private Matrix CalculateConstitutiveStiffness()
{
var constitutiveStiffness = SymmetricMatrix.CreateZero(FREEDOM_DEGREE_COUNT);
double E = this.material.YoungModulus;
double G = E / (2d * (1d + this.material.PoissonRatio));
double I = this.beamSection.Inertia;
double A = this.beamSection.Area;
double L = this.currentLength;
double LSqruared = L * L;
double LCubed = L * L * L;
double phi = (12.0 * E * I) / (LSqruared * G * A);
double psi = 1.0 / (1.0 + phi);
double EAOverL = (E * A) / L;
double EIOverL = (E * I) / L;
constitutiveStiffness[0, 0] = EAOverL;
constitutiveStiffness[0, 3] = -EAOverL;
constitutiveStiffness[1, 1] = 12.0 * psi * E * I / LCubed;
constitutiveStiffness[1, 2] = 6.0 * psi * E * I / LSqruared;
constitutiveStiffness[1, 4] = -12.0 * psi * E * I / LCubed;
constitutiveStiffness[1, 5] = 6.0 * psi * E * I / LSqruared;
constitutiveStiffness[2, 2] = (3.0 * psi + 1.0) * EIOverL;
constitutiveStiffness[2, 4] = -6.0 * psi * E * I / LSqruared;
constitutiveStiffness[2, 5] = (3.0 * psi - 1.0) * EIOverL;
constitutiveStiffness[3, 3] = EAOverL;
constitutiveStiffness[4, 4] = 12.0 * psi * E * I / LCubed;
constitutiveStiffness[4, 5] = -6.0 * psi * E * I / LSqruared;
constitutiveStiffness[5, 5] = (3.0 * psi + 1.0) * EIOverL;
return(constitutiveStiffness.CopyToFullMatrix());
}
private IMatrix PorousMatrix(IElement element)
{
IPorousFiniteElement elementType = (IPorousFiniteElement)element.ElementType;
int dofs = 0;
foreach (IList <IDofType> dofTypes in elementType.DofEnumerator.GetDofTypesForMatrixAssembly(element))
{
foreach (IDofType dofType in dofTypes)
{
dofs++;
}
}
var poreStiffness = SymmetricMatrix.CreateZero(dofs);
IMatrix stiffness = solidStiffnessProvider.Matrix(element);
IMatrix permeability = elementType.PermeabilityMatrix(element);
int matrixRow = 0;
int solidRow = 0;
int fluidRow = 0;
foreach (IList <IDofType> dofTypesRow in elementType.DofEnumerator.GetDofTypesForMatrixAssembly(element))
{
foreach (IDofType dofTypeRow in dofTypesRow)
{
int matrixCol = 0;
int solidCol = 0;
int fluidCol = 0;
foreach (IList <IDofType> dofTypesCol in elementType.DofEnumerator.GetDofTypesForMatrixAssembly(element))
{
foreach (IDofType dofTypeCol in dofTypesCol)
{
if (dofTypeCol == PorousMediaDof.Pressure)
{
if (dofTypeRow == PorousMediaDof.Pressure)
{
// H correction
poreStiffness[matrixRow, matrixCol] = -permeability[fluidRow, fluidCol];
}
//poreStiffness[matrixRow, matrixCol] = permeability[fluidRow, fluidCol];
fluidCol++;
}
else
{
if (dofTypeRow != PorousMediaDof.Pressure)
{
poreStiffness[matrixRow, matrixCol] = stiffness[solidRow, solidCol] * stiffnessCoefficient;
}
solidCol++;
}
matrixCol++;
}
}
if (dofTypeRow == PorousMediaDof.Pressure)
{
fluidRow++;
}
else
{
solidRow++;
}
matrixRow++;
}
}
return(poreStiffness);
}
private IMatrix PorousMatrix(IElement element)
{
IPorousFiniteElement elementType = (IPorousFiniteElement)element.ElementType;
int dofs = 0;
foreach (IList <IDofType> dofTypes in elementType.DofEnumerator.GetDofTypesForMatrixAssembly(element))
{
foreach (IDofType dofType in dofTypes)
{
dofs++;
}
}
var poreDamping = SymmetricMatrix.CreateZero(dofs);
IMatrix damping = solidDampingProvider.Matrix(element);
IMatrix saturation = elementType.SaturationMatrix(element);
IMatrix coupling = elementType.CouplingMatrix(element);
int matrixRow = 0;
int solidRow = 0;
int fluidRow = 0;
foreach (IList <IDofType> dofTypesRow in elementType.DofEnumerator.GetDofTypesForMatrixAssembly(element))
{
foreach (IDofType dofTypeRow in dofTypesRow)
{
int matrixCol = 0;
int solidCol = 0;
int fluidCol = 0;
foreach (IList <IDofType> dofTypesCol in elementType.DofEnumerator.GetDofTypesForMatrixAssembly(element))
{
foreach (IDofType dofTypeCol in dofTypesCol)
{
if (dofTypeCol == PorousMediaDof.Pressure)
{
if (dofTypeRow == PorousMediaDof.Pressure)
{
poreDamping[matrixRow, matrixCol] = -saturation[fluidRow, fluidCol];
}
else
{
poreDamping[matrixRow, matrixCol] = coupling[fluidCol, solidRow];
}
fluidCol++;
}
else
{
if (dofTypeRow != PorousMediaDof.Pressure)
{
poreDamping[matrixRow, matrixCol] = damping[solidRow, solidCol] * dampingCoefficient;
}
else
{
poreDamping[matrixRow, matrixCol] = coupling[fluidRow, solidCol];
}
solidCol++;
}
matrixCol++;
}
}
if (dofTypeRow == PorousMediaDof.Pressure)
{
fluidRow++;
}
else
{
solidRow++;
}
matrixRow++;
}
}
return(poreDamping);
}
/**
* Calculates the geometric stiffness of the element.
*
* @return The geometric stiffness
*/
private Matrix CalculateGeometricStiffness()
{
var geometricStiffness = SymmetricMatrix.CreateZero(FREEDOM_DEGREE_COUNT);
var forcesInNaturalSystem = this.CalculateForcesInNaturalSystem();
var forcesInLocalSystem = this.CalculateForcesInLocalSystem();
double torsionalMoment = forcesInNaturalSystem[NaturalDeformationMode3D.TORSION];
double axialForce = forcesInNaturalSystem[NaturalDeformationMode3D.EXTENSION];
double momentY_A = forcesInLocalSystem[4];
double momentZ_A = forcesInLocalSystem[5];
double momentY_B = forcesInLocalSystem[10];
double momentZ_B = forcesInLocalSystem[11];
double length = this.currentLength;
double Qy = -(momentZ_A + momentZ_B) / length;
double Qz = (momentY_A + momentY_B) / length;
double Qy_Over_L = Qy / length;
double Qz_Over_L = Qz / length;
double Qy_L_Over_6 = (Qy * length) / 6.0;
double Qz_L_Over_6 = (Qz * length) / 6.0;
double N_6_Over_5_L = (6.0 * axialForce) / (5.0 * length);
double N_Over_10 = axialForce / 10.0;
double N_L_4_Over_30 = (4.0 * axialForce * length) / 30.0;
double N_L_Over_30 = (axialForce * length) / 30.0;
double MyA_Over_L = momentY_A / length;
double MyB_Over_L = momentY_B / length;
double MzA_Over_L = momentZ_A / length;
double MzB_Over_L = momentZ_B / length;
double M_Over_L = torsionalMoment / length;
double M_3_Over_6 = (3.0 * torsionalMoment) / 6.0;
geometricStiffness[0, 1] = -Qy_Over_L;
geometricStiffness[0, 2] = -Qz_Over_L;
geometricStiffness[0, 7] = Qy_Over_L;
geometricStiffness[0, 8] = Qz_Over_L;
geometricStiffness[1, 1] = N_6_Over_5_L;
geometricStiffness[1, 3] = MyA_Over_L;
geometricStiffness[1, 4] = M_Over_L;
geometricStiffness[1, 5] = N_Over_10;
geometricStiffness[1, 6] = Qy_Over_L;
geometricStiffness[1, 7] = -N_6_Over_5_L;
geometricStiffness[1, 9] = MyB_Over_L;
geometricStiffness[1, 10] = -M_Over_L;
geometricStiffness[1, 11] = N_Over_10;
geometricStiffness[2, 2] = N_6_Over_5_L;
geometricStiffness[2, 3] = MzA_Over_L;
geometricStiffness[2, 4] = -N_Over_10;
geometricStiffness[2, 5] = M_Over_L;
geometricStiffness[2, 6] = Qz_Over_L;
geometricStiffness[2, 8] = -N_6_Over_5_L;
geometricStiffness[2, 9] = MzB_Over_L;
geometricStiffness[2, 10] = -N_Over_10;
geometricStiffness[2, 11] = -M_Over_L;
geometricStiffness[3, 4] = ((-2.0 * momentZ_A) + momentZ_B) / 6.0;
geometricStiffness[3, 5] = ((2.0 * momentY_A) - momentY_B) / 6.0;
geometricStiffness[3, 7] = -MyA_Over_L;
geometricStiffness[3, 8] = -MzA_Over_L;
geometricStiffness[3, 10] = Qy_L_Over_6;
geometricStiffness[3, 11] = Qz_L_Over_6;
geometricStiffness[4, 4] = N_L_4_Over_30;
geometricStiffness[4, 7] = -M_Over_L;
geometricStiffness[4, 8] = +N_Over_10;
geometricStiffness[4, 9] = Qy_L_Over_6;
geometricStiffness[4, 10] = -N_L_Over_30;
geometricStiffness[4, 11] = M_3_Over_6;
geometricStiffness[5, 5] = N_L_4_Over_30;
geometricStiffness[5, 7] = -N_Over_10;
geometricStiffness[5, 8] = -M_Over_L;
geometricStiffness[5, 9] = Qz_L_Over_6;
geometricStiffness[5, 10] = -M_3_Over_6;
geometricStiffness[5, 11] = -N_L_Over_30;
geometricStiffness[6, 7] = -Qy_Over_L;
geometricStiffness[6, 8] = -Qz_Over_L;
geometricStiffness[7, 7] = N_6_Over_5_L;
geometricStiffness[7, 9] = -MyB_Over_L;
geometricStiffness[7, 10] = M_Over_L;
geometricStiffness[7, 11] = -N_Over_10;
geometricStiffness[8, 8] = N_6_Over_5_L;
geometricStiffness[8, 9] = -MzB_Over_L;
geometricStiffness[8, 10] = N_Over_10;
geometricStiffness[8, 11] = M_Over_L;
geometricStiffness[9, 10] = ((-2.0 * momentZ_B) + momentZ_A) / 6.0;
geometricStiffness[9, 11] = ((+2.0 * momentY_B) - momentY_A) / 6.0;
geometricStiffness[10, 10] = N_L_4_Over_30;
geometricStiffness[11, 11] = N_L_4_Over_30;
return(geometricStiffness.CopyToFullMatrix());
}
/**
* Calculates the constitutive stiffness of the element.
*
* @return The constitutive stiffness
*/
private Matrix CalculateConstitutiveStiffness()
{
var constitutiveStiffness = SymmetricMatrix.CreateZero(FREEDOM_DEGREE_COUNT);
double E = this.material.YoungModulus;
double G = E / (2d * (1d + this.material.PoissonRatio));
double Iy = this.beamSection.InertiaY;
double Iz = this.beamSection.InertiaZ;
double J = this.beamSection.TorsionalInertia;
double A = this.beamSection.Area;
double Ay = this.beamSection.EffectiveAreaY;
double Az = this.beamSection.EffectiveAreaZ;
double l = this.currentLength;
double lSqruared = l * l;
double lCubed = l * l * l;
double phiY = (12.0 * E * Iy) / (l * l * G * Az);
double phiZ = (12.0 * E * Iz) / (l * l * G * Ay);
double psiY = 1.0 / (1.0 + phiY);
double psiZ = 1.0 / (1.0 + phiZ);
double EAOverL = (E * A) / l;
double GJOverL = (G * J) / l;
double psiZ_E_Iz_12_OverlCubed = (12.0 * psiZ * E * Iz) / lCubed;
double psiZ_E_Iz_6_OverlSquared = (6.0 * psiZ * E * Iz) / lSqruared;
double psiY_E_12_Iy_OverlCubed = (12.0 * psiY * E * Iy) / lCubed;
double psiY_E_6_Iy_OverlSquared = (6.0 * psiY * E * Iy) / lSqruared;
double psiZ_3_Plus_1_E_Iz_Overl = (((3.0 * psiZ) + 1.0) * E * Iz) / l;
double psiZ_3_Minus_1_E_Iz_Overl = (((3.0 * psiZ) - 1.0) * E * Iz) / l;
double psiY_3_Plus_1_E_Iy_Overl = (((3.0 * psiY) + 1.0) * E * Iy) / l;
double psiY_3_Minus_1_E_Iy_Overl = (((3.0 * psiY) - 1.0) * E * Iy) / l;
constitutiveStiffness[0, 0] = EAOverL;
constitutiveStiffness[0, 6] = -EAOverL;
constitutiveStiffness[1, 1] = psiZ_E_Iz_12_OverlCubed;
constitutiveStiffness[1, 5] = psiZ_E_Iz_6_OverlSquared;
constitutiveStiffness[1, 7] = -psiZ_E_Iz_12_OverlCubed;
constitutiveStiffness[1, 11] = psiZ_E_Iz_6_OverlSquared;
constitutiveStiffness[2, 2] = psiY_E_12_Iy_OverlCubed;
constitutiveStiffness[2, 4] = -psiY_E_6_Iy_OverlSquared;
constitutiveStiffness[2, 8] = -psiY_E_12_Iy_OverlCubed;
constitutiveStiffness[2, 10] = -psiY_E_6_Iy_OverlSquared;
constitutiveStiffness[3, 3] = GJOverL;
constitutiveStiffness[3, 9] = -GJOverL;
constitutiveStiffness[4, 4] = psiY_3_Plus_1_E_Iy_Overl;
constitutiveStiffness[4, 8] = psiZ_E_Iz_6_OverlSquared;
constitutiveStiffness[4, 10] = psiY_3_Minus_1_E_Iy_Overl;
constitutiveStiffness[5, 5] = psiZ_3_Plus_1_E_Iz_Overl;
constitutiveStiffness[5, 7] = -psiY_E_6_Iy_OverlSquared;
constitutiveStiffness[5, 11] = psiZ_3_Minus_1_E_Iz_Overl;
constitutiveStiffness[6, 6] = EAOverL;
constitutiveStiffness[7, 7] = psiZ_E_Iz_12_OverlCubed;
constitutiveStiffness[7, 11] = -psiZ_E_Iz_6_OverlSquared;
constitutiveStiffness[8, 8] = psiY_E_12_Iy_OverlCubed;
constitutiveStiffness[8, 10] = psiY_E_6_Iy_OverlSquared;
constitutiveStiffness[9, 9] = GJOverL;
constitutiveStiffness[10, 10] = psiY_3_Plus_1_E_Iy_Overl;
constitutiveStiffness[11, 11] = psiZ_3_Plus_1_E_Iz_Overl;
return(constitutiveStiffness.CopyToFullMatrix());
}
