private void CalculateStrains(IElement element, double[][] tx_i)
{
IReadOnlyList <double[]> shapeFunctions = Interpolation.EvaluateFunctionsAtGaussPoints(QuadratureForStiffness);
IReadOnlyList <Matrix> shapeFunctionsDerivatives = Interpolation.EvaluateNaturalGradientsAtGaussPoints(QuadratureForStiffness);
(Matrix[] ll1, Matrix[] J_0a) = JacobianShell8Calculations.Getll1AndJ_0a(QuadratureForStiffness, tk, shapeFunctions, shapeFunctionsDerivatives);
(Matrix[] J_0inv, double[] detJ_0) =
JacobianShell8Calculations.GetJ_0invAndDetJ_0(J_0a, element.Nodes, oVn_i, nGaussPoints);
Matrix[] J_1 = JacobianShell8Calculations.Get_J_1(nGaussPoints, tx_i, tU, J_0a);
Matrix[] DefGradTr;
Matrix[] GL;
DefGradTr = new Matrix[nGaussPoints];
GL = new Matrix[nGaussPoints];
for (int j = 0; j < nGaussPoints; j++)
{
DefGradTr[j] = Matrix.CreateZero(3, 3);
GL[j] = Matrix.CreateZero(3, 3);
}
GLvec = new double[nGaussPoints][];
for (int j = 0; j < nGaussPoints; j++)
{
DefGradTr[j] = J_0inv[j] * J_1[j];
GL[j] = DefGradTr[j] * DefGradTr[j].Transpose();
for (int k = 0; k < 3; k++)
{
GL[j][k, k] = GL[j][k, k] - 1;
}
GL[j].ScaleIntoThis(0.5);
GLvec[j] = new double[6];
for (int k = 0; k < 3; k++)
{
GLvec[j][k] = GL[j][k, k];
}
GLvec[j][3] = 2 * GL[j][0, 1];
GLvec[j][4] = 2 * GL[j][1, 2];
GLvec[j][5] = 2 * GL[j][2, 0];
}
}
private Matrix UpdateKmatrices(IElement element)
{
double[][] kck; // 1 per node and (one per Gauss point+1 for the addition) -->[GP][8 dofs_per_node*nodes]
Matrix[] KNL;
Matrix[] KL;
double[][] BL01plus1_2tSPKvec;
IReadOnlyList <double[]> shapeFunctions = Interpolation.EvaluateFunctionsAtGaussPoints(QuadratureForStiffness);
IReadOnlyList <Matrix> shapeFunctionsDerivatives = Interpolation.EvaluateNaturalGradientsAtGaussPoints(QuadratureForStiffness);
(Matrix[] ll1, Matrix[] J_0a) = JacobianShell8Calculations.Getll1AndJ_0a(QuadratureForStiffness, tk, shapeFunctions, shapeFunctionsDerivatives);
(Matrix[] J_0inv, double[] detJ_0) =
JacobianShell8Calculations.GetJ_0invAndDetJ_0(J_0a, element.Nodes, oVn_i, nGaussPoints);
Matrix[] BNL1;
BNL1 = GetBNL1(J_0inv);
Matrix[] BL13;
BL13 = GetBL13(shapeFunctionsDerivatives, tUvec, J_0a); //TODO: maybe cached from calcForces for problems of normal memory requirements
double[][,] ck;
ck = CalculateCk(J_0a, tU);
//
Matrix[] BL11a; //TODO: maybe cached from calcForces for problems of normal memory
BL11a = GetBL11a(J_0inv);
Matrix[] BL12;
BL12 = GetBL12(J_0inv);
//
Matrix[] BL; //TODO: maybe cached from calcForces for problems of normal memory
BL = new Matrix[nGaussPoints];
Matrix[] BL01plus1_2;
BL01plus1_2 = new Matrix[nGaussPoints];
for (int j = 0; j < nGaussPoints; j++)
{
BL[j] = Matrix.CreateZero(6, 40);
BL01plus1_2[j] = Matrix.CreateZero(6, 9);
}
//
var ll2 = Matrix.CreateZero(24, 3);
for (int j = 0; j < 8; j++)
{
for (int k = 0; k < 3; k++)
{
ll2[3 * j + 0, k] = tU[j][k];
ll2[3 * j + 1, k] = tU[j][3 + k];
ll2[3 * j + 2, k] = oVn_i[j][k];
}
}
Matrix[] l_circumflex;
l_circumflex = new Matrix[nGaussPoints];
for (int j = 0; j < nGaussPoints; j++)
{
l_circumflex[j] = Matrix.CreateZero(3, 3);
}
for (int j = 0; j < nGaussPoints; j++)
{
l_circumflex[j] = ll1[j] * ll2;
}
Matrix[] BL11b;
BL11b = new Matrix[nGaussPoints];
for (int j = 0; j < nGaussPoints; j++)
{
BL11b[j] = Matrix.CreateZero(9, 9);
}
for (int j = 0; j < nGaussPoints; j++)
{
for (int k = 0; k < 3; k++)
{
for (int l = 0; l < 3; l++)
{
for (int m = 0; m < 3; m++)
{
BL11b[j][3 * k + l, 3 * k + m] = l_circumflex[j][l, m];
}
}
}
}
Matrix[] BL11;
BL11 = new Matrix[nGaussPoints];
for (int j = 0; j < nGaussPoints; j++)
{
BL11[j] = Matrix.CreateZero(6, 9);
}
for (int j = 0; j < nGaussPoints; j++)
{
BL11[j] = BL11a[j] * BL11b[j];
}
Matrix[] BL1_2;
BL1_2 = new Matrix[nGaussPoints];
for (int j = 0; j < nGaussPoints; j++)
{
BL1_2[j] = Matrix.CreateZero(6, 9);
}
for (int j = 0; j < nGaussPoints; j++)
{
BL1_2[j] = BL11[j] * BL12[j];
for (int k = 0; k < 6; k++)
{
for (int l = 0; l < 9; l++)
{
BL01plus1_2[j][k, l] = BL1_2[j][k, l] + BL11a[j][k, l];
}
}
BL[j] = BL01plus1_2[j] * BL13[j];
}
KL = new Matrix[nGaussPoints + 1];
KNL = new Matrix[nGaussPoints + 1];
kck = new double[nGaussPoints + 1][];
BL01plus1_2tSPKvec = new double[nGaussPoints][];
for (int j = 0; j < nGaussPoints + 1; j++)
{
KL[j] = Matrix.CreateZero(40, 40);
KNL[j] = Matrix.CreateZero(40, 40);
}
for (int j = 0; j < nGaussPoints; j++)
{
var SPK_circumflex = Matrix.CreateZero(9, 9);
for (int k = 0; k < 3; k++)
{
for (int l = 0; l < 3; l++)
{
SPK_circumflex[3 * k + l, 3 * k + l] = materialsAtGaussPoints[j].Stresses[l];
}
SPK_circumflex[3 * k, 3 * k + 1] = materialsAtGaussPoints[j].Stresses[3];
SPK_circumflex[3 * k, 3 * k + 2] = materialsAtGaussPoints[j].Stresses[5];
SPK_circumflex[3 * k + 1, 3 * k + 2] = materialsAtGaussPoints[j].Stresses[4];
SPK_circumflex[3 * k + 1, 3 * k] = materialsAtGaussPoints[j].Stresses[3];
SPK_circumflex[3 * k + 2, 3 * k] = materialsAtGaussPoints[j].Stresses[5];
SPK_circumflex[3 * k + 2, 3 * k + 1] = materialsAtGaussPoints[j].Stresses[4];
}
var BNL = BNL1[j] * BL13[j];
BL01plus1_2tSPKvec[j] = new double[9];
for (int k = 0; k < 9; k++)
{
for (int m = 0; m < 6; m++)
{
BL01plus1_2tSPKvec[j][k] += BL01plus1_2[j][m, k] * materialsAtGaussPoints[j].Stresses[m];
}
}
kck[j] = new double[8];
for (int k = 0; k < 8; k++)
{
for (int m = 0; m < 9; m++)
{
kck[j][k] += ck[j][k, m] * BL01plus1_2tSPKvec[j][m];
}
}
var ConsBL = Matrix.CreateZero(6, 40);
for (int k = 0; k < 6; k++)
{
for (int l = 0; l < 40; l++)
{
for (int m = 0; m < 6; m++)
{
ConsBL[k, l] += materialsAtGaussPoints[j].ConstitutiveMatrix[k, m] * BL[j][m, l];
}
}
}
var S_BNL = SPK_circumflex * BNL;
KNL[j] = BNL.Transpose() * S_BNL;
KL[j] = BL[j].Transpose() * ConsBL;
}
var Kt = Matrix.CreateZero(40, 40);
for (int j = 0; j < nGaussPoints; j++)
{
for (int k = 0; k < 40; k++)
{
for (int l = 0; l < 40; l++)
{
Kt[k, l] += integrationCoefficient[j] * (KL[j][k, l] + KNL[j][k, l]);
}
}
for (int l = 0; l < 8; l++)
{
Kt[5 * l + 3, 5 * l + 3] += integrationCoefficient[j] * kck[j][l];
Kt[5 * l + 4, 5 * l + 4] += integrationCoefficient[j] * kck[j][l];
}
}
return(Kt);
}
private double[] UpdateForces(IElement element)
{
IReadOnlyList <double[]> shapeFunctions = Interpolation.EvaluateFunctionsAtGaussPoints(QuadratureForStiffness);
IReadOnlyList <Matrix> shapeFunctionsDerivatives = Interpolation.EvaluateNaturalGradientsAtGaussPoints(QuadratureForStiffness);
(Matrix[] ll1, Matrix[] J_0a) = JacobianShell8Calculations.Getll1AndJ_0a(QuadratureForStiffness, tk, shapeFunctions, shapeFunctionsDerivatives);
//BL11a etc. are not cached currently(declare here)
(Matrix[] J_0inv, double[] detJ_0) =
JacobianShell8Calculations.GetJ_0invAndDetJ_0(J_0a, element.Nodes, oVn_i, nGaussPoints);
Matrix[] BL11a;
BL11a = GetBL11a(J_0inv);
Matrix[] BL12;
BL12 = GetBL12(J_0inv);
Matrix[] BL13;
BL13 = GetBL13(shapeFunctionsDerivatives, tUvec, J_0a);
Matrix[] BL;
BL = new Matrix[nGaussPoints];
Matrix[] BL01plus1_2;
BL01plus1_2 = new Matrix[nGaussPoints];
for (int j = 0; j < nGaussPoints; j++)
{
BL[j] = Matrix.CreateZero(6, 40);
BL01plus1_2[j] = Matrix.CreateZero(6, 9);
}
double[][] Fxk = new double[nGaussPoints + 1][];
for (int j = 0; j < nGaussPoints + 1; j++)
{
Fxk[j] = new double[40];
}
Matrix ll2;
ll2 = Matrix.CreateZero(24, 3);
for (int j = 0; j < 8; j++)
{
for (int k = 0; k < 3; k++)
{
ll2[3 * j + 0, k] = tU[j][k];
ll2[3 * j + 1, k] = tU[j][3 + k];
ll2[3 * j + 2, k] = oVn_i[j][k];
}
}
Matrix[] l_circumflex;
l_circumflex = new Matrix[nGaussPoints];
for (int j = 0; j < nGaussPoints; j++)
{
l_circumflex[j] = Matrix.CreateZero(3, 3);
}
for (int j = 0; j < nGaussPoints; j++)
{
l_circumflex[j] = ll1[j] * ll2;
}
Matrix[] BL11b;
BL11b = new Matrix[nGaussPoints];
for (int j = 0; j < nGaussPoints; j++)
{
BL11b[j] = Matrix.CreateZero(9, 9);
}
for (int j = 0; j < nGaussPoints; j++)
{
for (int k = 0; k < 3; k++)
{
for (int l = 0; l < 3; l++)
{
for (int m = 0; m < 3; m++)
{
BL11b[j][3 * k + l, 3 * k + m] = l_circumflex[j][l, m];
} //don;t change that
}
}
}
Matrix[] BL11;
BL11 = new Matrix[nGaussPoints];
for (int j = 0; j < nGaussPoints; j++)
{
BL11[j] = BL11a[j] * BL11b[j];
}
Matrix[] BL1_2;
BL1_2 = new Matrix[nGaussPoints];
for (int j = 0; j < nGaussPoints; j++)
{
BL1_2[j] = BL11[j] * BL12[j];
for (int k = 0; k < 6; k++)
{
for (int l = 0; l < 9; l++)
{
BL01plus1_2[j][k, l] = BL1_2[j][k, l] + BL11a[j][k, l];
}
}
BL[j] = BL01plus1_2[j] * BL13[j];
}
for (int j = 0; j < nGaussPoints; j++)
{
for (int k = 0; k < 40; k++)
{
Fxk[j][k] = 0;
for (int m = 0; m < 6; m++)
{
Fxk[j][k] += BL[j][m, k] * materialsAtGaussPoints[j].Stresses[m];
}
}
}
for (int k = 0; k < 40; k++)
{
Fxk[nGaussPoints][k] = 0;
for (int j = 0; j < nGaussPoints; j++)
{
Fxk[nGaussPoints][k] += integrationCoefficient[j] * Fxk[j][k];
}
}
return(Fxk[nGaussPoints]);
}
private void CalculateInitialConfigurationData(IElement element, out double[][] tx_i)
{
double[] E;
double[] ni;
IReadOnlyList <double[]> shapeFunctions = Interpolation.EvaluateFunctionsAtGaussPoints(QuadratureForStiffness);
IReadOnlyList <Matrix> shapeFunctionsDerivatives = Interpolation.EvaluateNaturalGradientsAtGaussPoints(QuadratureForStiffness);
(Matrix[] ll1, Matrix[] J_0a) = JacobianShell8Calculations.Getll1AndJ_0a(
QuadratureForStiffness, tk, shapeFunctions, shapeFunctionsDerivatives);
//TODO J_0, J_0b etc. can be cached for not large scale models
tx_i = new double[8][];
(tU, tUvec) = Shell8DirectionVectorUtilities.GetInitialDirectionVectorValues(oVn_i);
double[][] oV1_i = new double[8][]; //tangent vector ''1'' initial configuration
for (int j = 0; j < 8; j++)
{
tx_i[j] = new double[] { element.Nodes[j].X, element.Nodes[j].Y, element.Nodes[j].Z, };
oV1_i[j] = new double[3];
oV1_i[j][0] = tUvec[j][0];
oV1_i[j][1] = tUvec[j][1];
oV1_i[j][2] = tUvec[j][2];
}
(Matrix[] J_0inv, double[] detJ_0) =
JacobianShell8Calculations.GetJ_0invAndDetJ_0(J_0a, element.Nodes, oVn_i, nGaussPoints);
for (int j = 0; j < nGaussPoints; j++)
{
double[] V3 = new double[3];
double V3_norm;
double[] V1 = new double[3];
double V1_norm;
for (int k = 0; k < 3; k++)
{
V3[k] = 0; V1[k] = 0; /* V2[k] = 0; */
}
for (int k = 0; k < 8; k++)
{
for (int l = 0; l < 3; l++)
{
V3[l] += shapeFunctions[j][k] * oVn_i[k][l];
V1[l] += shapeFunctions[j][k] * oV1_i[k][l];
}
}
V3_norm = Math.Sqrt(V3[0] * V3[0] + V3[1] * V3[1] + V3[2] * V3[2]);
V1_norm = Math.Sqrt(V1[0] * V1[0] + V1[1] * V1[1] + V1[2] * V1[2]);
for (int l = 0; l < 3; l++)
{
V3[l] = V3[l] / V3_norm;
V1[l] = V1[l] / V1_norm;
}
materialsAtGaussPoints[j].NormalVectorV3 = V3;
materialsAtGaussPoints[j].TangentVectorV1 = V1;
}
integrationCoefficient = new double[nGaussPoints];
for (int j = 0; j < nGaussPoints; j++)
{
integrationCoefficient[j] += QuadratureForStiffness.IntegrationPoints[j].Weight * detJ_0[j];
}
}