private void GetInitialGeometricDataAndInitializeMatrices(IElement element)
{
(tU, tUvec) = Shell8DirectionVectorUtilities.GetInitialDirectionVectorValues(oVn_i);
this.GetInitialGeometricDataForMidsurface(element);
ox_i = new double[16][];
if (ShellElementSide == 0)
{
for (int j = 0; j < 8; j++)
{
ox_i[j] = new double[] { ox_i_shell_midsurface[j][0] - 0.5 * tk[j] * tU[j][3], ox_i_shell_midsurface[j][1] - 0.5 * tk[j] * tU[j][4],
ox_i_shell_midsurface[j][2] - 0.5 * tk[j] * tU[j][5], };
}
for (int j = 8; j < 16; j++)
{
ox_i[j] = new double[] { element.Nodes[j].X, element.Nodes[j].Y, element.Nodes[j].Z, };
}
}
else
{
for (int j = 0; j < 8; j++)
{
ox_i[j] = new double[] { element.Nodes[j + 8].X, element.Nodes[j + 8].Y, element.Nodes[j + 8].Z, };
}
for (int j = 8; j < 16; j++)
{
ox_i[j] = new double[] { ox_i_shell_midsurface[j - 8][0] + 0.5 * tk[j - 8] * tU[j - 8][3], ox_i_shell_midsurface[j - 8][1] + 0.5 * tk[j - 8] * tU[j - 8][4],
ox_i_shell_midsurface[j - 8][2] + 0.5 * tk[j - 8] * tU[j - 8][5], };
}
}
x_local = new double[48];
}
private void UpdateCoordinateData(double[] localdisplacements, IElement element, out double[][] tx_i)
{
double[][] ox_i = new double[8][]; // this should be allocated in the constructor
for (int j = 0; j < 8; j++)
{
ox_i[j] = new double[] { element.Nodes[j].X, element.Nodes[j].Y, element.Nodes[j].Z, };
}
double ak;
double bk;
tx_i = new double[8][];
for (int k = 0; k < 8; k++)
{
tx_i[k] = new double[3];
for (int l = 0; l < 3; l++)
{
tx_i[k][l] = ox_i[k][l] + localdisplacements[5 * k + l];
}
//update tU andUvec
tU[k][0] = localdisplacements[5 * k + 0];
tU[k][1] = localdisplacements[5 * k + 1];
tU[k][2] = localdisplacements[5 * k + 2];
ak = localdisplacements[5 * k + 3] - ak_total[k];
ak_total[k] = localdisplacements[5 * k + 3];
bk = localdisplacements[5 * k + 4] - bk_total[k];
bk_total[k] = localdisplacements[5 * k + 4];
Shell8DirectionVectorUtilities.RotateNodalDirectionVectors(ak, bk, k, tU, tUvec);
}
}
private void UpdateCoordinateDataForDirectVectorsAndMidsurface(double[] localdisplacements, out double[][] tx_i_shell_midsurface)
{
double ak;
double bk;
tx_i_shell_midsurface = new double[8][];
for (int j = 0; j < 8; j++)
{
tx_i_shell_midsurface[j] = new double[3];
}
for (int k = 0; k < 8; k++)
{
for (int l = 0; l < 3; l++)
{
tx_i_shell_midsurface[k][l] = ox_i_shell_midsurface[k][l] + localdisplacements[5 * k + l];
}
//update tU & tUvec
tU[k][0] = localdisplacements[5 * k + 0];
tU[k][1] = localdisplacements[5 * k + 1];
tU[k][2] = localdisplacements[5 * k + 2];
ak = localdisplacements[5 * k + 3] - ak_total[k];
ak_total[k] = localdisplacements[5 * k + 3];
bk = localdisplacements[5 * k + 4] - bk_total[k];
bk_total[k] = localdisplacements[5 * k + 4];
Shell8DirectionVectorUtilities.RotateNodalDirectionVectors(ak, bk, k, tU, tUvec);
}
}
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];
}
}
