public double[] CreateInternalGlobalForcesVector()
{
double ksi1 = ClosestPointProjection();
if (Math.Abs(ksi1) <= 1.05)
{
Tuple <double[, ], double[, ]> positionMatrices = CalculatePositionMatrix(ksi1);
double[,] aMatrix = positionMatrices.Item1;
double[,] daMatrix = positionMatrices.Item2;
Tuple <double[], double, double[]> surfaceCharacteristics = SurfaceGeometry(daMatrix);
double m11 = surfaceCharacteristics.Item2;
double[] n = surfaceCharacteristics.Item3;
double ksi3 = CalculateNormalGap(aMatrix, n);
if (ksi3 <= 0)
{
double[,] AT = MatrixOperations.Transpose(aMatrix);
double[] AT_n = VectorOperations.MatrixVectorProduct(AT, n);
double[] internalGlobalForcesVector = VectorOperations.VectorScalarProductNew(AT_n, PenaltyFactor * ksi3);
return(internalGlobalForcesVector);
}
else
{
double[] internalGlobalForcesVector = new double[6];
return(internalGlobalForcesVector);
}
}
else
{
double[] internalGlobalForcesVector = new double[6];
return(internalGlobalForcesVector);
}
}
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);
}
public double[] CreateInternalGlobalForcesVector()
{
double[] ksiVector = Project(new double[2]);
if (Math.Abs(ksiVector[0]) <= 1.05 && ksiVector[1] <= 1.05)
{
Tuple <double[, ], double[, ], double[, ]> aMatrices = CalculatePositionMatrix(ksiVector[0], ksiVector[1]);
List <double[]> dRho = SurfaceVectors(ksiVector[0], ksiVector[1]);
double[,] m = MetricTensor(dRho);
double[] n = NormalVector(m, dRho);
double[] xUpdated = xUpdatedVector();
double ksi3 = CalculatePenetration(n, aMatrices.Item1, xUpdated);
if (ksi3 <= 0)
{
double[,] AT = MatrixOperations.Transpose(aMatrices.Item1);
double[] AT_n = VectorOperations.MatrixVectorProduct(AT, n);
double[] internalGlobalForcesVector = VectorOperations.VectorScalarProductNew(AT_n, PenaltyFactor * ksi3);
return(internalGlobalForcesVector);
}
else
{
return(new double[15]);
}
}
else
{
return(new double[15]);
}
}
public double[] CreateInternalGlobalForcesVector()
{
int nodesNumber = Properties.MasterSegmentPolynomialDegree + Properties.SlaveSegmentPolynomialDegree + 2;
double[] internalGlobalForcesVector = new double[2 * nodesNumber];
for (int i = 0; i < Properties.IntegrationPoints; i++)
{
double ksi2 = GaussPoints(i).Item1;
double gW = GaussPoints(i).Item2;
double ksi1 = Project(0.0, ksi2);
if (Math.Abs(ksi1) <= 1.05)
{
Tuple <double[, ], double[, ], double[, ], double[, ], double[, ]> positionMatrices = CalculatePositionMatrix(ksi1, ksi2);
double[,] aMatrix = positionMatrices.Item1;
double[,] daMatrix = positionMatrices.Item2;
double[,] da2Matrix = positionMatrices.Item3;
Tuple <double[], double, double[], double[], double> surfaceCharacteristics = MasterSegmentGeometry(daMatrix, da2Matrix);
double[] n = surfaceCharacteristics.Item3;
double ksi3 = CalculatePenetration(aMatrix, n);
if (ksi3 <= 0)
{
double slaveMetricTensor = SlaveSegmentGeometry(positionMatrices.Item4, positionMatrices.Item5).Item2;
double scalar = Math.Pow(slaveMetricTensor, 0.5) * gW;
double[,] AT = MatrixOperations.Transpose(aMatrix);
double[] AT_n = VectorOperations.MatrixVectorProduct(AT, n);
double[] internalLocalForcesVector = VectorOperations.VectorScalarProductNew(VectorOperations.VectorScalarProductNew(AT_n, PenaltyFactor * ksi3), scalar);
internalGlobalForcesVector = VectorOperations.VectorVectorAddition(internalGlobalForcesVector, internalLocalForcesVector);
}
}
}
return(internalGlobalForcesVector);
}
public double[] CreateInternalGlobalForcesVector()
{
double penetration = CalculateNormalGap();
if (penetration <= 0)
{
double[,] A = CalculatePositionMatrix();
double[,] AT = MatrixOperations.Transpose(A);
double[] n = CalculateNormalUnitVector();
double[] t = CalculateTangentUnitVector();
double[] AT_n = VectorOperations.MatrixVectorProduct(AT, n);
double[] AT_t = VectorOperations.MatrixVectorProduct(AT, t);
double ksi = CalculateNormalGap();
double Tr = CalculateTangentialTraction();
double[] ksi_AT_n = VectorOperations.VectorScalarProductNew(AT_n, ksi);
double[] e_ksi_AT_n = VectorOperations.VectorScalarProductNew(ksi_AT_n, PenaltyFactor);
double[] Tr_AT_t = VectorOperations.VectorScalarProductNew(AT_t, Tr);
double[] internalForcesvector = VectorOperations.VectorVectorAddition(e_ksi_AT_n, Tr_AT_t);
return(internalForcesvector);
}
else
{
double[] internalGlobalForcesVector = new double[4];
return(internalGlobalForcesVector);
}
}
public override double[] Solve(double[,] stiffnessMatrix, double[] forceVector)
{
double[,] lowerMatrix = Cholesky(stiffnessMatrix);
double[,] upperMatrix = MatrixOperations.Transpose(lowerMatrix);
double[] intermediateVector = ForwardSubstitution(lowerMatrix, forceVector);
double[] solutionuberVector = BackSubstitution(upperMatrix, intermediateVector);
return(solutionuberVector);
}
private double CalculatePenetration(double[] normalVector, double[,] aMatrix, double[] xUpdated)
{
double ksi3 = VectorOperations.VectorDotProduct(
xUpdated, VectorOperations.MatrixVectorProduct(
MatrixOperations.Transpose(aMatrix), normalVector));
return(ksi3);
}
public double[,] CreateGlobalStiffnessMatrix()
{
double[,] globalStiffnessMatrix = new double[6, 6];
//double E = Properties.YoungMod;
//double A = Properties.SectionArea;
//double I = Properties.MomentOfInertia;
//double L = CalculateElementLength();
//double c = CalculateElementCosinus();
//double s = CalculateElementSinus();
//globalStiffnessMatrix[0, 0] = (12 * E * I * s * s / Math.Pow(L, 3)) + (A * E * c * c / L);
//globalStiffnessMatrix[0, 1] = (A * E * c * s / L) - (12 * E * I * c * s / Math.Pow(L, 3));
//globalStiffnessMatrix[0, 2] = -6 * E * I * s / Math.Pow(L, 2);
//globalStiffnessMatrix[0, 3] = (-12 * E * I * s * s / Math.Pow(L, 3)) - (A * E * c * c / L);
//globalStiffnessMatrix[0, 4] = (12 * E * I * c * s / Math.Pow(L, 3)) - (A * E * c * s / L);
//globalStiffnessMatrix[0, 5] = -6 * E * I * s / Math.Pow(L, 2);
//globalStiffnessMatrix[1, 0] = globalStiffnessMatrix[0, 1];
//globalStiffnessMatrix[1, 1] = (A * E * s * s / L) + (12 * E * I * c * c / Math.Pow(L, 3));
//globalStiffnessMatrix[1, 2] = 6 * E * I * c / Math.Pow(L, 2);
//globalStiffnessMatrix[1, 3] = (12 * E * I * c * s / Math.Pow(L, 3)) - (A * E * c * s / L);
//globalStiffnessMatrix[1, 4] = -(A * E * s * s / L) - (12 * E * I * c * c / Math.Pow(L, 3));
//globalStiffnessMatrix[1, 5] = 6 * E * I * c / Math.Pow(L, 2);
//globalStiffnessMatrix[2, 0] = globalStiffnessMatrix[0, 2];
//globalStiffnessMatrix[2, 1] = globalStiffnessMatrix[1, 2];
//globalStiffnessMatrix[2, 2] = 4 * E * I / L;
//globalStiffnessMatrix[2, 3] = 6 * E * I * s / Math.Pow(L, 2);
//globalStiffnessMatrix[2, 4] = -6 * E * I * c / Math.Pow(L, 2);
//globalStiffnessMatrix[2, 5] = 2 * E * I / L;
//globalStiffnessMatrix[3, 0] = globalStiffnessMatrix[0, 3];
//globalStiffnessMatrix[3, 1] = globalStiffnessMatrix[1, 3];
//globalStiffnessMatrix[3, 2] = globalStiffnessMatrix[2, 3];
//globalStiffnessMatrix[3, 3] = (12 * E * I * s * s / Math.Pow(L, 3)) + (A * E * c * c / L);
//globalStiffnessMatrix[3, 4] = (A * E * c * s / L) - (12 * E * I * c * s / Math.Pow(L, 3));
//globalStiffnessMatrix[3, 5] = 6 * E * I * s / Math.Pow(L, 2);
//globalStiffnessMatrix[4, 0] = globalStiffnessMatrix[0, 4];
//globalStiffnessMatrix[4, 1] = globalStiffnessMatrix[1, 4];
//globalStiffnessMatrix[4, 2] = globalStiffnessMatrix[2, 4];
//globalStiffnessMatrix[4, 3] = globalStiffnessMatrix[3, 4];
//globalStiffnessMatrix[4, 4] = (A * E * s * s / L) + (12 * E * I * c * c / Math.Pow(L, 3));
//globalStiffnessMatrix[4, 5] = -6 * E * I * c / Math.Pow(L, 2);
//globalStiffnessMatrix[5, 0] = globalStiffnessMatrix[0, 5];
//globalStiffnessMatrix[5, 1] = globalStiffnessMatrix[1, 5];
//globalStiffnessMatrix[5, 2] = globalStiffnessMatrix[2, 5];
//globalStiffnessMatrix[5, 3] = globalStiffnessMatrix[3, 5];
//globalStiffnessMatrix[5, 4] = globalStiffnessMatrix[4, 5];
//globalStiffnessMatrix[5, 5] = 4 * E * I / L;
double[,] lambda = CreateLambdaMatrix();
double[,] localStiff = CreateLocalStiffnessMatrix();
double[,] transposeLocalStiff = MatrixOperations.Transpose(lambda);
double[,] KxL = MatrixOperations.MatrixProduct(localStiff, lambda);
globalStiffnessMatrix = MatrixOperations.MatrixProduct(transposeLocalStiff, KxL);
return(globalStiffnessMatrix);
}
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 CalculatePenetration(double[,] aMatrix, double[] n)
{
double[,] AT = MatrixOperations.Transpose(aMatrix);
double[] AT_n = VectorOperations.MatrixVectorProduct(AT, n);
double[] xupd = NodalXUpdated();
double normalGap = VectorOperations.VectorDotProduct(xupd, AT_n);
return(normalGap);
}
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[,] 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[,] 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 CalculateTangentialTraction()
{
double[,] A = CalculatePositionMatrix();
double[,] AT = MatrixOperations.Transpose(A);
double[] displacementVector = DisplacementVector;
double[] tangentUnitvector = CalculateTangentUnitVector();
double[] aT_t = VectorOperations.MatrixVectorProduct(AT, tangentUnitvector);
double tangentGap = VectorOperations.VectorDotProduct(displacementVector, aT_t);
double tangentialTraction = -PenaltyFactor * tangentGap;
return(tangentialTraction);
}
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[,] 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);
}
private double CalculateNormalGap(double[,] aMatrix, double[] n)
{
double[,] AT = MatrixOperations.Transpose(aMatrix);
double[] AT_n = VectorOperations.MatrixVectorProduct(AT, n);
double[] xupd = new double[] {
Nodes[1].XCoordinate + DisplacementVector[0],
Nodes[1].YCoordinate + DisplacementVector[1],
Nodes[2].XCoordinate + DisplacementVector[2],
Nodes[2].YCoordinate + DisplacementVector[3],
Nodes[3].XCoordinate + DisplacementVector[4],
Nodes[3].YCoordinate + DisplacementVector[5]
};
double normalGap = VectorOperations.VectorDotProduct(xupd, AT_n);
return(normalGap);
}
private double CalculateNormalGap()
{
double[,] A = CalculatePositionMatrix();
double[,] AT = MatrixOperations.Transpose(A);
double[] n = CalculateNormalUnitVector();
double[] AT_n = VectorOperations.MatrixVectorProduct(AT, n);
double[] xupd = new double[] {
Nodes[1].XCoordinate + DisplacementVector[0],
Nodes[1].YCoordinate + DisplacementVector[1],
Nodes[2].XCoordinate + DisplacementVector[2],
Nodes[2].YCoordinate + DisplacementVector[3]
};
double normalGap = VectorOperations.VectorDotProduct(xupd, AT_n);
return(normalGap);
}
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 CalculatePenetration(double ksi1, double ksi2)
{
double[] xUpdated = xUpdatedVector();
List <double[]> dRho = SurfaceVectors(ksi1, ksi2);
double[,] m = MetricTensor(dRho);
double[] n = NormalVector(m, dRho);
Tuple <double[, ], double[, ], double[, ]> aMatrices = CalculatePositionMatrix(ksi1, ksi2);
double[,] a = aMatrices.Item1;
double[,] aT = MatrixOperations.Transpose(a);
double ksi3 = VectorOperations.VectorDotProduct(
xUpdated, VectorOperations.MatrixVectorProduct(
aT, n));
return(ksi3);
}
public double[] CreateInternalGlobalForcesVector()
{
double[,] globalStiffnessMatrix = new double[6, 6];
double[,] lambda = CreateLambdaMatrix();
double[,] localStiff = CreateLocalStiffnessMatrix();
double[,] transposeLocalStiff = MatrixOperations.Transpose(lambda);
double[,] KxL = MatrixOperations.MatrixProduct(localStiff, lambda);
globalStiffnessMatrix = MatrixOperations.MatrixProduct(transposeLocalStiff, KxL);
double[] stiffPart = VectorOperations.MatrixVectorProduct(globalStiffnessMatrix, DisplacementVector);
//if (AccelerationVector != null)
//{
// double[,] globalMassMatrix = CreateMassMatrix();
// double[] massPart = VectorOperations.MatrixVectorProduct(globalMassMatrix, VectorOperations.VectorScalarProductNew(AccelerationVector, 1.0));
// stiffPart = VectorOperations.VectorVectorAddition(stiffPart, massPart);
//}
return(stiffPart);
}
public double[,] CreateMassMatrix()
{
double[,] lambda = CreateLambdaMatrix();
double[,] localMassMatrix;
if (ActivateLumbedMassMatrix == true)
{
localMassMatrix = CreateLumpedMassMatrix();
}
else
{
localMassMatrix = CreateConsistentMassMatrix();
}
double[,] globalMassMatrix = MatrixOperations.MatrixProduct
(
MatrixOperations.Transpose(lambda), MatrixOperations.MatrixProduct(localMassMatrix, lambda)
);
return(globalMassMatrix);
}
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);
}
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)
);
//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[] CreateInternalGlobalForcesVector()
{
//double ksi1 = ClosestPointProjection();
Ksi1Current = 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[] n = surfaceCharacteristics.Item3;
double[] tVector = surfaceCharacteristics.Item4;
double detM = surfaceCharacteristics.Item5;
double ksi3 = CalculateNormalGap(aMatrix, n);
if (ksi3 <= 0)
{
double[,] AT = MatrixOperations.Transpose(aMatrix);
double[] AT_n = VectorOperations.MatrixVectorProduct(AT, n);
double[] AT_t = VectorOperations.MatrixVectorProduct(AT, tVector);
double deltaKsi = CalculateTangentialVelocity(Ksi1Current, Ksi1Initial);
//Console.WriteLine(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[] internalGlobalForcesVector = VectorOperations.VectorVectorAddition(
VectorOperations.VectorScalarProductNew(AT_n, PenaltyFactor * ksi3),
VectorOperations.VectorScalarProductNew(AT_t, T1 * Math.Sqrt(m11)));
return(internalGlobalForcesVector);
}
else
{
double T1 = (Tr1 / Math.Abs(Tr1)) * mhid * PenaltyFactor * Math.Abs(ksi3) * Math.Sqrt(detM);
double[] internalGlobalForcesVector = VectorOperations.VectorVectorAddition(
VectorOperations.VectorScalarProductNew(AT_n, PenaltyFactor * ksi3),
VectorOperations.VectorScalarProductNew(AT_t, T1 * Math.Sqrt(m11)));
return(internalGlobalForcesVector);
}
}
else
{
double[] internalGlobalForcesVector = new double[6];
return(internalGlobalForcesVector);
}
}
else
{
double[] internalGlobalForcesVector = new double[6];
return(internalGlobalForcesVector);
}
}
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);
}
}
public double[,] CreateGlobalStiffnessMatrix()
{
double[,] K = new double[24, 24];
double[,] E = CalculateStressStrainMatrix(Properties.YoungMod, Properties.PoissonRatio);
for (int i = 0; i < 2; i++)
{
for (int j = 0; j < 2; j++)
{
for (int k = 0; k < 2; k++)
{
double[] gP = GaussPoints(i, j, k).Item1;
double[] gW = GaussPoints(i, j, k).Item2;
Dictionary <string, double[]> localdN = CalculateShapeFunctionsLocalDerivatives(gP);
double[,] J = CalculateJacobian(localdN);
double[,] invJ = CalculateInverseJacobian(J).Item1;
double detJ = CalculateInverseJacobian(J).Item2;
Dictionary <int, double[]> globaldN = CalculateShapeFunctionsGlobalDerivatives(localdN, invJ);
double[,] B = CalculateBMatrix(globaldN);
K = MatrixOperations.MatrixAddition(K, MatrixOperations.ScalarMatrixProductNew(detJ * gW[0] * gW[1] * gW[2],
MatrixOperations.MatrixProduct(MatrixOperations.Transpose(B), MatrixOperations.MatrixProduct(E, B))));
}
}
}
return(K);
}
public double[] CreateInternalGlobalForcesVector()
{
double[] fInt = new double[24];
double[,] E = CalculateStressStrainMatrix(Properties.YoungMod, Properties.PoissonRatio);
for (int i = 0; i < 2; i++)
{
for (int j = 0; j < 2; j++)
{
for (int k = 0; k < 2; k++)
{
double[] gP = GaussPoints(i, j, k).Item1;
double[] gW = GaussPoints(i, j, k).Item2;
Dictionary <string, double[]> localdN = CalculateShapeFunctionsLocalDerivatives(gP);
double[,] J = CalculateJacobian(localdN);
double[,] invJ = CalculateInverseJacobian(J).Item1;
double detJ = CalculateInverseJacobian(J).Item2;
Dictionary <int, double[]> globaldN = CalculateShapeFunctionsGlobalDerivatives(localdN, invJ);
double[,] B = CalculateBMatrix(globaldN);
double[] strainVector = CalculateStrainsVector(B);
double[] stressVector = CalculateStressVector(E, strainVector);
fInt = VectorOperations.VectorVectorAddition(fInt, VectorOperations.VectorScalarProductNew(
VectorOperations.MatrixVectorProduct(MatrixOperations.Transpose(B), stressVector), detJ * gW[0] * gW[1] * gW[2]));
}
}
}
//double[,] Kstiff = CreateGlobalStiffnessMatrix();
//double[] uDisp = DisplacementVector;
//double[] fInt = VectorOperations.MatrixVectorProduct(Kstiff, uDisp);
//fInt = VectorOperations.VectorScalarProductNew(fInt, 1.0);
return(fInt);
}