// Get strains at integration point.
// ip - integration point number (stress);
// returns strain vector (ex, ey, ez, gxy, gyz, gzx)
public override double[] getStrainsAtIntPoint(int ip)
{
// Derivatives of shape functions
ShapeLin3D.deriv(gs.xii[ip], gs.eti[ip], gs.zei[ip], ind, xy, dnxy);
// Derivatives of displacements
double dux, duy, duz, dvx, dvy, dvz, dwx, dwy, dwz;
dux = duy = duz = dvx = dvy = dvz = dwx = dwy = dwz = 0;
for (int i = 0; i < 8; i++)
{
double dnx = dnxy[i][0];
double dny = dnxy[i][1];
double dnz = dnxy[i][2];
double u = evec[3 * i];
double v = evec[3 * i + 1];
double w = evec[3 * i + 2];
dux += dnx * u; duy += dny * u; duz += dnz * u;
dvx += dnx * v; dvy += dny * v; dvz += dnz * v;
dwx += dnx * w; dwy += dny * w; dwz += dnz * w;
}
// Strains
double[] strain = new double[6];
strain[0] = dux; strain[1] = dvy; strain[2] = dwz;
strain[3] = duy + dvx;
strain[4] = dvz + dwy;
strain[5] = duz + dwx;
return(strain);
}
// Compute equivalent stress vector (with negative sign)
public override void equivStressVector()
{
for (int i = 0; i < 24; i++)
{
evec[i] = 0.0;
}
for (int ip = 0; ip < gs.nIntPoints; ip++)
{
// Accumulated stress s
double[] s = new double[6];
for (int i = 0; i < 6; i++)
{
s[i] = str[ip].sStress[i] + str[ip].dStress[i];
}
double det = ShapeLin3D.deriv(gs.xii[ip], gs.eti[ip], gs.zei[ip], ind, xy, dnxy);
double dv = det * gs.wi[ip];
for (int i = 0; i < 8; i++)
{
double a0 = dnxy[i][0];
double a1 = dnxy[i][1];
double a2 = dnxy[i][2];
evec[i * 3] -= (a0 * s[0] + a1 * s[3] + a2 * s[5]) * dv;
evec[i * 3 + 1] -= (a1 * s[1] + a0 * s[3] + a2 * s[4]) * dv;
evec[i * 3 + 2] -= (a2 * s[2] + a1 * s[4] + a0 * s[5]) * dv;
}
}
}
// Compute thermal vector
public override void thermalVector()
{
for (int i = 0; i < 24; i++)
{
evec[i] = 0.0;
}
mat = (Material)fem.materials[matName];
double alpha = mat.getAlpha();
double lambda = mat.getLambda();
double mu = mat.getMu();
double g = 3.0 * lambda + 2.0 * mu;
for (int ip = 0; ip < gh.nIntPoints; ip++)
{
ShapeLin3D.shape(gh.xii[ip], gh.eti[ip], gh.zei[ip], ind, an);
// Temperature at integration point
double t = 0;
for (int i = 0; i < 8; i++)
{
t += an[i] * dtn[i];
}
double det = ShapeLin3D.deriv(gh.xii[ip], gh.eti[ip], gh.zei[ip], ind, xy, dnxy);
double dv = g * alpha * t * det * gh.wi[ip];
for (int i = 0; i < 8; i++)
{
for (int j = 0; j < 3; j++)
{
evec[i * 3 + j] += dnxy[i][j] * dv;
}
}
}
}
// Returns temperature at integration point (stress)
public override double getTemperatureAtIntPoint(int ip)
{
ShapeLin3D.shape(gs.xii[ip], gs.eti[ip], gs.zei[ip], ind, an);
double t = 0;
for (int i = 0; i < 8; i++)
{
t += an[i] * dtn[i];
}
return(t);
}
// Compute stiffness matrix
public override void stiffnessMatrix()
{
for (int i = 0; i < 24; i++)
{
for (int j = i; j < 24; j++)
{
kmat[i][j] = 0.0;
}
}
// Material mat
mat = (Material)fem.materials[matName];
if (mat == null)
{
UTIL.errorMsg("Element material name: " + matName);
}
double lambda = mat.getLambda();
double mu = mat.getMu();
double beta = lambda + 2 * mu;
for (int ip = 0; ip < gk.nIntPoints; ip++)
{
double det = ShapeLin3D.deriv(gk.xii[ip], gk.eti[ip], gk.zei[ip], ind, xy, dnxy);
double dv = det * gk.wi[ip];
// Upper symmetrical part of the matrix by rows
for (int i = 0; i < 8; i++)
{ // i = row
// dNi/dx, dNi/dy, dNi/dz
double dix = dnxy[i][0];
double diy = dnxy[i][1];
double diz = dnxy[i][2];
for (int j = i; j < 8; j++)
{ // j = column
// dNj/dx, dNj/dy, dNj/dz
double djx = dnxy[j][0];
double djy = dnxy[j][1];
double djz = dnxy[j][2];
kmat[i * 3][j * 3] += (beta * dix * djx
+ mu * (diy * djy + diz * djz)) * dv;
kmat[i * 3][j * 3 + 1] += (lambda * dix * djy
+ mu * diy * djx) * dv;
kmat[i * 3][j * 3 + 2] += (lambda * dix * djz
+ mu * diz * djx) * dv;
if (j > i)
{
kmat[i * 3 + 1][j * 3]
+= (lambda * diy * djx + mu * dix * djy) * dv;
}
kmat[i * 3 + 1][j * 3 + 1] += (beta * diy * djy
+ mu * (diz * djz + dix * djx)) * dv;
kmat[i * 3 + 1][j * 3 + 2] += (lambda * diy * djz
+ mu * diz * djy) * dv;
if (j > i)
{
kmat[i * 3 + 2][j * 3]
+= (lambda * diz * djx + mu * dix * djz) * dv;
kmat[i * 3 + 2][j * 3 + 1]
+= (lambda * diz * djy + mu * diy * djz) * dv;
}
kmat[i * 3 + 2][j * 3 + 2] += (beta * diz * djz
+ mu * (dix * djx + diy * djy)) * dv;
}
}
}
}
// Set nodal equivalent of distributed face load to evec.
// surLd - object describing element face load;
// returns loaded element face
// or -1 (loaded nodes does not match element face)
public override int equivFaceLoad(ElemFaceLoad surLd)
{
// Shape functons
double[] an = new double[4];
// Derivatives of shape functions
double[][] xin = new double[4][] { new double[2], new double[2], new double[2], new double[2] };
// Tangent vectors along xi and eta
double[][] e = new double[2][] { new double[3], new double[3] };
// Normal vector
double[] g = new double[3];
double[] ps = new double[3];
for (int i = 0; i < 24; i++)
{
evec[i] = 0.0;
}
int loadedFace = surLd.rearrange(faceInd, ind);
if (loadedFace == -1)
{
return(-1);
}
for (int ip = 0; ip < gf.nIntPoints; ip++)
{
ShapeLin3D.shapeDerivFace(gf.xii[ip], gf.eti[ip], ind, an, xin);
double p = 0.0;
for (int i = 0; i < 4; i++)
{
p += an[i] * surLd.forceAtNodes[i];
}
// Tangent vectors
for (int i = 0; i < 2; i++)
{
for (int j = 0; j < 3; j++)
{
double s = 0;
for (int k = 0; k < 4; k++)
{
s += xin[k][i] * xy[faceInd[loadedFace][k]][j];
}
e[i][j] = s;
}
}
// Normal vector g
g[0] = (e[0][1] * e[1][2] - e[1][1] * e[0][2]);
g[1] = (e[0][2] * e[1][0] - e[1][2] * e[0][0]);
g[2] = (e[0][0] * e[1][1] - e[1][0] * e[0][1]);
// Element of surface ds
double ds = Math.Sqrt(g[0] * g[0] + g[1] * g[1] + g[2] * g[2]);
if (ds <= 0)
{
UTIL.errorMsg("Negative/zero element face");
}
// Surface load components ps:
// direction=0 - normal, x=1, y=2, z=3
if (surLd.direction == 0)
{
for (int i = 0; i < 3; i++)
{
ps[i] = p * g[i] / ds;
}
}
else
{
for (int i = 0; i < 3; i++)
{
ps[i] = 0;
}
ps[surLd.direction - 1] = p;
}
for (int i = 0; i < 4; i++)
{
int k = faceInd[loadedFace][i];
for (int j = 0; j < 3; j++)
{
evec[3 * k + j] += an[i] * ps[j] * ds * gf.wi[ip];
}
}
}
return(loadedFace);
}