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 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);
}
}
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 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);
}
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]);
}
}
private double[] PCG(double[,] stiffnessMatrix, double[] forceVector)
{
double[] solutionVector = new double[forceVector.Length];
double[,] preconditioner = new double[stiffnessMatrix.GetLength(0), stiffnessMatrix.GetLength(1)];
for (int i = 0; i < preconditioner.GetLength(0); i++)
{
preconditioner[i, i] = 1 / stiffnessMatrix[i, i];
}
double[] residual = VectorOperations.VectorVectorSubtraction(
forceVector,
VectorOperations.MatrixVectorProduct(stiffnessMatrix, solutionVector)
);
double[] preconVector = VectorOperations.MatrixVectorProduct(preconditioner, residual);
for (int iter = 0; iter < maxIterations; iter++)
{
double[] u = VectorOperations.MatrixVectorProduct(stiffnessMatrix, preconVector);
double residualDotOld = VectorOperations.VectorDotProduct(residual, preconVector);
double alpha = residualDotOld / VectorOperations.VectorDotProduct(preconVector, u);
solutionVector = VectorOperations.VectorVectorAddition(solutionVector, VectorOperations.VectorScalarProductNew(preconVector, alpha));
residual = VectorOperations.VectorVectorSubtraction(residual, VectorOperations.VectorScalarProductNew(u, alpha));
if (VectorOperations.VectorDotProduct(residual, residual) < tolerance)
{
break;
}
double residualDotNew = VectorOperations.VectorDotProduct(residual, VectorOperations.MatrixVectorProduct(preconditioner, residual));
double beta = residualDotNew / residualDotOld;
preconVector = VectorOperations.VectorVectorAddition(
VectorOperations.MatrixVectorProduct(preconditioner, residual),
VectorOperations.VectorScalarProductNew(preconVector, beta)
);
}
return(solutionVector);
}
private Tuple <double[], double, double[], double[], double> MasterSegmentGeometry(double[,] daMatrix, double[,] da2Matrix)
{
double Xm1 = Nodes[1].XCoordinate + DisplacementVector[0];
double Ym1 = Nodes[1].YCoordinate + DisplacementVector[1];
double Xm2 = Nodes[2].XCoordinate + DisplacementVector[2];
double Ym2 = Nodes[2].YCoordinate + DisplacementVector[3];
double Xm3 = Nodes[3].XCoordinate + DisplacementVector[4];
double Ym3 = Nodes[3].YCoordinate + DisplacementVector[5];
double Xs = Nodes[4].XCoordinate + DisplacementVector[6];
double Ys = Nodes[4].YCoordinate + DisplacementVector[7];
double[] xupd = new double[] { -Xm1, -Ym1, -Xm2, -Ym2, -Xm3, -Ym3, -Xs, -Ys };
double[] surfaceVector = VectorOperations.MatrixVectorProduct(daMatrix, xupd);
double[] surfaceVectorDerivative = VectorOperations.MatrixVectorProduct(da2Matrix, xupd);
double detm = VectorOperations.VectorDotProduct(surfaceVector, surfaceVector);
double m11 = 1.0 / detm;
double[] vector = new double[] { -surfaceVector[1], surfaceVector[0] };
double scalarCoef = 1.0 / (Math.Sqrt(detm));
double[] normalUnitVec = VectorOperations.VectorScalarProductNew(vector, scalarCoef);
double[] tangentVector = VectorOperations.VectorScalarProductNew(surfaceVector, scalarCoef);
double scalarCoef2 = Math.Pow(m11, 2.0);
double curvatureTensor = scalarCoef2 * VectorOperations.VectorDotProduct(surfaceVectorDerivative, normalUnitVec);
return(new Tuple <double[], double, double[], double[], double>(surfaceVector, m11, normalUnitVec, tangentVector, curvatureTensor));
}
public double[] CreateInternalGlobalForcesVector()
{
double[] F = new double[8];
double[,] E = CalculateStressStrainMatrix(Properties.YoungMod, 0.30); //needs fixing in poisson v
for (int i = 0; i < 2; i++)
{
for (int j = 0; j < 2; j++)
{
double[] gP = GaussPoints(i, j).Item1;
double[] gW = GaussPoints(i, j).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);
F = VectorOperations.VectorVectorAddition(F, VectorOperations.VectorScalarProductNew(
VectorOperations.MatrixVectorProduct(MatrixOperations.Transpose(B), stressVector), detJ * gW[0] * gW[1] * Properties.Thickness));
}
}
return(F);
}
private double[] LoadControlledNR(double[] forceVector)
{
lambda = 1.0 / numberOfLoadSteps;
double[] incrementDf = VectorOperations.VectorScalarProductNew(forceVector, lambda);
double[] solutionVector = new double[forceVector.Length];
double[] incrementalExternalForcesVector = new double[forceVector.Length];
double[] tempSolutionVector = new double[solutionVector.Length];
double[] deltaU = new double[solutionVector.Length];
double[] internalForcesTotalVector;
double[] dU;
double[] residual;
double residualNorm;
//Assembler.UpdateAccelerations(CalculateAccelerations(InitialValues.InitialAccelerationVector));
for (int i = 0; i < numberOfLoadSteps; i++)
{
incrementalExternalForcesVector = VectorOperations.VectorVectorAddition(incrementalExternalForcesVector, incrementDf);
Assembler.UpdateDisplacements(solutionVector);
Assembler.UpdateAccelerations(explicitAcceleration.Values.Last());
internalForcesTotalVector = Assembler.CreateTotalInternalForcesVector();
double[,] tangentMatrix = CalculateHatMMatrix();
dU = LinearSolver.Solve(tangentMatrix, incrementDf);
solutionVector = VectorOperations.VectorVectorAddition(solutionVector, dU);
Assembler.UpdateDisplacements(solutionVector);
tangentMatrix = CalculateHatMMatrix();
internalForcesTotalVector = Assembler.CreateTotalInternalForcesVector();
residual = VectorOperations.VectorVectorSubtraction(internalForcesTotalVector, incrementalExternalForcesVector);
residualNorm = VectorOperations.VectorNorm2(residual);
int iteration = 0;
Array.Clear(deltaU, 0, deltaU.Length);
while (residualNorm > tolerance && iteration < maxIterations)
{
tangentMatrix = CalculateHatMMatrix();
deltaU = VectorOperations.VectorVectorSubtraction(deltaU, LinearSolver.Solve(tangentMatrix, residual));
tempSolutionVector = VectorOperations.VectorVectorAddition(solutionVector, deltaU);
Assembler.UpdateDisplacements(tempSolutionVector);
//Assembler.UpdateAccelerations(CalculateAccelerations(solutionVector));
internalForcesTotalVector = Assembler.CreateTotalInternalForcesVector();
residual = VectorOperations.VectorVectorSubtraction(internalForcesTotalVector, incrementalExternalForcesVector);
residualNorm = VectorOperations.VectorNorm2(residual);
iteration = iteration + 1;
}
solutionVector = VectorOperations.VectorVectorAddition(solutionVector, deltaU);
if (iteration >= maxIterations)
{
Console.WriteLine("Newton-Raphson: Solution not converged at current iterations");
}
}
return(solutionVector);
}
private double[] LoadControlledNR(double[] forceVector)
{
double[] incrementDf = VectorOperations.VectorScalarProductNew(forceVector, lambda);
double[] solutionVector = localSolutionVector;
double[] incrementalExternalForcesVector = new double[forceVector.Length];
double[] tempSolutionVector = new double[solutionVector.Length];
double[] deltaU = new double[solutionVector.Length];
double[] internalForcesTotalVector;
double[] dU;
double[] residual;
double residualNorm;
for (int i = 0; i < numberOfLoadSteps; i++)
{
incrementalExternalForcesVector = VectorOperations.VectorVectorAddition(incrementalExternalForcesVector, incrementDf);
discretization.UpdateDisplacements(solutionVector);
internalForcesTotalVector = discretization.CreateTotalInternalForcesVector();
double[,] stiffnessMatrix = discretization.CreateTotalStiffnessMatrix();
//OnConvergenceResult("Newton-Raphson: Solution not converged at load step" + i);
dU = linearSolver.Solve(stiffnessMatrix, incrementDf);
solutionVector = VectorOperations.VectorVectorAddition(solutionVector, dU);
residual = VectorOperations.VectorVectorSubtraction(internalForcesTotalVector, incrementalExternalForcesVector);
residualNorm = VectorOperations.VectorNorm2(residual);
int iteration = 0;
Array.Clear(deltaU, 0, deltaU.Length);
while (residualNorm > Tolerance && iteration < MaxIterations)
{
stiffnessMatrix = discretization.CreateTotalStiffnessMatrix();
deltaU = VectorOperations.VectorVectorSubtraction(deltaU, linearSolver.Solve(stiffnessMatrix, residual));
tempSolutionVector = VectorOperations.VectorVectorAddition(solutionVector, deltaU);
discretization.UpdateDisplacements(tempSolutionVector);
internalForcesTotalVector = discretization.CreateTotalInternalForcesVector();
residual = VectorOperations.VectorVectorSubtraction(internalForcesTotalVector, incrementalExternalForcesVector);
residualNorm = VectorOperations.VectorNorm2(residual);
if (residualNorm <= Tolerance)
{
OnConvergenceResult("Newton-Raphson: Load Step " + i + " - Solution converged at iteration " + iteration + " - Residual Norm = " + residualNorm);
}
else
{
OnConvergenceResult("Newton-Raphson: Load Step " + i + " - Solution not converged at iteration " + iteration + " - Residual Norm = " + residualNorm);
}
iteration = iteration + 1;
//(Application.Current.Windows[0] as MainWindow).LogTool.Text = "ok";
//OnConvergenceResult("Newton-Raphson: Solution not converged at load step" + iteration);
}
InternalForces.Add(i + 1, internalForcesTotalVector);
solutionVector = VectorOperations.VectorVectorAddition(solutionVector, deltaU);
Solutions.Add(i + 1, solutionVector);
if (iteration >= MaxIterations)
{
OnConvergenceResult("Newton-Raphson did not converge at Load Step " + i + ". Exiting solution.");
LoadStepConvergence.Add("Solution not converged.");
break;
}
LoadStepConvergence.Add("Solution converged.");
}
return(solutionVector);
}
private double[] NormalVector(double[,] m, List <double[]> dRho)
{
double detm = MetricTensorDet(m);
double[] drhoBydrho = VectorOperations.VectorCrossProduct(dRho[0], dRho[1]);
double[] n = VectorOperations.VectorScalarProductNew(drhoBydrho, 1.0 / (Math.Sqrt(detm)));
return(n);
}
private double[] CalculatePreviousDisplacementVector()
{
double[] previousDisp = VectorOperations.VectorVectorAddition(
VectorOperations.VectorVectorSubtraction(InitialValues.InitialDisplacementVector,
VectorOperations.VectorScalarProductNew(InitialValues.InitialVelocityVector, timeStep)),
VectorOperations.VectorScalarProductNew(InitialValues.InitialAccelerationVector, a3));
return(previousDisp);
}
public double[] CreateInternalGlobalForcesVector()
{
double[] intForces;
double[,] stiff = CreateGlobalStiffnessMatrix();
intForces = VectorOperations.MatrixVectorProduct(stiff, DisplacementVector);
intForces = VectorOperations.VectorScalarProductNew(intForces, 1.0);
return(intForces);
}
private double[] BiCGSTAB(double[,] stiffnessMatrix, double[] forceVector)
{
double[] solutionVector = new double[forceVector.Length];
double[] xVector = new double[forceVector.Length];
double[] pVector = new double[forceVector.Length];
double[] vVector = new double[forceVector.Length];
double[,] K = stiffnessMatrix;
double[] bVector = forceVector;
double[] rVector = VectorOperations.VectorVectorSubtraction(bVector, VectorOperations.MatrixVectorProduct(K, xVector));
double[] r0hatVector = rVector;
double rho0 = 1.0;
double w = 1.0;
double a = 1.0;
double rho1 = VectorOperations.VectorDotProduct(r0hatVector, rVector);
double b;
double[] sVector;
double[] tVector;
int iters = 100;
double converged;
for (int i = 0; i < iters; i++)
{
b = (rho1 / rho0) * (a / w);
pVector = VectorOperations.VectorVectorAddition(rVector,
VectorOperations.VectorScalarProductNew(
VectorOperations.VectorVectorSubtraction(pVector,
VectorOperations.VectorScalarProductNew(vVector, w)), b));
vVector = VectorOperations.MatrixVectorProduct(K, pVector);
a = rho1 / VectorOperations.VectorDotProduct(r0hatVector, vVector);
sVector = VectorOperations.VectorVectorSubtraction(rVector,
VectorOperations.VectorScalarProductNew(vVector, a));
tVector = VectorOperations.MatrixVectorProduct(K, sVector);
w = VectorOperations.VectorDotProduct(tVector, sVector) / VectorOperations.VectorDotProduct(tVector, tVector);
rho0 = rho1;
rho1 = -w *VectorOperations.VectorDotProduct(r0hatVector, tVector);
xVector = VectorOperations.VectorVectorAddition(xVector,
VectorOperations.VectorScalarProductNew(pVector, a));
xVector = VectorOperations.VectorVectorAddition(xVector,
VectorOperations.VectorScalarProductNew(sVector, w));
rVector = VectorOperations.VectorVectorSubtraction(sVector,
VectorOperations.VectorScalarProductNew(tVector, w));
converged = VectorOperations.VectorNorm2(rVector);
if (i == iters | converged < 0.00000001)
{
break;
}
}
solutionVector = xVector;
return(solutionVector);
}
//private double[] UpdatedF(double[] forceVector)
//{
// lambda = 1.0 / numberOfLoadSteps;
// double[] incrementDf = VectorOperations.VectorScalarProductNew(forceVector, lambda);
// double[] solutionVector = new double[forceVector.Length];
// double[] incrementalExternalForcesVector = new double[forceVector.Length];
// double[] tempSolutionVector = new double[solutionVector.Length];
// double[] deltaU = new double[solutionVector.Length];
// double[] internalForcesTotalVector;
// double[] dU;
// double[] currentU = explicitSolution.Values.Last();
// Assembler.UpdateDisplacements(currentU);
// internalForcesTotalVector = Assembler.CreateTotalInternalForcesVector();
// double[,] TotalMassMatrix = Assembler.CreateTotalMassMatrix();
// double[] a2_M_ut = VectorOperations.MatrixVectorProduct(
// MatrixOperations.ScalarMatrixProductNew(a2, TotalMassMatrix), currentU);
// double[] a0_M_ut = VectorOperations.MatrixVectorProduct(
// MatrixOperations.ScalarMatrixProductNew(a0, TotalMassMatrix), currentU);
// double[,] hatMMatrix = CalculateHatMMatrix();
// double[] hatM_utprevious = VectorOperations.MatrixVectorProduct(hatMMatrix, )
//double[,] hatK = MatrixOperations.MatrixSubtraction(TotalStiffnessMatrix,
// MatrixOperations.ScalarMatrixProductNew(a2, TotalMassMatrix));
//double[] hatCurrentU = VectorOperations.MatrixVectorProduct(hatKMatrix, explicitSolution[i - 1]);
// double[] hatPreviousU = VectorOperations.MatrixVectorProduct(hatMMatrix, explicitSolution[i - 2]);
// double[] hatR = VectorOperations.VectorVectorSubtraction(ExternalForcesVector,
// VectorOperations.VectorVectorAddition(hatCurrentU, hatPreviousU));
// double[,] tangentMatrix = CalculateHatMMatrix();
// dU = LinearSolver.Solve(tangentMatrix, incrementDf);
// solutionVector = VectorOperations.VectorVectorAddition(solutionVector, dU);
// Assembler.UpdateDisplacements(solutionVector);
// tangentMatrix = CalculateHatMMatrix();
// internalForcesTotalVector = Assembler.CreateTotalInternalForcesVector();
// residual = VectorOperations.VectorVectorSubtraction(internalForcesTotalVector, incrementalExternalForcesVector);
// residualNorm = VectorOperations.VectorNorm2(residual);
// int iteration = 0;
// Array.Clear(deltaU, 0, deltaU.Length);
// return solutionVector;
//}
/// <summary>
/// Calculates accelerations for time t
/// </summary>
/// <returns></returns>
private double[] CalculateAccelerations() //Bathe page 771
{
int steps = explicitSolution.Count;
double[] aCurrent =
VectorOperations.VectorScalarProductNew(
VectorOperations.VectorVectorAddition(explicitSolution[steps - 4],
VectorOperations.VectorVectorAddition(
VectorOperations.VectorScalarProductNew(explicitSolution[steps - 3], -2.0), explicitSolution[steps - 2])), a0);
return(aCurrent);
}
private double[] CalculateVelocityNewmark(int step, List <double> aConstants)
{
double[] dUt = explicitVelocity[step - 1];
double[] ddUt = explicitAcceleration[step - 1];
double[] ddUtplusDt = explicitAcceleration[step];
double[] part1 = VectorOperations.VectorScalarProductNew(ddUt, aConstants[6]);
double[] part2 = VectorOperations.VectorScalarProductNew(ddUtplusDt, aConstants[7]);
double[] dUtplusDt = VectorOperations.VectorVectorAddition(dUt,
VectorOperations.VectorVectorAddition(part1, part2));
return(dUtplusDt);
}
private double[] CalculateDeltaKsi(double detm, double[,] mTensor, double[] fVector, double e)
{
double scalar = 1.0 / (detm - Math.Pow(e, 2) + 2.0 * e * mTensor[0, 1]);
double[,] matrix = new double[, ]
{
{ mTensor[1, 1], e - mTensor[0, 1] },
{ e - mTensor[1, 0], mTensor[0, 0] }
};
double[] deltaKsi = VectorOperations.VectorScalarProductNew(
VectorOperations.MatrixVectorProduct(matrix, fVector),
scalar);
return(deltaKsi);
}
private double[] CalculateAccelerationNewmark(int step, List <double> aConstants)
{
double[] dUt = explicitVelocity[step - 1];
double[] ut = explicitSolution[step - 1];
double[] utplusDt = explicitSolution[step];
double[] ddUt = explicitAcceleration[step - 1];
double[] part1 = VectorOperations.VectorScalarProductNew(
VectorOperations.VectorVectorSubtraction(utplusDt, ut), aConstants[0]);
double[] part2 = VectorOperations.VectorScalarProductNew(dUt, aConstants[2]);
double[] part3 = VectorOperations.VectorScalarProductNew(ddUt, aConstants[3]);
double[] ddUtplusDt = VectorOperations.VectorVectorSubtraction(part1,
VectorOperations.VectorVectorAddition(part2, part3));
return(ddUtplusDt);
}
private List <double[]> SurfaceVectors(double ksi1, double ksi2)
{
Tuple <double[, ], double[, ], double[, ]> positionsMatrices = CalculatePositionMatrix(ksi1, ksi2);
double[,] da1 = positionsMatrices.Item2;
double[,] da2 = positionsMatrices.Item3;
double[] xUpdated = xUpdatedVector();
List <double[]> dRho = new List <double[]>();
dRho.Add(VectorOperations.VectorScalarProductNew(
VectorOperations.MatrixVectorProduct(da1, xUpdated), -1.0));
dRho.Add(VectorOperations.VectorScalarProductNew(
VectorOperations.MatrixVectorProduct(da2, xUpdated), -1.0));
return(dRho);
}
private double[] NewtonIterations(double[] forceVector)
{
lambda = 1.0 / numberOfLoadSteps;
double[] incrementDf = VectorOperations.VectorScalarProductNew(forceVector, lambda);
double[] solutionVector = new double[forceVector.Length];
double[] deltaU = new double[solutionVector.Length];
double[] internalForcesTotalVector;
double[] dU;
double[] residual;
double residualNorm;
solutionVector = explicitSolution.Values.Last();
Assembler.UpdateDisplacements(solutionVector);
Assembler.UpdateAccelerations(explicitAcceleration.Values.Last());
residual = VectorOperations.VectorVectorSubtraction(forceVector, Assembler.CreateTotalInternalForcesVector());
int iteration = 0;
Array.Clear(deltaU, 0, deltaU.Length);
for (int i = 0; i < maxIterations; i++)
{
double[,] tangentMatrix = CalculateHatMMatrix();
deltaU = LinearSolver.Solve(tangentMatrix, residual);
solutionVector = VectorOperations.VectorVectorAddition(solutionVector, deltaU);
Assembler.UpdateDisplacements(solutionVector);
//Assembler.UpdateAccelerations(CalculateAccelerations());
internalForcesTotalVector = Assembler.CreateTotalInternalForcesVector();
residual = VectorOperations.VectorVectorSubtraction(forceVector, internalForcesTotalVector);
residualNorm = VectorOperations.VectorNorm2(residual);
if (residualNorm < tolerance)
{
break;
}
iteration = iteration + 1;
}
Console.WriteLine(iteration);
if (iteration >= maxIterations)
{
Console.WriteLine("Newton-Raphson: Solution not converged at current iterations");
}
return(solutionVector);
}
private double[] LoadControlledNR(double[] forceVector)
{
double[] incrementDf = VectorOperations.VectorScalarProductNew(forceVector, lambda);
double[] solutionVector = new double[forceVector.Length];
double[] incrementalExternalForcesVector = new double[forceVector.Length];
double[] tempSolutionVector = new double[solutionVector.Length];
double[] deltaU = new double[solutionVector.Length];
double[] internalForcesTotalVector;
double[] dU;
double[] residual;
double residualNorm;
for (int i = 0; i < numberOfLoadSteps; i++)
{
incrementalExternalForcesVector = VectorOperations.VectorVectorAddition(incrementalExternalForcesVector, incrementDf);
base.UpdateDisplacements(solutionVector);
internalForcesTotalVector = base.CreateTotalInternalForcesVector();
double[,] stiffnessMatrix = base.CreateTotalStiffnessMatrix();
dU = linearSolver.Solve(stiffnessMatrix, incrementDf);
solutionVector = VectorOperations.VectorVectorAddition(solutionVector, dU);
residual = VectorOperations.VectorVectorSubtraction(internalForcesTotalVector, incrementalExternalForcesVector);
residualNorm = VectorOperations.VectorNorm2(residual);
int iteration = 0;
Array.Clear(deltaU, 0, deltaU.Length);
while (residualNorm > tolerance && iteration < maxIterations)
{
stiffnessMatrix = base.CreateTotalStiffnessMatrix();
deltaU = VectorOperations.VectorVectorSubtraction(deltaU, linearSolver.Solve(stiffnessMatrix, residual));
tempSolutionVector = VectorOperations.VectorVectorAddition(solutionVector, deltaU);
base.UpdateDisplacements(tempSolutionVector);
internalForcesTotalVector = base.CreateTotalInternalForcesVector();
residual = VectorOperations.VectorVectorSubtraction(internalForcesTotalVector, incrementalExternalForcesVector);
residualNorm = VectorOperations.VectorNorm2(residual);
iteration = iteration + 1;
}
solutionVector = VectorOperations.VectorVectorAddition(solutionVector, deltaU);
if (iteration >= maxIterations)
{
Console.WriteLine("Newton-Raphson: Solution not converged at current iterations");
}
}
return(solutionVector);
}
private Tuple <double[], double, double[], double[], double> SlaveSegmentGeometry(double[,] daMatrix, double[,] da2Matrix)
{
double[] xupd = NodalXUpdated();
double[] surfaceVector = VectorOperations.MatrixVectorProduct(daMatrix, xupd);
double[] surfaceVectorDerivative = VectorOperations.MatrixVectorProduct(da2Matrix, xupd);
double detm = VectorOperations.VectorDotProduct(surfaceVector, surfaceVector);
double m11 = 1.0 / detm;
double[] vector = new double[] { -surfaceVector[1], surfaceVector[0] };
double scalarCoef = 1.0 / (Math.Sqrt(detm));
double[] normalUnitVec = VectorOperations.VectorScalarProductNew(vector, scalarCoef);
double[] tangentVector = VectorOperations.VectorScalarProductNew(surfaceVector, scalarCoef);
double scalarCoef2 = Math.Pow(m11, 2.0);
double curvatureTensor = scalarCoef2 * VectorOperations.VectorDotProduct(surfaceVectorDerivative, normalUnitVec);
return(new Tuple <double[], double, double[], double[], double>(surfaceVector, detm, normalUnitVec, tangentVector, curvatureTensor));
}
private double[] CalculateHatRVectorNewmarkNL(int i, List <double> aConstants, double[] previousIterationSolution)
{
double[,] TotalMassMatrix;
double[,] TotalDampingMatrix;
double[,] TotalStiffnessMatrix;
if (CustomMassMatrix != null)
{
TotalMassMatrix = CustomMassMatrix;
TotalDampingMatrix = CustomDampingMatrix;
TotalStiffnessMatrix = CustomStiffnessMatrix;
}
else
{
TotalMassMatrix = Assembler.CreateTotalMassMatrix();
TotalDampingMatrix = Assembler.CreateTotalDampingMatrix();
TotalStiffnessMatrix = Assembler.CreateTotalStiffnessMatrix();
}
double[] currentU = explicitSolution[i - 1];
double[] currentdU = explicitVelocity[i - 1];
double[] currentddU = explicitAcceleration[i - 1];
double[] a0U = VectorOperations.VectorScalarProductNew(
VectorOperations.VectorVectorSubtraction(currentU, previousIterationSolution), aConstants[0]);
double[] a2dU = VectorOperations.VectorScalarProductNew(currentdU, aConstants[2]);
double[] a3ddU = VectorOperations.VectorScalarProductNew(currentddU, aConstants[3]);
double[] a1U = VectorOperations.VectorScalarProductNew(currentU, aConstants[1]);
double[] a4dU = VectorOperations.VectorScalarProductNew(currentdU, aConstants[4]);
double[] a5ddU = VectorOperations.VectorScalarProductNew(currentddU, aConstants[5]);
double[] vectorSum1 = VectorOperations.VectorVectorAddition(a0U,
VectorOperations.VectorVectorAddition(a2dU, a3ddU));
double[] vectorSum2 = VectorOperations.VectorVectorAddition(a1U,
VectorOperations.VectorVectorAddition(a4dU, a5ddU));
double[] part1 = VectorOperations.MatrixVectorProduct(TotalMassMatrix, vectorSum1);
double[] part2 = VectorOperations.MatrixVectorProduct(TotalDampingMatrix, vectorSum2);
double[] hatR = VectorOperations.VectorVectorAddition(ExternalForcesVector,
VectorOperations.VectorVectorAddition(part1, part2));
return(hatR);
}
private Tuple <double[], double, double[]> SurfaceGeometry(double[,] daMatrix)
{
double Xm1 = Nodes[1].XCoordinate + DisplacementVector[0];
double Ym1 = Nodes[1].YCoordinate + DisplacementVector[1];
double Xm2 = Nodes[2].XCoordinate + DisplacementVector[2];
double Ym2 = Nodes[2].YCoordinate + DisplacementVector[3];
double Xs = Nodes[3].XCoordinate + DisplacementVector[4];
double Ys = Nodes[3].YCoordinate + DisplacementVector[5];
double[] xupd = new double[] { -Xm1, -Ym1, -Xm2, -Ym2, -Xs, -Ys };
double[] surfaceVector = VectorOperations.MatrixVectorProduct(daMatrix, xupd);
double detm = VectorOperations.VectorDotProduct(surfaceVector, surfaceVector);
double m11 = 1.0 / detm;
double[] vector = new double[] { Ym2 - Ym1, Xm1 - Xm2 };
double scalarCoef = -1.0 / (2.0 * Math.Sqrt(detm));
double[] normalUnitVec = VectorOperations.VectorScalarProductNew(vector, scalarCoef);
return(new Tuple <double[], double, double[]>(surfaceVector, m11, normalUnitVec));
}
private Tuple <double[], double, double[], double[], double> MasterSegmentGeometry(double[,] daMatrix, double[,] da2Matrix)
{
double[] xupd = VectorOperations.VectorScalarProduct(NodalXUpdated(), -1);
double[] surfaceVector = VectorOperations.MatrixVectorProduct(daMatrix, xupd);
double[] surfaceVectorDerivative = VectorOperations.MatrixVectorProduct(da2Matrix, xupd);
double detm = VectorOperations.VectorDotProduct(surfaceVector, surfaceVector);
double m11 = 1.0 / detm;
double[] vector = new double[2];
double scalarCoef = new double();
double scalarCoef2 = Math.Pow(m11, 2.0);
double[] tangentVector = new double[2];
double curvatureTensor = new double();
if (Properties.MasterSegmentPolynomialDegree == 1)
{
double Xm1 = Nodes[1].XCoordinate + DisplacementVector[0];
double Ym1 = Nodes[1].YCoordinate + DisplacementVector[1];
double Xm2 = Nodes[2].XCoordinate + DisplacementVector[2];
double Ym2 = Nodes[2].YCoordinate + DisplacementVector[3];
vector[0] = Ym2 - Ym1;
vector[1] = Xm1 - Xm2;
scalarCoef = -1.0 / (2.0 * Math.Sqrt(detm));
}
else
{
vector[0] = -surfaceVector[1];
vector[1] = surfaceVector[0];
scalarCoef = 1.0 / (Math.Sqrt(detm));
tangentVector = VectorOperations.VectorScalarProductNew(surfaceVector, scalarCoef);
}
double[] normalUnitVec = VectorOperations.VectorScalarProductNew(vector, scalarCoef);
curvatureTensor = scalarCoef2 * VectorOperations.VectorDotProduct(surfaceVectorDerivative, normalUnitVec);
return(new Tuple <double[], double, double[], double[], double>(surfaceVector, m11, normalUnitVec, tangentVector, curvatureTensor));
}
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);
}
}