private double[,] CalculateDeformationMatrix(
Jacobian3D jacobian, ShapeFunctionNaturalDerivatives3D[] shapeFunctionDerivatives)
{
double[,] jacobianInverse = jacobian.CalculateJacobianInverse();
double[,] b = new double[6, 24];
for (int shapeFunction = 0; shapeFunction < 8; shapeFunction++)
{
b[0, (3 * shapeFunction) + 0] = (jacobianInverse[0, 0] * shapeFunctionDerivatives[shapeFunction].Xi) +
(jacobianInverse[0, 1] * shapeFunctionDerivatives[shapeFunction].Eta) +
(jacobianInverse[0, 2] * shapeFunctionDerivatives[shapeFunction].Zeta);
b[1, (3 * shapeFunction) + 1] = (jacobianInverse[1, 0] * shapeFunctionDerivatives[shapeFunction].Xi) +
(jacobianInverse[1, 1] * shapeFunctionDerivatives[shapeFunction].Eta) +
(jacobianInverse[1, 2] * shapeFunctionDerivatives[shapeFunction].Zeta);
b[2, (3 * shapeFunction) + 2] = (jacobianInverse[2, 0] * shapeFunctionDerivatives[shapeFunction].Xi) +
(jacobianInverse[2, 1] * shapeFunctionDerivatives[shapeFunction].Eta) +
(jacobianInverse[2, 2] * shapeFunctionDerivatives[shapeFunction].Zeta);
b[3, (3 * shapeFunction) + 0] = b[1, (3 * shapeFunction) + 1];
b[3, (3 * shapeFunction) + 1] = b[0, (3 * shapeFunction) + 0];
b[4, (3 * shapeFunction) + 1] = b[2, (3 * shapeFunction) + 2];
b[4, (3 * shapeFunction) + 2] = b[1, (3 * shapeFunction) + 1];
b[5, (3 * shapeFunction) + 0] = b[2, (3 * shapeFunction) + 2];
b[5, (3 * shapeFunction) + 2] = b[0, (3 * shapeFunction) + 0];
}
return(b);
}
private GaussLegendrePoint3D[] CalculateGaussMatrices(double[,] nodeCoordinates)
{
GaussLegendrePoint1D[] integrationPointsPerAxis =
GaussQuadrature.GetGaussLegendrePoints(iInt);
int totalSamplingPoints = (int)Math.Pow(integrationPointsPerAxis.Length, 3);
GaussLegendrePoint3D[] integrationPoints = new GaussLegendrePoint3D[totalSamplingPoints];
int counter = -1;
foreach (GaussLegendrePoint1D pointXi in integrationPointsPerAxis)
{
foreach (GaussLegendrePoint1D pointEta in integrationPointsPerAxis)
{
foreach (GaussLegendrePoint1D pointZeta in integrationPointsPerAxis)
{
counter += 1;
double xi = pointXi.Coordinate;
double eta = pointEta.Coordinate;
double zeta = pointZeta.Coordinate;
ShapeFunctionNaturalDerivatives3D[] shapeDerivativeValues =
this.CalculateShapeDerivativeValues(xi, eta, zeta);
Jacobian3D jacobian = new Jacobian3D(nodeCoordinates, shapeDerivativeValues);
double[,] deformationMatrix = this.CalculateDeformationMatrix(jacobian, shapeDerivativeValues);
double weightFactor = pointXi.WeightFactor * pointEta.WeightFactor * pointZeta.WeightFactor *
jacobian.Determinant;
integrationPoints[counter] = new GaussLegendrePoint3D(
xi, eta, zeta, deformationMatrix, weightFactor);
}
}
}
return(integrationPoints);
}
