////[ 140*c^2+156*s^2, -16*c*s, -22*s*L, 70*c^2+54*s^2, 16*c*s, 13*s*L]
////[ -16*c*s, 140*s^2+156*c^2, 22*c*L, 16*c*s, 70*s^2+54*c^2, -13*c*L]
////[ -22*s*L, 22*c*L, 4*L^2, -13*s*L, 13*c*L, -3*L^2]
////[ 70*c^2+54*s^2, 16*c*s, -13*s*L, 140*c^2+156*s^2, -16*c*s, 22*s*L]
////[ 16*c*s, 70*s^2+54*c^2, 13*c*L, -16*c*s, 140*s^2+156*c^2, -22*c*L]
////[ 13*s*L, -13*c*L, -3*L^2, 22*s*L, -22*c*L, 4*L^2]
//public IMatrix2D<double> MassMatrix(Element element)
//{
// double x2 = Math.Pow(element.Nodes[1].X - element.Nodes[0].X, 2);
// double y2 = Math.Pow(element.Nodes[1].Y - element.Nodes[0].Y, 2);
// double L = Math.Sqrt(x2 + y2);
// double L2 = L * L;
// double c = (element.Nodes[1].X - element.Nodes[0].X) / L;
// double c2 = c * c;
// double s = (element.Nodes[1].Y - element.Nodes[0].Y) / L;
// double s2 = s * s;
// double dAL420 = Density * SectionArea * L / 420;
// return new SymmetricMatrix2D<double>(new double[] { dAL420*(140*c2+156*s2), -16*dAL420*c*s, -22*dAL420*s*L, dAL420*(70*c2+54*s2), 16*dAL420*c*s, 13*dAL420*s*L,
// dAL420*(140*s2+156*c2), 22*dAL420*c*L, 16*dAL420*c*s, dAL420*(70*s2+54*c2), -13*dAL420*c*L,
// 4*dAL420*L2, -13*dAL420*s*L, 13*dAL420*c*L, -3*dAL420*L2,
// dAL420*(140*c2+156*s2), -16*dAL420*c*s, 22*dAL420*s*L,
// dAL420*(140*s2+156*c2), -22*dAL420*c*L,
// 4*dAL420*L2 });
//}
//[ 140*c^2+156*s^2, -16*c*s, -22*s*L, 70*c^2+54*s^2, 16*c*s, 13*s*L]
//[ -16*c*s, 140*s^2+156*c^2, 22*c*L, 16*c*s, 70*s^2+54*c^2, -13*c*L]
//[ -22*s*L, 22*c*L, 4*L^2, -13*s*L, 13*c*L, -3*L^2]
//[ 70*c^2+54*s^2, 16*c*s, -13*s*L, 140*c^2+156*s^2, -16*c*s, 22*s*L]
//[ 16*c*s, 70*s^2+54*c^2, 13*c*L, -16*c*s, 140*s^2+156*c^2, -22*c*L]
//[ 13*s*L, -13*c*L, -3*L^2, 22*s*L, -22*c*L, 4*L^2]
public IMatrix MassMatrix(IElement element)
{
double x2 = Math.Pow(element.Nodes[1].X - element.Nodes[0].X, 2);
double y2 = Math.Pow(element.Nodes[1].Y - element.Nodes[0].Y, 2);
double L = Math.Sqrt(x2 + y2);
double L2 = L * L;
double c = (element.Nodes[1].X - element.Nodes[0].X) / L;
double c2 = c * c;
double s = (element.Nodes[1].Y - element.Nodes[0].Y) / L;
double s2 = s * s;
double dAL420 = Density * SectionArea * L / 420;
double totalMass = Density * SectionArea * L;
double totalMassOfDiagonalTerms = 2 * dAL420 * (140 * c2 + 156 * s2) + 2 * dAL420 * (140 * s2 + 156 * c2);
double scale = totalMass / totalMassOfDiagonalTerms;
//TODO: optimize this
int order = 6;
return(SymmetricMatrix.CreateFromPackedRowMajorArray(new double[]
{
dAL420 *(140 * c2 + 156 * s2) * scale, 0, 0, 0, 0, 0,
dAL420 * (140 * s2 + 156 * c2) * scale, 0, 0, 0, 0,
0, 0, 0, 0,
dAL420 * (140 * c2 + 156 * s2) * scale, 0, 0,
dAL420 * (140 * s2 + 156 * c2) * scale, 0,
0
}, order));
}
//[ c^2*E*A/L+12*s^2*E*I/L^3, s*E*A/L*c-12*c*E*I/L^3*s, -6*E*I/L^2*s, -c^2*E*A/L-12*s^2*E*I/L^3, -s*E*A/L*c+12*c*E*I/L^3*s, -6*E*I/L^2*s]
//[ s*E*A/L*c-12*c*E*I/L^3*s, s^2*E*A/L+12*c^2*E*I/L^3, 6*E*I/L^2*c, -s*E*A/L*c+12*c*E*I/L^3*s, -s^2*E*A/L-12*c^2*E*I/L^3, 6*E*I/L^2*c]
//[ -6*E*I/L^2*s, 6*E*I/L^2*c, 4*E*I/L, 6*E*I/L^2*s, -6*E*I/L^2*c, 2*E*I/L]
//[ -c^2*E*A/L-12*s^2*E*I/L^3, -s*E*A/L*c+12*c*E*I/L^3*s, 6*E*I/L^2*s, c^2*E*A/L+12*s^2*E*I/L^3, s*E*A/L*c-12*c*E*I/L^3*s, 6*E*I/L^2*s]
//[ -s*E*A/L*c+12*c*E*I/L^3*s, -s^2*E*A/L-12*c^2*E*I/L^3, -6*E*I/L^2*c, s*E*A/L*c-12*c*E*I/L^3*s, s^2*E*A/L+12*c^2*E*I/L^3, -6*E*I/L^2*c]
//[ -6*E*I/L^2*s, 6*E*I/L^2*c, 2*E*I/L, 6*E*I/L^2*s, -6*E*I/L^2*c, 4*E*I/L]
public virtual IMatrix StiffnessMatrix(IElement element)
{
double x2 = Math.Pow(element.Nodes[1].X - element.Nodes[0].X, 2);
double y2 = Math.Pow(element.Nodes[1].Y - element.Nodes[0].Y, 2);
double L = Math.Sqrt(x2 + y2);
double c = (element.Nodes[1].X - element.Nodes[0].X) / L;
double c2 = c * c;
double s = (element.Nodes[1].Y - element.Nodes[0].Y) / L;
double s2 = s * s;
double EL = this.youngModulus / L;
double EAL = EL * SectionArea;
double EIL = EL * MomentOfInertia;
double EIL2 = EIL / L;
double EIL3 = EIL2 / L;
//TODO: optimize this
int order = 6;
var k = SymmetricMatrix.CreateFromPackedRowMajorArray(new double[]
{
c2 *EAL + 12 *s2 *EIL3, c *s *EAL - 12 *c *s *EIL3, -6 *s *EIL2, -c2 *EAL - 12 *s2 *EIL3, -c *s *EAL + 12 *c *s *EIL3, -6 *s *EIL2,
s2 *EAL + 12 *c2 *EIL3, 6 *c *EIL2, -s *c *EAL + 12 *c *s *EIL3, -s2 *EAL - 12 *c2 *EIL3, 6 *c *EIL2,
4 *EIL, 6 *s *EIL2, -6 *c *EIL2, 2 *EIL,
c2 *EAL + 12 *s2 *EIL3, s *c *EAL - 12 *c *s *EIL3, 6 *s *EIL2,
s2 *EAL + 12 *c2 *EIL3, -6 *c *EIL2,
4 *EIL
}, order);
return(dofEnumerator.GetTransformedMatrix(k));
}
public virtual IMatrix StiffnessMatrix(IElement element)
{
double[, ,] afE = new double[iInt3, 6, 6];
for (int i = 0; i < iInt3; i++)
{
IMatrixView constitutive = materialsAtGaussPoints[i].ConstitutiveMatrix;
for (int j = 0; j < 6; j++)
{
for (int k = 0; k < 6; k++)
{
afE[i, j, k] = constitutive[j, k];
}
}
}
double[,] faXYZ = GetCoordinates(element);
double[,] faDS = new double[iInt3, 24];
double[,] faS = new double[iInt3, 8];
double[, ,] faB = new double[iInt3, 24, 6];
double[] faDetJ = new double[iInt3];
double[, ,] faJ = new double[iInt3, 3, 3];
double[] faWeight = new double[iInt3];
double[] faK = new double[300];
CalcH8GaussMatrices(ref iInt, faXYZ, faWeight, faS, faDS, faJ, faDetJ, faB);
CalcH8K(ref iInt, afE, faB, faWeight, faK);
return(dofEnumerator.GetTransformedMatrix(SymmetricMatrix.CreateFromPackedRowMajorArray(faK)));
}
public double[] CalculateForces(IElement element, double[] localTotalDisplacements, double[] localDisplacements)
{
double[,] faStresses = new double[iInt3, 6];
for (int i = 0; i < materialsAtGaussPoints.Length; i++)
{
for (int j = 0; j < 6; j++)
{
faStresses[i, j] = materialsAtGaussPoints[i].Stresses[j];
}
}
double[,] faXYZ = GetCoordinates(element);
double[,] faDS = new double[iInt3, 24];
double[,] faS = new double[iInt3, 8];
double[, ,] faB = new double[iInt3, 24, 6];
double[] faDetJ = new double[iInt3];
double[, ,] faJ = new double[iInt3, 3, 3];
double[] faWeight = new double[iInt3];
double[] solidForces = new double[24];
CalcH8GaussMatrices(ref iInt, faXYZ, faWeight, faS, faDS, faJ, faDetJ, faB);
CalcH8Forces(ref iInt, faB, faWeight, faStresses, solidForces);
double[] faH = new double[36];
double[] faPermeability = new double[] { Permeability, Permeability, Permeability, Permeability,
Permeability, Permeability, Permeability, Permeability };
CalcH20u8pH(ref iInt, faPermeability, faS, faB, faWeight, faH);
//double[,] faQ = new double[8, 24];
//double fPoreA = PoreA;
//double[] faXw = new double[] { Xw, Xw, Xw, Xw, Xw, Xw, Xw, Xw };
//CalcH8u8pQMinus(ref iInt, ref fPoreA, faXw, faB, faS, faWeight, faQ);
//Matrix<double> q = (new Matrix<double>(faQ)).Transpose();
// Changed! Check for errors...
//Vector<double> fluidDisplacements = new Vector<double>(ExtractFluidVector(localDisplacements));
var fluidDisplacements = ExtractFluidVector(localTotalDisplacements);
//double[] solidAndFluidForces = solidForces;
////double[] solidAndFluidForces = q * fluidDisplacements + (new Vector<double>(solidForces));
// H correction
fluidDisplacements.ScaleIntoThis(-1.0);
double[] fluidDrags = SymmetricMatrix.CreateFromPackedRowMajorArray(faH).Multiply(fluidDisplacements);
double[] totalForces = new double[GetAllDOFs()];
ScatterFromFluidVector(fluidDrags, totalForces);
ScatterFromSolidVector(solidForces, totalForces);
return(totalForces);
}
public IMatrix SaturationMatrix(IElement element)
{
double[,] faXYZ = GetCoordinates(element);
double[,] faDS = new double[iInt3, 24];
double[,] faS = new double[iInt3, 8];
double[, ,] faB = new double[iInt3, 24, 6];
double[] faDetJ = new double[iInt3];
double[, ,] faJ = new double[iInt3, 3, 3];
double[] faWeight = new double[iInt3];
double[] faXwDivQ = new double[] { Xw *QInv, Xw *QInv, Xw *QInv, Xw *QInv, Xw *QInv,
Xw *QInv, Xw *QInv, Xw *QInv };
double[] faSaturation = new double[36];
CalcH8GaussMatrices(ref iInt, faXYZ, faWeight, faS, faDS, faJ, faDetJ, faB);
CalcH20u8pS(ref iInt, faXwDivQ, faS, faWeight, faSaturation);
return(SymmetricMatrix.CreateFromPackedRowMajorArray(faSaturation));
}
public IMatrix PermeabilityMatrix(IElement element)
{
double[,] faXYZ = GetCoordinates(element);
double[,] faDS = new double[iInt3, 24];
double[,] faS = new double[iInt3, 8];
double[, ,] faB = new double[iInt3, 24, 6];
double[] faDetJ = new double[iInt3];
double[, ,] faJ = new double[iInt3, 3, 3];
double[] faWeight = new double[iInt3];
double[] faPermeability = new double[] { Permeability, Permeability, Permeability, Permeability,
Permeability, Permeability, Permeability, Permeability };
double[] faH = new double[36];
CalcH8GaussMatrices(ref iInt, faXYZ, faWeight, faS, faDS, faJ, faDetJ, faB);
CalcH20u8pH(ref iInt, faPermeability, faS, faB, faWeight, faH);
return(SymmetricMatrix.CreateFromPackedRowMajorArray(faH));
}
public IMatrix MassMatrix(IElement element)
{
double[,] faXYZ = GetCoordinates(element);
double[,] faDS = new double[iInt3, 24];
double[,] faS = new double[iInt3, 8];
double[, ,] faB = new double[iInt3, 24, 6];
double[] faDetJ = new double[iInt3];
double[, ,] faJ = new double[iInt3, 3, 3];
double[] faWeight = new double[iInt3];
double[] faM = new double[300];
double fDensity = Density;
CalcH8GaussMatrices(ref iInt, faXYZ, faWeight, faS, faDS, faJ, faDetJ, faB);
CalcH8MLumped(ref iInt, ref fDensity, faWeight, faM);
return(SymmetricMatrix.CreateFromPackedRowMajorArray(faM));
}
public IMatrix MassMatrix(IElement element)
{
double x2 = Math.Pow(element.Nodes[1].X - element.Nodes[0].X, 2);
double y2 = Math.Pow(element.Nodes[1].Y - element.Nodes[0].Y, 2);
double z2 = Math.Pow(element.Nodes[1].Z - element.Nodes[0].Z, 2);
double L = 1d / Math.Sqrt(x2 + y2 + z2);
//double halfMass = 0.5 * Density * SectionArea * L;
//var massMatrix = new SymmetricMatrix<double>(new double[] { halfMass, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
// halfMass, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
// halfMass, 0, 0, 0, 0, 0, 0, 0, 0, 0,
// halfMass, 0, 0, 0, 0, 0, 0, 0, 0,
// halfMass, 0, 0, 0, 0, 0, 0, 0,
// halfMass, 0, 0, 0, 0, 0, 0,
// halfMass, 0, 0, 0, 0, 0,
// halfMass, 0, 0, 0, 0,
// halfMass, 0, 0, 0,
// halfMass, 0, 0,
// halfMass, 0,
// halfMass
//});
double halfMass = Density * SectionArea / L / 6d;
int order = 12;
Matrix massMatrix = SymmetricMatrix.CreateFromPackedRowMajorArray(
new double[] { halfMass, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
halfMass, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
halfMass, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0,
halfMass, 0, 0, 0, 0, 0,
halfMass, 0, 0, 0, 0,
halfMass, 0, 0, 0,
0, 0, 0,
0, 0,
0 }, order).CopyToFullMatrix();
var refx = new double[] { 1, 1, 1 };
var beamTransformation = Matrix.CreateZero(order, order);
beamTransformation[0, 0] = (element.Nodes[1].X - element.Nodes[0].X) * L;
beamTransformation[0, 1] = (element.Nodes[1].Y - element.Nodes[0].Y) * L;
beamTransformation[0, 2] = (element.Nodes[1].Z - element.Nodes[0].Z) * L;
beamTransformation[1, 0] = refx[1] * beamTransformation[0, 2] - refx[2] * beamTransformation[0, 1];
beamTransformation[1, 1] = refx[2] * beamTransformation[0, 0] - refx[0] * beamTransformation[0, 2];
beamTransformation[1, 2] = refx[0] * beamTransformation[0, 1] - refx[1] * beamTransformation[0, 0];
double dn = 1.0 / Math.Sqrt(beamTransformation[1, 0] * beamTransformation[1, 0] + beamTransformation[1, 1] * beamTransformation[1, 1] + beamTransformation[1, 2] * beamTransformation[1, 2]);
beamTransformation[1, 0] = beamTransformation[1, 0] * dn;
beamTransformation[1, 1] = beamTransformation[1, 1] * dn;
beamTransformation[1, 2] = beamTransformation[1, 2] * dn;
beamTransformation[2, 0] = beamTransformation[0, 1] * beamTransformation[1, 2] - beamTransformation[0, 2] * beamTransformation[1, 1];
beamTransformation[2, 1] = beamTransformation[0, 2] * beamTransformation[1, 0] - beamTransformation[0, 0] * beamTransformation[1, 2];
beamTransformation[2, 2] = beamTransformation[0, 0] * beamTransformation[1, 1] - beamTransformation[0, 1] * beamTransformation[1, 0];
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
beamTransformation[i + 3, j + 3] = beamTransformation[i, j];
beamTransformation[i + 6, j + 6] = beamTransformation[i, j];
beamTransformation[i + 9, j + 9] = beamTransformation[i, j];
}
}
CalculateRotTranformation(element);
return(dofEnumerator.GetTransformedMatrix(
rotTransformation.ThisTransposeTimesOtherTimesThis(
beamTransformation.ThisTransposeTimesOtherTimesThis(massMatrix))));
}
private IMatrix StiffnessMatrixPure(IElement element)
{
double x2 = Math.Pow(element.Nodes[1].X - element.Nodes[0].X, 2);
double y2 = Math.Pow(element.Nodes[1].Y - element.Nodes[0].Y, 2);
double z2 = Math.Pow(element.Nodes[1].Z - element.Nodes[0].Z, 2);
double L = 1 / Math.Sqrt(x2 + y2 + z2);
double L2 = L * L;
double L3 = L2 * L;
//double EIx = m.YoungModulus * MomentOfInertiaX;
double EIy = this.youngModulus * MomentOfInertiaY;
double EIz = this.youngModulus * MomentOfInertiaZ;
double GJL = this.youngModulus * L * MomentOfInertiaPolar / (2 * (1 + this.poissonRatio));
double EAL = this.youngModulus * SectionArea * L;
//TODO: optimize this
int order = 12;
Matrix stiffnessMatrix = SymmetricMatrix.CreateFromPackedRowMajorArray(new double[]
{
EAL, 0, 0, 0, 0, 0, -EAL, 0, 0, 0, 0, 0,
12 * EIz * L3, 0, 0, 0, 6 * EIz * L2, 0, -12 * EIz * L3, 0, 0, 0, 6 * EIz * L2,
12 * EIy * L3, 0, -6 * EIy * L2, 0, 0, 0, -12 * EIy * L3, 0, -6 * EIy * L2, 0,
GJL, 0, 0, 0, 0, 0, -GJL, 0, 0,
4 * EIy * L, 0, 0, 0, 6 * EIy * L2, 0, 2 * EIy * L, 0,
4 * EIz * L, 0, -6 * EIz * L2, 0, 0, 0, 2 * EIz * L,
EAL, 0, 0, 0, 0, 0,
12 * EIz * L3, 0, 0, 0, -6 * EIz * L2,
12 * EIy * L3, 0, 6 * EIy * L2, 0,
GJL, 0, 0,
4 * EIy * L, 0,
4 * EIz * L
}, order).CopyToFullMatrix();
var refx = new double[] { 1, 1, 1 };
var beamTransformation = Matrix.CreateZero(order, order);
beamTransformation[0, 0] = (element.Nodes[1].X - element.Nodes[0].X) * L;
beamTransformation[0, 1] = (element.Nodes[1].Y - element.Nodes[0].Y) * L;
beamTransformation[0, 2] = (element.Nodes[1].Z - element.Nodes[0].Z) * L;
//beamTransformation[2, 0] = refx[0];
//beamTransformation[2, 1] = refx[1];
//beamTransformation[2, 2] = refx[2];
//beamTransformation[1, 0] = beamTransformation[2, 1] * beamTransformation[0, 2] - beamTransformation[2, 2] * beamTransformation[0, 1];
//beamTransformation[1, 1] = beamTransformation[2, 2] * beamTransformation[0, 0] - beamTransformation[2, 0] * beamTransformation[0, 2];
//beamTransformation[1, 2] = beamTransformation[2, 0] * beamTransformation[0, 1] - beamTransformation[2, 1] * beamTransformation[0, 0];
beamTransformation[1, 0] = refx[1] * beamTransformation[0, 2] - refx[2] * beamTransformation[0, 1];
beamTransformation[1, 1] = refx[2] * beamTransformation[0, 0] - refx[0] * beamTransformation[0, 2];
beamTransformation[1, 2] = refx[0] * beamTransformation[0, 1] - refx[1] * beamTransformation[0, 0];
double dn = 1.0 / Math.Sqrt(beamTransformation[1, 0] * beamTransformation[1, 0] + beamTransformation[1, 1] * beamTransformation[1, 1] + beamTransformation[1, 2] * beamTransformation[1, 2]);
beamTransformation[1, 0] = beamTransformation[1, 0] * dn;
beamTransformation[1, 1] = beamTransformation[1, 1] * dn;
beamTransformation[1, 2] = beamTransformation[1, 2] * dn;
beamTransformation[2, 0] = beamTransformation[0, 1] * beamTransformation[1, 2] - beamTransformation[0, 2] * beamTransformation[1, 1];
beamTransformation[2, 1] = beamTransformation[0, 2] * beamTransformation[1, 0] - beamTransformation[0, 0] * beamTransformation[1, 2];
beamTransformation[2, 2] = beamTransformation[0, 0] * beamTransformation[1, 1] - beamTransformation[0, 1] * beamTransformation[1, 0];
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
beamTransformation[i + 3, j + 3] = beamTransformation[i, j];
beamTransformation[i + 6, j + 6] = beamTransformation[i, j];
beamTransformation[i + 9, j + 9] = beamTransformation[i, j];
}
}
return(beamTransformation.ThisTransposeTimesOtherTimesThis(stiffnessMatrix));
////if (element.Nodes.Count(n => n.EmbeddedInElement != null) == 0) return stiffnessMatrix;
//stiffnessMatrix = new SymmetricMatrix<double>(beamTransformation.Transpose() * stiffnessMatrix.ToMatrix() * beamTransformation);
//if (embeddedNodes.Count == 0) return stiffnessMatrix;
////var hostElements = element.Nodes.Select(x => x.EmbeddedInElement).Distinct();
//var size = GetElementDOFTypes(element).SelectMany(x => x).Count();
//transformation = new Matrix<double>(dofs.SelectMany(d => d).Count(), size);
//isNodeEmbedded = new bool[element.Nodes.Count];
////TODO : SEPARATE FROM ELEMENT!!
////TODO: Must match DOFs of host with embedded element
//int row = 0;
//int col = 0;
//hostElementList = new List<Element>();
//for (int i = 0; i < element.Nodes.Count; i++)
//{
// var node = element.Nodes[i];
// var embeddedNode = embeddedNodes.Where(x => x.Node == node).FirstOrDefault();
// //var hostElement = node.EmbeddedInElement;
// Element hostElement = embeddedNode == null ? null : embeddedNode.EmbeddedInElement;
// if (hostElement == null)
// {
// isNodeEmbedded[i] = false;
// for (int j = 0; j < dofs[i].Length; j++)
// {
// transformation[row, col] = 1;
// row++;
// col++;
// }
// }
// else
// {
// isNodeEmbedded[i] = true;
// //double[] hostShapeFunctions = ((IEmbeddedHostElement)hostElement.ElementType).GetShapeFunctionsForNode(hostElement, node);
// double[] hostShapeFunctions = ((IEmbeddedHostElement)hostElement.ElementType).GetShapeFunctionsForNode(hostElement, embeddedNode);
// if (hostElementList.IndexOf(hostElement) < 0)
// hostElementList.Add(hostElement);
// else
// col -= hostShapeFunctions.Length * hostDofsPerNode;
// for (int j = 0; j < commonDofsPerNode; j++)
// {
// for (int k = 0; k < hostShapeFunctions.Length; k++)
// transformation[row, hostDofsPerNode * k + col + j] = hostShapeFunctions[k];
// row++;
// }
// row += embeddedDofsPerNode - commonDofsPerNode;
// col += hostShapeFunctions.Length * hostDofsPerNode;
// }
//}
//// Add identity matrix
//int index = 0;
//if (isNodeEmbedded[0])
//{
// transformation[3, col] = 1;
// transformation[4, col + 1] = 1;
// transformation[5, col + 2] = 1;
// index += 3;
//}
//if (isNodeEmbedded[1])
//{
// transformation[9, col + index] = 1;
// transformation[10, col + index + 1] = 1;
// transformation[11, col + index + 2] = 1;
//}
//var transformedMatrix = new SymmetricMatrix<double>(transformation.Transpose() * stiffnessMatrix.ToMatrix() * transformation);
////var sw = File.CreateText(@"d:\BeamTransformed.txt");
////for (int i = 0; i < 54; i++)
////{
//// var s = string.Empty;
//// for (int j = 0; j < 54; j++)
//// s += transformedMatrix[i, j].ToString() + ";";
//// sw.WriteLine(s);
////}
////sw.Close();
//return transformedMatrix;
}