// alfa*{N}{N}T dS
private double[,] CalculateH_bc(int alfa)
{
pc = new IntegrationPoint[4][];
for (int i = 0; i < 4; i++)
{
pc[i] = new IntegrationPoint[2];
}
// na kazdy bok przypadają dwa punkty całkowania
pc[0][0] = new IntegrationPoint(-1 / Math.Sqrt(3), -1, 1, 1);
pc[0][1] = new IntegrationPoint(1 / Math.Sqrt(3), -1, 1, 1);
pc[1][0] = new IntegrationPoint(1, -1 / Math.Sqrt(3), 1, 1);
pc[1][1] = new IntegrationPoint(1, 1 / Math.Sqrt(3), 1, 1);
pc[2][0] = new IntegrationPoint(1 / Math.Sqrt(3), 1, 1, 1);
pc[2][1] = new IntegrationPoint(-1 / Math.Sqrt(3), 1, 1, 1);
pc[3][0] = new IntegrationPoint(-1, 1 / Math.Sqrt(3), 1, 1);
pc[3][1] = new IntegrationPoint(-1, -1 / Math.Sqrt(3), 1, 1);
double[,] H_bc = new double[4, 4];
//SPRAWDZANIE WARUNKU BRZEGOWEGO
for (int i = 0; i < 4; i++)
{
if (Nodes[i].IsBoundary && Nodes[(i + 1) % 4].IsBoundary)
{
Node bc1 = Nodes[i];
Node bc2 = Nodes[(i + 1) % 4];
double distance = Math.Sqrt(Math.Pow((bc1.GlobalX - bc2.GlobalX), 2) + Math.Pow((bc1.GlobalY - bc2.GlobalY), 2));
double detJ = distance / 2;
IntegrationPoint[] pcForBoundary = pc[i];
double[,] matrixFor1pc = new double[4, 4];
double[,] matrixFor2pc = new double[4, 4];
// alfa * {N} * {N}transposed dla kazdego pc
matrixFor1pc = MatrixUtils.MultiplyMatrices(UniversalElement.NVector(pcForBoundary[0]), UniversalElement.NVectorTransposed(pcForBoundary[0]));
matrixFor2pc = MatrixUtils.MultiplyMatrices(UniversalElement.NVector(pcForBoundary[1]), UniversalElement.NVectorTransposed(pcForBoundary[1]));
matrixFor1pc = MatrixUtils.MultiplyMatrix(matrixFor1pc, alfa);
matrixFor2pc = MatrixUtils.MultiplyMatrix(matrixFor2pc, alfa);
//H_bc += matrixFor1pc * pcForBoundary[0].WeightEta * detJ + matrixFor2pc * pcForBoundary[1].WeightEta * detJ;
H_bc = MatrixUtils.AddMatrices(H_bc, MatrixUtils.AddMatrices(MatrixUtils.MultiplyMatrix((MatrixUtils.MultiplyMatrix(matrixFor1pc, pcForBoundary[0].WeightEta)), detJ), MatrixUtils.MultiplyMatrix(MatrixUtils.MultiplyMatrix(matrixFor2pc, pcForBoundary[1].WeightEta), detJ)));
}
else
{
continue;
}
}
this.HLocalMatrix = MatrixUtils.AddMatrices(this.HLocalMatrix, H_bc);
return(H_bc);
}
// -alfa*{N} dS
private void CalculateP(int alfa, double ambientTemperature)
{
pc = new IntegrationPoint[4][];
for (int i = 0; i < 4; i++)
{
pc[i] = new IntegrationPoint[2];
}
// na kazdy bok przypadają dwa punkty całkowania
pc[0][0] = new IntegrationPoint(-1 / Math.Sqrt(3), -1, 1, 1);
pc[0][1] = new IntegrationPoint(1 / Math.Sqrt(3), -1, 1, 1);
pc[1][0] = new IntegrationPoint(1, -1 / Math.Sqrt(3), 1, 1);
pc[1][1] = new IntegrationPoint(1, 1 / Math.Sqrt(3), 1, 1);
pc[2][0] = new IntegrationPoint(1 / Math.Sqrt(3), 1, 1, 1);
pc[2][1] = new IntegrationPoint(-1 / Math.Sqrt(3), 1, 1, 1);
pc[3][0] = new IntegrationPoint(-1, 1 / Math.Sqrt(3), 1, 1);
pc[3][1] = new IntegrationPoint(-1, -1 / Math.Sqrt(3), 1, 1);
double[,] P = new double[4, 1];
//SPRAWDZANIE WARUNKU BRZEGOWEGO - lewy i prawy dolny róg mają warunek brzegowy ustawiony na 1
for (int i = 0; i < 4; i++)
{
if (Nodes[i].IsBoundary && Nodes[(i + 1) % 4].IsBoundary)
{
Node bc1 = Nodes[i];
Node bc2 = Nodes[(i + 1) % 4];
double distance = Math.Sqrt(Math.Pow((bc1.GlobalX - bc2.GlobalX), 2) + Math.Pow((bc1.GlobalY - bc2.GlobalY), 2));
double detJ = distance / 2;
IntegrationPoint[] pcForBoundary = pc[i];
double[,] matrixFor1pc = new double[4, 1];
double[,] matrixFor2pc = new double[4, 1];
// temp otoczenia * alfa * {N} dla kazdego pc
matrixFor1pc = UniversalElement.NVector(pcForBoundary[0]);
matrixFor2pc = UniversalElement.NVector(pcForBoundary[1]);
matrixFor1pc = MatrixUtils.MultiplyMatrix(matrixFor1pc, alfa * ambientTemperature);
matrixFor2pc = MatrixUtils.MultiplyMatrix(matrixFor2pc, alfa * ambientTemperature);
double[,] integralMatrix = MatrixUtils.AddMatrices(MatrixUtils.MultiplyMatrix(matrixFor1pc, detJ), MatrixUtils.MultiplyMatrix(matrixFor2pc, detJ));
//P += matrixFor1pc * pcForBoundary[0].WeightEta * detJ + matrixFor2pc * pcForBoundary[1].WeightEta * detJ;
P = MatrixUtils.AddMatrices(P, MatrixUtils.MultiplyMatrix(integralMatrix, -1));
}
else
{
continue;
}
}
LocalP = P;
}
public static double[,] NVectorTransposed(IntegrationPoint integrationPoint) // {N} transponowanie
{
double[,] NVectTransposed = new double[1, 4];
NVectTransposed[0, 0] = N1_local(integrationPoint);
NVectTransposed[0, 1] = N2_local(integrationPoint);
NVectTransposed[0, 2] = N3_local(integrationPoint);
NVectTransposed[0, 3] = N4_local(integrationPoint);
return(NVectTransposed);
}
public static double[,] NVector(IntegrationPoint integrationPoint) // {N} z poszczegilnych N1..N4
{
double[,] NVect = new double[4, 1];
NVect[0, 0] = N1_local(integrationPoint);
NVect[1, 0] = N2_local(integrationPoint);
NVect[2, 0] = N3_local(integrationPoint);
NVect[3, 0] = N4_local(integrationPoint);
return(NVect);
}
public static double N3_local(IntegrationPoint integrationPoint)
{
double N3 = 0.25 * (1 + integrationPoint.Ksi) * (1 + integrationPoint.Eta);
return(N3);
}
public static double N2_local(IntegrationPoint integrationPoint)
{
double N2 = 0.25 * (1 + integrationPoint.Ksi) * (1 - integrationPoint.Eta);
return(N2);
}
public static double N1_local(IntegrationPoint integrationPoint)
{
double N1 = 0.25 * (1 - integrationPoint.Ksi) * (1 - integrationPoint.Eta);
return(N1);
}