + dHisodh*alphan1 + Hiso*dalphadh);
J.Solve(b, dx);
depsPdh[0] += dx(2)*two3*xsi[0] + dg*two3*dx(0);
depsPdh[1] += dx(2)* 2.0*xsi[1] + dg* 2.0*dx(1);
sigma(0) = dx(0) + Hkin*depsPdh[0] + dHkindh*epsPn1[0];
sigma(1) = dx(1) + one3*Hkin*depsPdh[1] + one3*dHkindh*epsPn1[1];
}
return sigma;
}
const Vector&
J2BeamFiber2d::getStress (void)
{
double G = 0.5*E/(1.0+nu);
sigma(0) = E*(Tepsilon(0)-epsPn[0]);
sigma(1) = G*(Tepsilon(1)-epsPn[1]);
static const double one3 = 1.0/3;
static const double two3 = 2.0*one3;
static const double root23 = sqrt(two3);
double xsi[2];
//xsi[0] = sigma(0) - two3*Hkin*1.5*epsPn[0];
//xsi[1] = sigma(1) - two3*Hkin*0.5*epsPn[1];
xsi[0] = sigma(0) - Hkin*epsPn[0];
xsi[1] = sigma(1) - one3*Hkin*epsPn[1];
double q = sqrt(two3*xsi[0]*xsi[0] + 2.0*xsi[1]*xsi[1]);
double F = q - root23*(sigmaY + Hiso*alphan);
if (F < -100*DBL_EPSILON) {
epsPn1[0] = epsPn[0];
epsPn1[1] = epsPn[1];
}
else {
// Solve for dg
double dg = 0.0;
static Vector R(3);
R(0) = 0.0; R(1) = 0.0; R(2) = F;
static Vector x(3);
x(0) = xsi[0]; x(1) = xsi[1]; x(2) = dg;
static Matrix J(3,3);
static Vector dx(3);
int iter = 0; int maxIter = 25;
while (iter < maxIter && R.Norm() > sigmaY*1.0e-14) {
iter++;
J(0,0) = 1.0 + dg*two3*(E+Hkin); J(0,1) = 0.0;
J(1,0) = 0.0; J(1,1) = 1.0 + dg*(2.0*G+two3*Hkin);
J(0,2) = two3*(E+Hkin)*x(0);
J(1,2) = (2.0*G+two3*Hkin)*x(1);
//J(2,0) = x(0)*two3/q; J(2,1) = x(1)*2.0/q;
J(2,0) = (1.0-two3*Hiso*dg)*x(0)*two3/q;
J(2,1) = (1.0-two3*Hiso*dg)*x(1)*2.0/q;
//J(2,2) = -root23*Hiso;
J(2,2) = -two3*Hiso*q;
J.Solve(R, dx);
x = x-dx;
dg = x(2);
dg_n1 = dg;
q = sqrt(two3*x(0)*x(0) + 2.0*x(1)*x(1));
R(0) = x(0) - xsi[0] + dg*two3*(E+Hkin)*x(0);
R(1) = x(1) - xsi[1] + dg*(2.0*G+two3*Hkin)*x(1);
R(2) = q - root23*(sigmaY + Hiso*(alphan+dg*root23*q));
}
if (iter == maxIter) {
//opserr << "J2BeamFiber2d::getStress -- maxIter reached " << R.Norm() << endln;
}
alphan1 = alphan + dg*root23*q;
epsPn1[0] = epsPn[0] + dg*two3*x(0);
epsPn1[1] = epsPn[1] + dg*2.0*x(1);
//sigma(0) = x(0) + two3*Hkin*1.5*epsPn1[0];
//sigma(1) = x(1) + two3*Hkin*0.5*epsPn1[1];
sigma(0) = x(0) + Hkin*epsPn1[0];
sigma(1) = x(1) + one3*Hkin*epsPn1[1];
}
return sigma;
}
const Matrix&
J2BeamFiber2d::getTangent (void)
{
double twoG = E/(1.0+nu);
double G = 0.5*twoG;
double sig[2];
sig[0] = E*(Tepsilon(0)-epsPn[0]);
sig[1] = G*(Tepsilon(1)-epsPn[1]);
static const double one3 = 1.0/3;
static const double two3 = 2.0*one3;
static const double root23 = sqrt(two3);
double two3Hkin = two3*Hkin;
double xsi[2];
//xsi[0] = sig[0] - two3*Hkin*1.5*epsPn[0];
//xsi[1] = sig[1] - two3*Hkin*0.5*epsPn[1];
xsi[0] = sig[0] - Hkin*epsPn[0];
xsi[1] = sig[1] - one3*Hkin*epsPn[1];
double q = sqrt(two3*xsi[0]*xsi[0] + 2.0*xsi[1]*xsi[1]);
double F = q - root23*(sigmaY + Hiso*alphan);
if (F < -100*DBL_EPSILON) {
D(0,0) = E;
D(1,1) = G;
D(0,1) = D(1,0) = 0.0;
epsPn1[0] = epsPn[0];
epsPn1[1] = epsPn[1];
}
else {
// Solve for dg
double dg = 0.0;
static Vector R(3);
R(0) = 0.0; R(1) = 0.0; R(2) = F;
static Vector x(3);
x(0) = xsi[0]; x(1) = xsi[1]; x(2) = dg;
static Matrix J(3,3);
static Vector dx(3);
int iter = 0; int maxIter = 25;
while (iter < maxIter && R.Norm() > sigmaY*1.0e-14) {
iter++;
J(0,0) = 1.0 + dg*two3*(E+Hkin); J(0,1) = 0.0;
J(1,0) = 0.0; J(1,1) = 1.0 + dg*(twoG+two3Hkin);
J(0,2) = two3*(E+Hkin)*x(0);
J(1,2) = (twoG+two3Hkin)*x(1);
//J(2,0) = x(0)*two3/q; J(2,1) = x(1)*2.0/q;
J(2,0) = (1.0-two3*Hiso*dg)*x(0)*two3/q;
J(2,1) = (1.0-two3*Hiso*dg)*x(1)*2.0/q;
//J(2,2) = -root23*Hiso;
J(2,2) = -two3*Hiso*q;
J.Solve(R, dx);
x.addVector(1.0, dx, -1.0);
dg = x(2);
dg_n1 = dg;
q = sqrt(two3*x(0)*x(0) + 2.0*x(1)*x(1));
R(0) = x(0) - xsi[0] + dg*two3*(E+Hkin)*x(0);
R(1) = x(1) - xsi[1] + dg*(twoG+two3Hkin)*x(1);
R(2) = q - root23*(sigmaY + Hiso*(alphan+dg*root23*q));
}
if (iter == maxIter) {
//opserr << "J2BeamFiber2d::getTangent -- maxIter reached " << R.Norm() << endln;
}
alphan1 = alphan + dg*root23*q;
epsPn1[0] = epsPn[0] + dg*two3*x(0);
epsPn1[1] = epsPn[1] + dg*2.0*x(1);
//J(2,0) = (1.0-two3*Hiso*dg)*x(0)*two3/q; J(2,1) = (1.0-two3*Hiso*dg)*x(1)*2.0/q;
//J(2,2) = -two3*Hiso*q;
//static Matrix invJ(3,3);
//J.Invert(invJ);
J(0,0) = 1.0 + dg*two3*E/(1.0+dg*two3Hkin); J(0,1) = 0.0;
J(1,0) = 0.0; J(1,1) = 1.0 + dg*twoG/(1.0+dg*two3Hkin);
J(0,2) = (two3*E-dg*two3*E/(1.0+dg*two3Hkin)*two3Hkin)*x(0);
J(1,2) = (twoG -dg* twoG/(1.0+dg*two3Hkin)*two3Hkin)*x(1);
//J(2,0) = x(0)/q*two3/(1.0+dg*two3Hkin);
//J(2,1) = x(1)/q* 2.0/(1.0+dg*two3Hkin);
J(2,0) = (1.0-two3*Hiso*dg)*x(0)/q*two3/(1.0+dg*two3Hkin);
J(2,1) = (1.0-two3*Hiso*dg)*x(1)/q* 2.0/(1.0+dg*two3Hkin);
//J(2,2) = -(x(0)/q*two3/(1.0+dg*two3Hkin)*two3Hkin*x(0))
// -(x(1)/q* 2.0/(1.0+dg*two3Hkin)*two3Hkin*x(1));
//J(2,2) = -q*two3Hkin/(1.0+dg*two3Hkin) - root23*Hiso;
J(2,2) = -q*two3Hkin/(1.0+dg*two3Hkin) - two3*Hiso*q;
static Matrix invJ(3,3);
J.Invert(invJ);
D(0,0) = invJ(0,0)*E;
D(1,0) = invJ(1,0)*E;
D(0,1) = invJ(0,1)*G;
D(1,1) = invJ(1,1)*G;
}
return D;
}
