// Set displacement differentiation matrix bmat.
// xi, et - local coordinates,
// returns determinant of Jacobian matrix
private double setBmatrix(double xi, double et)
{
// Derivatives of shape functions
double det = ShapeLin2D.deriv(xi, et, ind, xy, dnxy);
if (det <= 0)
{
UTIL.errorMsg("Negative/zero 4N element area");
}
if (FeModel.stressState == FeModel.StrStates.axisym)
{
ShapeLin2D.shape(xi, et, ind, an);
r = 0.0;
for (int i = 0; i < 4; i++)
{
r += an[i] * xy[i][0];
}
}
// Four blocks of the displacement differentiation matrix
for (int ib = 0; ib < 4; ib++)
{
bmat[0][2 * ib] = dnxy[ib][0];
bmat[0][2 * ib + 1] = 0.0;
bmat[1][2 * ib] = 0.0;
bmat[1][2 * ib + 1] = dnxy[ib][1];
bmat[2][2 * ib] = dnxy[ib][1];
bmat[2][2 * ib + 1] = dnxy[ib][0];
if (FeModel.stressState == FeModel.StrStates.axisym)
{
bmat[3][2 * ib] = an[ib] / r;
bmat[3][2 * ib + 1] = 0.0;
}
}
return(det);
}
// Compute thermal vector
public override void thermalVector()
{
// Zeros to thermal vector evec
for (int i = 0; i < 8; i++)
{
evec[i] = 0.0;
}
int ld = (FeModel.stressState == FeModel.StrStates.axisym) ? 4 : 3;
// Material mat
mat = (Material)fem.materials[matName];
mat.elasticityMatrix(emat);
double alpha = mat.getAlpha();
double nu = mat.getNu();
// Gauss integration loop
for (int ip = 0; ip < gh.nIntPoints; ip++)
{
// Set displacement differentiation matrix bmat
double det = setBmatrix(gh.xii[ip], gh.eti[ip]);
// Shape functions an
ShapeLin2D.shape(gh.xii[ip], gh.eti[ip], ind, an);
double t = 0.0;
for (int i = 0; i < 4; i++)
{
t += an[i] * dtn[i];
}
double dv = det * gh.wi[ip];
if (FeModel.stressState == FeModel.StrStates.axisym)
{
dv *= 2.0 * Math.PI * r;
}
ept[0] = alpha * t;
if (FeModel.stressState == FeModel.StrStates.plstrain)
{
ept[0] *= (1 + nu);
}
ept[1] = ept[0];
ept[2] = 0.0;
ept[3] = ept[0];
for (int i = 0; i < 8; i++)
{
double s = 0;
for (int j = 0; j < ld; j++)
{
for (int k = 0; k < ld; k++)
{
s += bmat[k][i] * emat[j][k] * ept[j] * this.t;
}
}
evec[i] += s * dv;
}
}
}
// Get temperature at integration point (stress)
public override double getTemperatureAtIntPoint(int ip)
{
ShapeLin2D.shape(gs.xii[ip], gs.eti[ip], ind, an);
double t = 0;
for (int i = 0; i < 4; i++)
{
t += an[i] * dtn[i];
}
return(t);
}