private void button1_Click(object sender, EventArgs e)
{
PreprocessingModelling.getGaussianCoordinates(comboBox1.SelectedIndex);
int NumbersOfNodes = PreprocessingModelling.getElementNodesNumber();
int DegreeOfFreedom = 3;
PreprocessingModelling.removeExcessEtopol();
int NumbersOfElements = PreprocessingModelling.getNumberOfElements();
double[,] NodalCoordinates = Analysis.getNodalCoordinates();
int GaussianNumber = MainInterface.XGaussianCoordinates.GetLength(0);
double[,] ShapeFunctionDerivatives = Analysis.getShapeFunctionDerivatives(MainInterface.XGaussianCoordinates, MainInterface.YGaussianCoordinates, MainInterface.ZGaussianCoordinates);
double[,] GlobalStiffnessMatrix = new double[MainInterface.Nodes.Count() * DegreeOfFreedom, MainInterface.Nodes.Count() * DegreeOfFreedom]; //
for (int i = 0; i < NumbersOfElements; i++)
{
double[,] StiffnessMatrix = new double[NumbersOfNodes * DegreeOfFreedom, NumbersOfNodes *DegreeOfFreedom];
double[,] ElementNodalCoordinates = Analysis.getElementNodalCoordinates(i, NodalCoordinates);
double[,] Jacobian = Analysis.getJacobian(ElementNodalCoordinates);
for (int j = 0; j < GaussianNumber; j++)
{
double[,] GaussianJacobian = Analysis.getGaussianJacobian(j, Jacobian);
double JacobianDeterminant = Accord.Math.Matrix.Determinant(GaussianJacobian);
double[,] GaussianShapeFunctionDerivative = Analysis.getGaussianShapeFunctionDerivatives(j, ShapeFunctionDerivatives);
double[,] ShapeFunctionDerivativeWRTCoordinates = Accord.Math.Matrix.Solve(GaussianJacobian, GaussianShapeFunctionDerivative);
double[,] StrainDisplacementMatrix = Analysis.getStrainDisplacementMatrix(ShapeFunctionDerivativeWRTCoordinates);
double[,] ConstitutiveMatrix = Analysis.getConstitutiveMatrix(i);
StiffnessMatrix = Analysis.addStiffnessMatrix(StiffnessMatrix, StrainDisplacementMatrix, ConstitutiveMatrix, JacobianDeterminant, j);
}
GlobalStiffnessMatrix = Analysis.addGlobalStiffnessMatrix(i, GlobalStiffnessMatrix, StiffnessMatrix);
}
Analysis.calculateDisplacement(GlobalStiffnessMatrix);
this.Close();
}
public ElementCreation(int element_Type)
{
Nodes_Added = 0;
NumberOfNodes = PreprocessingModelling.getElementNodesNumber(element_Type);
PreprocessingModelling.removeExcessEtopol(element_Type);
InitializeComponent();
dataGridView1.DataSource = MainInterface.Nodes.Select(vector => new { X = vector.X, Y = vector.Y, Z = vector.Z }).ToList();
this.dataGridView1.SelectionMode = DataGridViewSelectionMode.FullRowSelect;
}
public static double[,] getNodalCoordinates()
{
int NumbersOfNodes = PreprocessingModelling.getElementNodesNumber();
int NumbersOfElements = PreprocessingModelling.getNumberOfElements();
double[,] NodalCoordinates = new double[NumbersOfElements * NumbersOfNodes, 3];
for (int i = 0; i < NumbersOfElements * NumbersOfNodes; i++)
{
NodalCoordinates[i, 0] = MainInterface.Nodes[MainInterface.Etopol[i]].X;
NodalCoordinates[i, 1] = MainInterface.Nodes[MainInterface.Etopol[i]].Y;
NodalCoordinates[i, 2] = MainInterface.Nodes[MainInterface.Etopol[i]].Z;
}
return(NodalCoordinates);
}
public static double[,] getElementNodalCoordinates(int elementBeingCalculated, double[,] nodalCoordinates)
{
int NumbersOfNodes = PreprocessingModelling.getElementNodesNumber();
double[,] ElementNodalCoordinates = new double[NumbersOfNodes, 3];
int j = 0;
for (int i = elementBeingCalculated * NumbersOfNodes; i < (elementBeingCalculated + 1) * NumbersOfNodes; i++)
{
ElementNodalCoordinates[j, 0] = nodalCoordinates[i, 0];
ElementNodalCoordinates[j, 1] = nodalCoordinates[i, 1];
ElementNodalCoordinates[j, 2] = nodalCoordinates[i, 2];
j += 1;
}
return(ElementNodalCoordinates);
}
public static double[,] addGlobalStiffnessMatrix(int elementBeingCalculated, double[,] existingGlobalStiffnessMatrix, double[,] stiffnessMatrix)
{
int NumbersOfNodes = PreprocessingModelling.getElementNodesNumber();
int LocalStiffnessMatrixSize = stiffnessMatrix.GetLength(0);
int[] GlobalStiffnessMatrixLocation = new int[LocalStiffnessMatrixSize];
for (int i = 0; i < NumbersOfNodes; i++)
{
GlobalStiffnessMatrixLocation[i * 3] = MainInterface.Etopol[(NumbersOfNodes * elementBeingCalculated) + i] * 3;
GlobalStiffnessMatrixLocation[(i * 3) + 1] = GlobalStiffnessMatrixLocation[i * 3] + 1;
GlobalStiffnessMatrixLocation[(i * 3) + 2] = GlobalStiffnessMatrixLocation[i * 3] + 2;
}
for (int i = 0; i < LocalStiffnessMatrixSize; i++)
{
for (int j = 0; j < LocalStiffnessMatrixSize; j++)
{
existingGlobalStiffnessMatrix[GlobalStiffnessMatrixLocation[i], GlobalStiffnessMatrixLocation[j]] += stiffnessMatrix[i, j];
}
}
return(existingGlobalStiffnessMatrix);
}
public static double[,] getStrainDisplacementMatrix(double[,] shapeFunctionDerivativeWRTCoordinates)
{
int NumbersOfNodes = PreprocessingModelling.getElementNodesNumber();
int DegreeOfFreedom = 3;
double[,] StrainDisplacementMatrix = new double[6, NumbersOfNodes *DegreeOfFreedom]; //TODO: Account for 9 rows situations and other cases too.
for (int i = 0; i < NumbersOfNodes; i++)
{
int j = (3 * (i + 1)) - 3;
StrainDisplacementMatrix[0, j] = shapeFunctionDerivativeWRTCoordinates[0, i];
StrainDisplacementMatrix[1, j + 1] = shapeFunctionDerivativeWRTCoordinates[1, i];
StrainDisplacementMatrix[2, j + 2] = shapeFunctionDerivativeWRTCoordinates[2, i];
StrainDisplacementMatrix[3, j] = shapeFunctionDerivativeWRTCoordinates[1, i];
StrainDisplacementMatrix[3, j + 1] = shapeFunctionDerivativeWRTCoordinates[0, i];
StrainDisplacementMatrix[4, j + 1] = shapeFunctionDerivativeWRTCoordinates[2, i];
StrainDisplacementMatrix[4, j + 2] = shapeFunctionDerivativeWRTCoordinates[1, i];
StrainDisplacementMatrix[5, j] = shapeFunctionDerivativeWRTCoordinates[2, i];
StrainDisplacementMatrix[5, j + 2] = shapeFunctionDerivativeWRTCoordinates[0, i];
}
return(StrainDisplacementMatrix);
}
public static double[,] getShapeFunctionDerivatives(int element_Type, double[,] xsi, double[,] eta, double[,] zet)
{
int NumberofNodes = PreprocessingModelling.getElementNodesNumber(element_Type);
int GaussianNumber = xsi.GetLength(0);
double[,] ShapeFunctionDerivatives = new double[3 * NumberofNodes, GaussianNumber];
if (NumberofNodes == 8)
{
for (int i = 0; i < NumberofNodes; i++)
{
for (int j = 0; j < GaussianNumber; j++)
{
ShapeFunctionDerivatives[(3 * (j + 1)) - 3, i] = (Math.Sign(xsi[i, 0]) * (1 + Math.Sign(eta[i, 0]) * eta[j, 0]) * (1 + Math.Sign(zet[i, 0]) * zet[j, 0])) / 8;
ShapeFunctionDerivatives[(3 * (j + 1)) - 2, i] = (Math.Sign(eta[i, 0]) * (1 + Math.Sign(xsi[i, 0]) * xsi[j, 0]) * (1 + Math.Sign(zet[i, 0]) * zet[j, 0])) / 8;
ShapeFunctionDerivatives[(3 * (j + 1)) - 1, i] = (Math.Sign(zet[i, 0]) * (1 + Math.Sign(xsi[i, 0]) * xsi[j, 0]) * (1 + Math.Sign(eta[i, 0]) * eta[j, 0])) / 8;
}
}
}
// TODO: Fill in the other Shape Function Derivatives.
return(ShapeFunctionDerivatives);
}
public static double[,] getShapeFunction(double[,] xsi, double[,] eta, double[,] zet)
{
int NumberofNodes = PreprocessingModelling.getElementNodesNumber();
int GaussianNumber = xsi.GetLength(0);
double[,] ShapeFunction = new double[GaussianNumber, NumberofNodes];
if (GaussianNumber == 8)
{
for (int i = 0; i < GaussianNumber; i++)
{
ShapeFunction[i, 0] = 0.125 * (1 - xsi[i, 0]) * (1 - eta[i, 0]) * (1 - zet[i, 0]);
ShapeFunction[i, 1] = 0.125 * (1 - xsi[i, 0]) * (1 - eta[i, 0]) * (1 + zet[i, 0]);
ShapeFunction[i, 2] = 0.125 * (1 + xsi[i, 0]) * (1 - eta[i, 0]) * (1 + zet[i, 0]);
ShapeFunction[i, 3] = 0.125 * (1 + xsi[i, 0]) * (1 - eta[i, 0]) * (1 - zet[i, 0]);
ShapeFunction[i, 4] = 0.125 * (1 - xsi[i, 0]) * (1 + eta[i, 0]) * (1 - zet[i, 0]);
ShapeFunction[i, 5] = 0.125 * (1 - xsi[i, 0]) * (1 + eta[i, 0]) * (1 + zet[i, 0]);
ShapeFunction[i, 6] = 0.125 * (1 + xsi[i, 0]) * (1 + eta[i, 0]) * (1 + zet[i, 0]);
ShapeFunction[i, 7] = 0.125 * (1 + xsi[i, 0]) * (1 + eta[i, 0]) * (1 - zet[i, 0]);
}
}
// TODO: Fill in the other Shape Functions.
return(ShapeFunction);
}