private double[,] MainStiffnessPart(double penaltyFactor, double[] normalVector, double[,] aMatrix)
{
double[,] nxn = VectorOperations.VectorVectorTensorProduct(normalVector, normalVector);
double[,] aT = MatrixOperations.Transpose(aMatrix);
double[,] nxna = MatrixOperations.MatrixProduct(nxn, aMatrix);
double[,] aTnxna = MatrixOperations.MatrixProduct(aT, nxna);
double[,] Kmain = MatrixOperations.ScalarMatrixProductNew(penaltyFactor, aTnxna);
return(Kmain);
}
private double[,] CalculateMainStiffnessPart(double ksi1, double[] n)
{
double[,] mainStiffnessMatrix = new double[6, 6];
double N1 = 1.0 / 2.0 * (1.0 - ksi1);
double N2 = 1.0 / 2.0 * (1.0 + ksi1);
Tuple <double[, ], double[, ]> positionMatrices = CalculatePositionMatrix(ksi1);
double[,] A = positionMatrices.Item1;
double[,] nxn = VectorOperations.VectorVectorTensorProduct(n, n);
double[,] nxn_A = MatrixOperations.MatrixProduct(nxn, A);
double[,] AT_nxn_A = MatrixOperations.MatrixProduct(MatrixOperations.Transpose(A), nxn_A);
mainStiffnessMatrix = MatrixOperations.ScalarMatrixProductNew(PenaltyFactor, AT_nxn_A);
//mainStiffnessMatrix[0, 0] = N1 * N1 * n[0] * n[0] * PenaltyFactor;
//mainStiffnessMatrix[0, 1] = N1 * N1 * n[0] * n[1] * PenaltyFactor;
//mainStiffnessMatrix[0, 2] = N1 * N2 * n[0] * n[0] * PenaltyFactor;
//mainStiffnessMatrix[0, 3] = N1 * N1 * n[0] * n[1] * PenaltyFactor;
//mainStiffnessMatrix[0, 4] = -N1 * n[0] * n[0] * PenaltyFactor;
//mainStiffnessMatrix[0, 5] = -N1 * n[0] * n[1] * PenaltyFactor;
//mainStiffnessMatrix[1, 0] = mainStiffnessMatrix[0, 1];
//mainStiffnessMatrix[1, 1] = N1 * N1 * n[1] * n[1] * PenaltyFactor;
//mainStiffnessMatrix[1, 2] = N1 * N2 * n[0] * n[1] * PenaltyFactor;
//mainStiffnessMatrix[1, 3] = N1 * N2 * n[1] * n[1] * PenaltyFactor;
//mainStiffnessMatrix[1, 4] = -N1 * n[0] * n[1] * PenaltyFactor;
//mainStiffnessMatrix[1, 5] = -N1 * n[1] * n[1] * PenaltyFactor;
//mainStiffnessMatrix[2, 0] = mainStiffnessMatrix[0, 2];
//mainStiffnessMatrix[2, 1] = mainStiffnessMatrix[1, 2];
//mainStiffnessMatrix[2, 2] = N2 * N2 * n[0] * n[0] * PenaltyFactor;
//mainStiffnessMatrix[2, 3] = N2 * N2 * n[0] * n[1] * PenaltyFactor;
//mainStiffnessMatrix[2, 4] = -N2 * n[0] * n[0] * PenaltyFactor;
//mainStiffnessMatrix[2, 5] = -N2 * n[0] *n[1] * PenaltyFactor;
//mainStiffnessMatrix[3, 0] = mainStiffnessMatrix[0, 3];
//mainStiffnessMatrix[3, 1] = mainStiffnessMatrix[1, 3];
//mainStiffnessMatrix[3, 2] = mainStiffnessMatrix[2, 3];
//mainStiffnessMatrix[3, 3] = N2 * N2 * n[1] * n[1] * PenaltyFactor;
//mainStiffnessMatrix[3, 4] = -N2 * n[0] * n[1] * PenaltyFactor;
//mainStiffnessMatrix[3, 5] = -N2 * n[1] * n[1] * PenaltyFactor;
//mainStiffnessMatrix[4, 0] = mainStiffnessMatrix[0, 4];
//mainStiffnessMatrix[4, 1] = mainStiffnessMatrix[1, 4];
//mainStiffnessMatrix[4, 2] = mainStiffnessMatrix[2, 4];
//mainStiffnessMatrix[4, 3] = mainStiffnessMatrix[3, 4];
//mainStiffnessMatrix[4, 4] = n[0] * n[0] * PenaltyFactor;
//mainStiffnessMatrix[4, 5] = n[0] * n[1] * PenaltyFactor;
//mainStiffnessMatrix[5, 0] = mainStiffnessMatrix[0, 5];
//mainStiffnessMatrix[5, 1] = mainStiffnessMatrix[1, 5];
//mainStiffnessMatrix[5, 2] = mainStiffnessMatrix[2, 5];
//mainStiffnessMatrix[5, 3] = mainStiffnessMatrix[3, 5];
//mainStiffnessMatrix[5, 4] = mainStiffnessMatrix[4, 5];
//mainStiffnessMatrix[5, 5] = n[1] * n[1] * PenaltyFactor;
return(mainStiffnessMatrix);
}
private double[,] CalculateNormalStiffnessMatrix()
{
double[] n = CalculateNormalUnitVector();
double[,] A = CalculatePositionMatrix();
double[,] AT = MatrixOperations.Transpose(A);
double[,] nxn = VectorOperations.VectorVectorTensorProduct(n, n);
double[,] nxn_A = MatrixOperations.MatrixProduct(nxn, A);
double[,] AT_nxn_A = MatrixOperations.MatrixProduct(AT, nxn_A);
double[,] globalStiffnessMatrix = MatrixOperations.ScalarMatrixProductNew(PenaltyFactor, AT_nxn_A);
return(globalStiffnessMatrix);
}
private double[,] CalculateTangentialStiffnessMatrixForStick()
{
double[] t = CalculateTangentUnitVector();
double[,] A = CalculatePositionMatrix();
double[,] AT = MatrixOperations.Transpose(A);
double[,] txt = VectorOperations.VectorVectorTensorProduct(t, t);
double[,] txt_A = MatrixOperations.MatrixProduct(txt, A);
double[,] AT_txt_A = MatrixOperations.MatrixProduct(AT, txt_A);
double[,] tangentialStiffnessMatrix = MatrixOperations.ScalarMatrixProductNew(-PenaltyFactor, AT_txt_A);
return(tangentialStiffnessMatrix);
}
private double[,] CalculateMainStiffnessPart(double ksi1, double[] n)
{
double[,] mainStiffnessMatrix = new double[8, 8];
Tuple <double[, ], double[, ], double[, ]> positionMatrices = CalculatePositionMatrix(ksi1);
double[,] A = positionMatrices.Item1;
double[,] nxn = VectorOperations.VectorVectorTensorProduct(n, n);
double[,] nxn_A = MatrixOperations.MatrixProduct(nxn, A);
double[,] AT_nxn_A = MatrixOperations.MatrixProduct(MatrixOperations.Transpose(A), nxn_A);
mainStiffnessMatrix = MatrixOperations.ScalarMatrixProductNew(PenaltyFactor, AT_nxn_A);
return(mainStiffnessMatrix);
}
private double[,] CalculateMainStiffnessPart(double ksi1, double ksi2, double[] n)
{
int numberOfNodes = Properties.MasterSegmentPolynomialDegree + Properties.SlaveSegmentPolynomialDegree + 2;
double[,] mainStiffnessMatrix = new double[2 * numberOfNodes, 2 * numberOfNodes];
Tuple <double[, ], double[, ], double[, ], double[, ], double[, ]> positionMatrices = CalculatePositionMatrix(ksi1, ksi2);
double[,] A = positionMatrices.Item1;
double[,] nxn = VectorOperations.VectorVectorTensorProduct(n, n);
double[,] nxn_A = MatrixOperations.MatrixProduct(nxn, A);
double[,] AT_nxn_A = MatrixOperations.MatrixProduct(MatrixOperations.Transpose(A), nxn_A);
mainStiffnessMatrix = MatrixOperations.ScalarMatrixProductNew(PenaltyFactor, AT_nxn_A);
return(mainStiffnessMatrix);
}
private double[,] CalculateTangentialStiffnessMatrixForSlip(double tangentialTraction)
{
double Tr = tangentialTraction;
double[] t = CalculateTangentUnitVector();
double[] n = CalculateNormalUnitVector();
double[,] A = CalculatePositionMatrix();
double[,] AT = MatrixOperations.Transpose(A);
double[,] txn = VectorOperations.VectorVectorTensorProduct(t, n);
double[,] txn_A = MatrixOperations.MatrixProduct(txn, A);
double[,] AT_txn_A = MatrixOperations.MatrixProduct(AT, txn_A);
double scalarFactor = -FrictionCoef * PenaltyFactor * (Tr / Math.Abs(Tr));
double[,] tangentialStiffnessMatrix = MatrixOperations.ScalarMatrixProductNew(scalarFactor, AT_txn_A);
return(tangentialStiffnessMatrix);
}
private double[,] CalculateCurvatureStiffnessPart(double[,] A, double ksi3, double m11, double[] dRho, double h11)
{
double coef = PenaltyFactor * ksi3 * m11 * h11;
double[,] curvaturePart;
double[,] dRho_x_dRho = VectorOperations.VectorVectorTensorProduct(dRho, dRho);
double[,] Matrix = MatrixOperations.MatrixProduct(
MatrixOperations.Transpose(A),
MatrixOperations.MatrixProduct(dRho_x_dRho, A)
);
curvaturePart = MatrixOperations.ScalarMatrixProductNew(
coef,
Matrix
);
return(curvaturePart);
}
public double[,] CreateGlobalStiffnessMatrix()
{
double penetration = CalculateNormalGap();
if (penetration <= 0)
{
double[] n = CalculateNormalUnitVector();
double[,] A = CalculatePositionMatrix();
double[,] AT = MatrixOperations.Transpose(A);
double[,] nxn = VectorOperations.VectorVectorTensorProduct(n, n);
double[,] nxn_A = MatrixOperations.MatrixProduct(nxn, A);
double[,] AT_nxn_A = MatrixOperations.MatrixProduct(AT, nxn_A);
double[,] globalStiffnessMatrix = MatrixOperations.ScalarMatrixProductNew(PenaltyFactor, AT_nxn_A);
return(globalStiffnessMatrix);
}
else
{
double[,] globalStifnessMatrix = new double[4, 4];
return(globalStifnessMatrix);
}
}
private double[,] CalculateRotationalStiffnessPart(double[,] A, double[,] dA, double[] n, double ksi3, double m11, double[] dRho)
{
double coef = PenaltyFactor * ksi3 * m11;
double[,] rotationalPart;
double[,] n_x_dRho = VectorOperations.VectorVectorTensorProduct(n, dRho);
double[,] dRho_x_n = VectorOperations.VectorVectorTensorProduct(dRho, n);
double[,] firstTerm = MatrixOperations.MatrixProduct(
MatrixOperations.Transpose(dA),
MatrixOperations.MatrixProduct(n_x_dRho, A)
);
double[,] secondTerm = MatrixOperations.MatrixProduct(
MatrixOperations.Transpose(A),
MatrixOperations.MatrixProduct(dRho_x_n, dA)
);
rotationalPart = MatrixOperations.ScalarMatrixProductNew(
coef,
MatrixOperations.MatrixAddition(firstTerm, secondTerm)
);
return(rotationalPart);
}
private double[,] CalculateRotationalStiffnessPart(double[,] A, double[,] dA, double[] n, double ksi3, double m11, double[] dRho)
{
double coef = PenaltyFactor * ksi3 * m11;
double[,] rotationalPart;
double[,] n_x_dRho = VectorOperations.VectorVectorTensorProduct(n, dRho);
double[,] dRho_x_n = VectorOperations.VectorVectorTensorProduct(dRho, n);
double[,] firstTerm = MatrixOperations.MatrixProduct(
MatrixOperations.Transpose(dA),
MatrixOperations.MatrixProduct(n_x_dRho, A)
);
double[,] secondTerm = MatrixOperations.MatrixProduct(
MatrixOperations.Transpose(A),
MatrixOperations.MatrixProduct(dRho_x_n, dA)
);
rotationalPart = MatrixOperations.ScalarMatrixProductNew(
coef,
MatrixOperations.MatrixAddition(firstTerm, secondTerm)
);
//double[,] rotationalPart = new double[6, 6];
//double N1 = 1 / 2 * (1 - ksi1);
//double N2 = 1 / 2 * (1 + ksi1);
//double coef = PenaltyFactor * ksi3 * m11;
//rotationalPart[0, 0] = -coef * N1 * drho[0] * n[0];
//rotationalPart[0, 1] = -coef * (N1 * drho[0] * n[1] / 2) - coef * (N1 * drho[1] * n[0] / 2);
//rotationalPart[0, 2] = coef * (N1 * drho[0] * n[0] / 2) - coef * (N2 * drho[0] * n[0] / 2);
//rotationalPart[0, 3] = coef * (N1 * drho[0] * n[1] / 2) - coef * (N2 * drho[1] * n[0] / 2);
//rotationalPart[0, 4] = coef * (drho[0] * n[0] / 2);
//rotationalPart[0, 5] = coef * (drho[1] * n[0] / 2) - coef * (N1 * drho[0] * n[1]);
//rotationalPart[1, 0] = rotationalPart[0, 1];
//rotationalPart[1, 1] = -coef * N1 * drho[1] * n[1];
//rotationalPart[1, 2] = coef * (N1 * drho[1] * n[0] / 2) - coef * (N2 * drho[0] * n[1] / 2);
//rotationalPart[1, 3] = coef * (N1 * drho[1] * n[1] / 2) - coef * (N2 * drho[1] * n[1] / 2);
//rotationalPart[1, 4] = coef * drho[0] * n[1] / 2;
//rotationalPart[1, 5] = coef * (drho[1] * n[1] / 2) - coef * (N1 * drho[1] * n[1]);
return(rotationalPart);
}
public double[,] CreateGlobalStiffnessMatrix()
{
//double ksi1 = ClosestPointProjection();
if (counter == 1)
{
Ksi1Initial = Ksi1Current;
}
counter = counter + 1;
if (Math.Abs(Ksi1Current) <= 1.05)
{
Tuple <double[, ], double[, ]> positionMatrices = CalculatePositionMatrix(Ksi1Current);
double[,] aMatrix = positionMatrices.Item1;
double[,] daMatrix = positionMatrices.Item2;
Tuple <double[], double, double[], double[], double> surfaceCharacteristics = SurfaceGeometry(daMatrix);
double m11 = surfaceCharacteristics.Item2;
double[] dRho = surfaceCharacteristics.Item1;
double[] n = surfaceCharacteristics.Item3;
double[] tVector = surfaceCharacteristics.Item4;
double detM = surfaceCharacteristics.Item5;
double ksi3 = CalculateNormalGap(aMatrix, n);
if (ksi3 <= 0)
{
double[,] sN = CalculateMainStiffnessPart(Ksi1Current, n);
double deltaKsi = CalculateTangentialVelocity(Ksi1Current, Ksi1Initial);
double Tr1 = CalculateTangentialTraction(deltaKsi, detM);
double phi = Math.Sqrt(Tr1 * Tr1 * m11) - FrictionCoef * PenaltyFactor * Math.Abs(ksi3);
if (phi <= 0.0)
{
double T1 = Tr1;
double[,] sT1 = MatrixOperations.ScalarMatrixProductNew(TangentPenaltyFactor,
MatrixOperations.MatrixProduct(
MatrixOperations.Transpose(aMatrix),
MatrixOperations.MatrixProduct(
VectorOperations.VectorVectorTensorProduct(tVector, tVector), aMatrix)));
double[,] sT2 = MatrixOperations.ScalarMatrixProductNew(T1 * m11,
MatrixOperations.MatrixProduct(
MatrixOperations.Transpose(daMatrix),
MatrixOperations.MatrixProduct(
VectorOperations.VectorVectorTensorProduct(tVector, tVector), aMatrix)));
double[,] sT = MatrixOperations.MatrixAddition(
MatrixOperations.ScalarMatrixProductNew(-1.0, sT1),
MatrixOperations.MatrixAddition(sT2,
MatrixOperations.Transpose(sT2)));
double[,] globalStiffnessMatrix = MatrixOperations.MatrixAddition(sN, sT);
return(globalStiffnessMatrix);
}
else
{
double T1 = (Tr1 / Math.Abs(Tr1)) * mhid * PenaltyFactor * Math.Abs(ksi3) * Math.Sqrt(detM);
double[,] sT1 = MatrixOperations.ScalarMatrixProductNew(mhid * PenaltyFactor * (Tr1 / Math.Abs(Tr1)),
MatrixOperations.MatrixProduct(
MatrixOperations.Transpose(aMatrix),
MatrixOperations.MatrixProduct(
VectorOperations.VectorVectorTensorProduct(tVector, n), aMatrix)));
double[,] sT2 = MatrixOperations.ScalarMatrixProductNew(mhid * PenaltyFactor * Math.Abs(ksi3) * (Tr1 / Math.Abs(Tr1)) * Math.Sqrt(m11),
MatrixOperations.MatrixProduct(
MatrixOperations.Transpose(daMatrix),
MatrixOperations.MatrixProduct(
VectorOperations.VectorVectorTensorProduct(tVector, tVector), aMatrix)));
double[,] sT = MatrixOperations.MatrixAddition(
MatrixOperations.ScalarMatrixProductNew(-1.0, sT1),
MatrixOperations.MatrixAddition(sT2,
MatrixOperations.Transpose(sT2)));
double[,] globalStiffnessMatrix = MatrixOperations.MatrixAddition(sN, sT);
return(globalStiffnessMatrix);
}
//double[,] rotationalPart = CalculateRotationalStiffnessPart(aMatrix, daMatrix, n, ksi3, m11, dRho);
//double[,] globalStiffnessMatrix = MatrixOperations.MatrixAddition(mainPart, rotationalPart);
}
else
{
double[,] globalStifnessMatrix = new double[6, 6];
return(globalStifnessMatrix);
}
}
else
{
double[,] globalStifnessMatrix = new double[6, 6];
return(globalStifnessMatrix);
}
}
private double[,] RotationalStiffnessPart(double penaltyFactor, double[] normalVector, double[,] aMatrix, double[,] a1Matrix, double[,] a2Matrix, List <double[]> dRho, double ksi3)
{
double[,] m = MetricTensor(dRho);
double[,] mInv = InverseMetricTensor(m);
double scalar1 = penaltyFactor * ksi3 * mInv[0, 0];
double scalar2 = penaltyFactor * ksi3 * mInv[1, 0];
double scalar3 = penaltyFactor * ksi3 * mInv[0, 1];
double scalar4 = penaltyFactor * ksi3 * mInv[1, 1];
double[,] mat11 = MatrixOperations.MatrixProduct(MatrixOperations.Transpose(a1Matrix), MatrixOperations.MatrixProduct(VectorOperations.VectorVectorTensorProduct(normalVector, dRho[0]), aMatrix));
double[,] mat12 = MatrixOperations.MatrixProduct(MatrixOperations.Transpose(aMatrix), MatrixOperations.MatrixProduct(VectorOperations.VectorVectorTensorProduct(dRho[0], normalVector), a1Matrix));
double[,] mat21 = MatrixOperations.MatrixProduct(MatrixOperations.Transpose(a1Matrix), MatrixOperations.MatrixProduct(VectorOperations.VectorVectorTensorProduct(normalVector, dRho[1]), aMatrix));
double[,] mat22 = MatrixOperations.MatrixProduct(MatrixOperations.Transpose(aMatrix), MatrixOperations.MatrixProduct(VectorOperations.VectorVectorTensorProduct(dRho[0], normalVector), a2Matrix));
double[,] mat31 = MatrixOperations.MatrixProduct(MatrixOperations.Transpose(a2Matrix), MatrixOperations.MatrixProduct(VectorOperations.VectorVectorTensorProduct(normalVector, dRho[0]), aMatrix));
double[,] mat32 = MatrixOperations.MatrixProduct(MatrixOperations.Transpose(aMatrix), MatrixOperations.MatrixProduct(VectorOperations.VectorVectorTensorProduct(dRho[1], normalVector), a1Matrix));
double[,] mat41 = MatrixOperations.MatrixProduct(MatrixOperations.Transpose(a2Matrix), MatrixOperations.MatrixProduct(VectorOperations.VectorVectorTensorProduct(normalVector, dRho[1]), aMatrix));
double[,] mat42 = MatrixOperations.MatrixProduct(MatrixOperations.Transpose(aMatrix), MatrixOperations.MatrixProduct(VectorOperations.VectorVectorTensorProduct(dRho[1], normalVector), a2Matrix));
double[,] mat1 = MatrixOperations.MatrixAddition(mat11, mat12);
double[,] mat2 = MatrixOperations.MatrixAddition(mat21, mat22);
double[,] mat3 = MatrixOperations.MatrixAddition(mat31, mat32);
double[,] mat4 = MatrixOperations.MatrixAddition(mat41, mat42);
double[,] Kr = MatrixOperations.MatrixAddition(MatrixOperations.MatrixAddition(MatrixOperations.MatrixAddition(MatrixOperations.ScalarMatrixProductNew(scalar1, mat1),
MatrixOperations.ScalarMatrixProductNew(scalar2, mat2)),
MatrixOperations.ScalarMatrixProductNew(scalar3, mat3)),
MatrixOperations.ScalarMatrixProductNew(scalar4, mat4));
return(Kr);
}
