protected Matrix GetLocalUDerivativeMatrix(Vector previousU, IFiniteElement elementCurrent, double ksi, double eta)
{
Matrix derivativeMatrix = GetLocalDerivativeMatrix(elementCurrent, ksi, eta);
Vector uOnElement = new Vector(8);
if (previousU != null)
{
for (int i = 0; i < elementCurrent.Count; i++)
{
uOnElement[2 * i] = previousU[2 * elementCurrent[i].Index];
uOnElement[2 * i + 1] = previousU[2 * elementCurrent[i].Index + 1];
}
}
Vector uDerivative = Matrix.Transpose(derivativeMatrix) * uOnElement;
double d1u1 = uDerivative[0];
double d3u3 = uDerivative[1];
Matrix derivativeUMatrix = new Matrix(4, 4);
/*derivativeUMatrix[0, 0] = derivativeUMatrix[2, 2] = uDerivative[0];
* derivativeUMatrix[1, 1] = derivativeUMatrix[3, 3] = uDerivative[1];
* derivativeUMatrix[3, 0] = derivativeUMatrix[1, 2] = uDerivative[2];
* derivativeUMatrix[2, 1] = derivativeUMatrix[0, 3] = uDerivative[3];*/
derivativeUMatrix[0, 0] = (M1 * d1u1 + M2 * d3u3) * 0.5;
derivativeUMatrix[1, 1] = (M2 * d1u1 + M3 * d3u3) * 0.5;
derivativeUMatrix[2, 2] = (M2 * d1u1 + M3 * d3u3) * 0.5 + G13 * d1u1;
derivativeUMatrix[3, 3] = (M1 * d1u1 + M2 * d3u3) * 0.5 + G13 * d3u3;
derivativeUMatrix[2, 3] = G13 * d3u3;
derivativeUMatrix[3, 2] = G13 * d1u1;
return(derivativeUMatrix);
}
private Matrix GetLocalDerivativeMatrix(IFiniteElement element, double ksi, double eta)
{
Matrix LocalDerivativeMatrix = new Matrix(8, 4);
Matrix gradNksieta = new Matrix(2, 4);
gradNksieta[0, 0] = (eta - 1) * 0.25;
gradNksieta[1, 0] = (ksi - 1) * 0.25;
gradNksieta[0, 1] = (1 - eta) * 0.25;
gradNksieta[1, 1] = (-ksi - 1) * 0.25;
gradNksieta[0, 2] = (eta + 1) * 0.25;
gradNksieta[1, 2] = (ksi + 1) * 0.25;
gradNksieta[0, 3] = (-eta - 1) * 0.25;
gradNksieta[1, 3] = (1 - ksi) * 0.25;
JacobianRectangular J = new JacobianRectangular();
J.Element = element;
Matrix gradN = J.GetInverseJacobian(ksi, eta) * gradNksieta;
LocalDerivativeMatrix[0, 0] = LocalDerivativeMatrix[1, 3] = gradN[0, 0];
LocalDerivativeMatrix[2, 0] = LocalDerivativeMatrix[3, 3] = gradN[0, 1];
LocalDerivativeMatrix[4, 0] = LocalDerivativeMatrix[5, 3] = gradN[0, 2];
LocalDerivativeMatrix[6, 0] = LocalDerivativeMatrix[7, 3] = gradN[0, 3];
LocalDerivativeMatrix[1, 1] = LocalDerivativeMatrix[0, 2] = gradN[1, 0];
LocalDerivativeMatrix[3, 1] = LocalDerivativeMatrix[2, 2] = gradN[1, 1];
LocalDerivativeMatrix[5, 1] = LocalDerivativeMatrix[4, 2] = gradN[1, 2];
LocalDerivativeMatrix[7, 1] = LocalDerivativeMatrix[6, 2] = gradN[1, 3];
return LocalDerivativeMatrix;
}
public void Setup()
{
mocks = new MockRepository();
node1 = mocks.StrictMock <IFiniteElementNode>();
node2 = mocks.StrictMock <IFiniteElementNode>();
node3 = mocks.StrictMock <IFiniteElementNode>();
spring1 = mocks.StrictMock <IFiniteElement>();
spring2 = mocks.StrictMock <IFiniteElement>();
spring1Calculator = mocks.StrictMock <IElementStiffnessCalculator>();
spring2Calculator = mocks.StrictMock <IElementStiffnessCalculator>();
constraintProvider = mocks.StrictMock <IModelConstraintProvider>();
topologyQueryable = mocks.StrictMock <ITopologyQueryable>();
elementStiffnessMatrixBuilderFactory = mocks.StrictMock <IElementStiffnessMatrixBuilderFactory>();
Expect.Call(elementStiffnessMatrixBuilderFactory.Create(spring1))
.Return(spring1Calculator);
Expect.Call(elementStiffnessMatrixBuilderFactory.Create(spring2))
.Return(spring2Calculator);
SUT = new GlobalModelStiffnessMatrixBuilder(topologyQueryable, constraintProvider, elementStiffnessMatrixBuilderFactory);
}
private Matrix GetLocalDerivativeMatrix(IFiniteElement element, double ksi, double eta)
{
Matrix LocalDerivativeMatrix = new Matrix(8, 4);
Matrix gradNksieta = new Matrix(2, 4);
gradNksieta[0, 0] = (eta - 1) * 0.25;
gradNksieta[1, 0] = (ksi - 1) * 0.25;
gradNksieta[0, 1] = (1 - eta) * 0.25;
gradNksieta[1, 1] = (-ksi - 1) * 0.25;
gradNksieta[0, 2] = (eta + 1) * 0.25;
gradNksieta[1, 2] = (ksi + 1) * 0.25;
gradNksieta[0, 3] = (-eta - 1) * 0.25;
gradNksieta[1, 3] = (1 - ksi) * 0.25;
JacobianRectangular J = new JacobianRectangular();
J.Element = element;
Matrix gradN = J.GetInverseJacobian(ksi, eta) * gradNksieta;
LocalDerivativeMatrix[0, 0] = LocalDerivativeMatrix[1, 3] = gradN[0, 0];
LocalDerivativeMatrix[2, 0] = LocalDerivativeMatrix[3, 3] = gradN[0, 1];
LocalDerivativeMatrix[4, 0] = LocalDerivativeMatrix[5, 3] = gradN[0, 2];
LocalDerivativeMatrix[6, 0] = LocalDerivativeMatrix[7, 3] = gradN[0, 3];
LocalDerivativeMatrix[1, 1] = LocalDerivativeMatrix[0, 2] = gradN[1, 0];
LocalDerivativeMatrix[3, 1] = LocalDerivativeMatrix[2, 2] = gradN[1, 1];
LocalDerivativeMatrix[5, 1] = LocalDerivativeMatrix[4, 2] = gradN[1, 2];
LocalDerivativeMatrix[7, 1] = LocalDerivativeMatrix[6, 2] = gradN[1, 3];
return(LocalDerivativeMatrix);
}
protected Matrix GetLocalMassMatrixMatrix(IFiniteElement element)
{
elementCurrent = element;
Matrix localMassMatrix = Integration.GaussianIntegrationMatrix(LocalMassMatrixFunction);
return localMassMatrix;
}
protected Matrix GetLocalMassMatrixMatrix(IFiniteElement element)
{
elementCurrent = element;
Matrix localMassMatrix = Integration.GaussianIntegrationMatrix(LocalMassMatrixFunction);
return(localMassMatrix);
}
private Matrix GetLocalMassMatrixMatrix(IFiniteElement element)
{
elementCurrent = element;
Matrix localMassMatrix = _model.Material.Rho * Integration.GaussianIntegrationMatrix(LocalMassMatrixFunction);
return(localMassMatrix);
}
private Matrix GetLocalStiffnessMatrix(IFiniteElement element)
{
elementCurrent = element;
Matrix localStiffnessMatrix = Integration.GaussianIntegrationMatrix(LocalStiffnessMatrixFunction);
return(localStiffnessMatrix);
}
private Matrix GetNonlinearLocalTotalVector(IFiniteElement element)
{
elementCurrent = element;
Matrix NonlinearLocalTotalVector = Integration.GaussianIntegrationMatrix(LocalVectorFunction);
return(NonlinearLocalTotalVector);
}
private Matrix GetLocalNonlinearMatrix(IFiniteElement element, Vector u)
{
elementCurrent = element;
previousU = u;
Matrix localMassMatrix = Integration.GaussianIntegrationMatrix(LocalNonlinearMatrixFunction);
return(localMassMatrix);
}
public static Point TransformCoordinates(Point pointForm, IFiniteElement elementFrom, IFiniteElement elementTo)
{
Point res = new Point();
res.X = elementTo[0].Point.X +
((pointForm.X - elementFrom[0].Point.X) * (elementTo[2].Point.X - elementTo[0].Point.X)) / (elementFrom[2].Point.X - elementFrom[0].Point.X);
res.Y = elementTo[0].Point.Y +
((pointForm.Y - elementFrom[0].Point.Y) * (elementTo[2].Point.Y - elementTo[0].Point.Y)) / (elementFrom[2].Point.Y - elementFrom[0].Point.Y);
return res;
}
private void CheckElementType(IFiniteElement element)
{
bool validElement = element is Hexa8;
validElement |= element is Hexa8NonLinear;
if (!(validElement))
{
throw new ArgumentException("Host element is not Hexa8 or Hexa8NL.");
}
}
public static Point TransformCoordinates(Point pointForm, IFiniteElement elementFrom, IFiniteElement elementTo)
{
Point res = new Point();
res.X = elementTo[0].Point.X +
((pointForm.X - elementFrom[0].Point.X) * (elementTo[2].Point.X - elementTo[0].Point.X)) / (elementFrom[2].Point.X - elementFrom[0].Point.X);
res.Y = elementTo[0].Point.Y +
((pointForm.Y - elementFrom[0].Point.Y) * (elementTo[2].Point.Y - elementTo[0].Point.Y)) / (elementFrom[2].Point.Y - elementFrom[0].Point.Y);
return(res);
}
private void CheckElementType(IFiniteElement element)
{
bool isHexa8 = element.CellType == MSolve.Discretization.Mesh.CellType.Hexa8;
//bool validElement = element is Hexa8;
//validElement |= element is Hexa8NonLinear;
if (!(isHexa8))
{
throw new ArgumentException("Host element is not Hexa8 or Hexa8NL.");
}
}
private Vector GetUByElement(IFiniteElement element)
{
Vector res = new Vector(8);
if (U != null)
{
for (int i = 0; i < element.Count; i++)
{
res[2 * i] = U[2 * element[i].Index];
res[2 * i + 1] = U[2 * element[i].Index + 1];
}
}
return res;
}
private Vector GetUByElement(IFiniteElement element)
{
Vector res = new Vector(8);
if (U != null)
{
for (int i = 0; i < element.Count; i++)
{
res[2 * i] = U[2 * element[i].Index];
res[2 * i + 1] = U[2 * element[i].Index + 1];
}
}
return(res);
}
/// <summary>
///
/// </summary>
/// <param name="element"></param>
/// <returns></returns>
private IElementStiffnessCalculator GetElementStiffnessProvider(IFiniteElement element)
{
int elementHash = element.GetHashCode();
// check the cache, and retrieve if available
if (this.elementStiffnessProviderCache.ContainsKey(elementHash))
{
return((IElementStiffnessCalculator)this.elementStiffnessProviderCache[elementHash]);
}
IElementStiffnessCalculator builder = this.stiffnessMatrixBuilderFactory.Create(element);
// store in the cache
this.elementStiffnessProviderCache.Add(elementHash, builder);
return(builder);
}
/// <summary>
/// Adds a new finite element to the model.
/// </summary>
/// <param name="element">The element type (e.g. continuum element, beam, etc.)</param>
/// <param name="elementNodes">The element's nodes. Beware of their order.</param>
public void AddElement(IFiniteElement element, IReadOnlyList <Node> elementNodes)
{
int numElementsTotal = model.Elements.Count;
int numElementsSubdomain = model.Subdomains[0].Elements.Count;
var elementWrapper = new Element()
{
ID = numElementsTotal, ElementType = element
};
foreach (Node node in elementNodes)
{
elementWrapper.AddNode(node);
}
model.ElementsDictionary.Add(numElementsTotal, elementWrapper);
model.SubdomainsDictionary[0].Elements.Add(elementWrapper); //TODO: let the user decide which subdomain it will be added to.
}
private Matrix GetVariableVectorOnElement(IFiniteElement element, double ksi, double eta)
{
Matrix VariableVector = new Matrix(4, 1);
Vector du = previousRes.DU(ksi, eta, element);
double d1u1 = du[0];
double d3u3 = du[1];
double d3u1 = du[2];
double d1u3 = du[3];
VariableVector[0, 0] = 0.5 * M1 * d1u1 * d1u1 + 0.5 * M1 * d1u3 * d1u3 + 0.5 * M2 * d3u1 * d3u1 + 0.5 * M2 * d3u3 * d3u3;
VariableVector[1, 0] = 0.5 * M2 * d1u1 * d1u1 + 0.5 * M2 * d1u3 * d1u3 + 0.5 * M3 * d3u1 * d3u1 + 0.5 * M3 * d3u3 * d3u3;
VariableVector[2, 0] = G13 * (d1u1 * d3u1 + d1u3 * d3u3);
VariableVector[3, 0] = G13 * (d1u1 * d3u1 + d1u3 * d3u3);
return(VariableVector);
}
public Vector GetResultAtPoint(Point point, double t)
{
IFiniteElement element = getElementForPoint(point);
Vector result = null;
if (element != null)
{
FiniteElementRectangle elementKsiTeta = new FiniteElementRectangle()
{
Node1 = new FiniteElementNode(-1, -1),
Node3 = new FiniteElementNode(1, 1)
};
Point pointKsiTeta = ResultHelper.TransformCoordinates(point, element, elementKsiTeta);
Matrix finiteElementApproximationMatrix = getFiniteElementApproximationMatrix(pointKsiTeta);
result = GetUByElement(element) * (finiteElementApproximationMatrix * Math.Cos(_frequency * t));
}
return(result);
}
public Vector GetResultAtPoint(Point point, double t)
{
IFiniteElement element = getElementForPoint(point);
Vector result = null;
if (element != null)
{
int time = (int)(cutTime(t) / _deltaTime);
FiniteElementRectangle elementKsiTeta = new FiniteElementRectangle()
{
Node1 = new FiniteElementNode(-1, -1),
Node3 = new FiniteElementNode(1, 1)
};
Point pointKsiTeta = ResultHelper.TransformCoordinates(point, element, elementKsiTeta);
Matrix finiteElementApproximationMatrix = getFiniteElementApproximationMatrix(pointKsiTeta);
result = GetUByElement(element, U[time]) * finiteElementApproximationMatrix;
}
return(result);
}
private Matrix GetLocalUDerivativeMatrix(Vector previousU, IFiniteElement elementCurrent, double ksi, double eta)
{
Matrix derivativeMatrix = GetLocalDerivativeMatrix(elementCurrent, ksi, eta);
Vector uOnElement = new Vector(8);
if (previousU != null)
{
for (int i = 0; i < elementCurrent.Count; i++)
{
uOnElement[2 * i] = previousU[2 * elementCurrent[i].Index];
uOnElement[2 * i + 1] = previousU[2 * elementCurrent[i].Index + 1];
}
}
Vector uDerivative = Matrix.Transpose(derivativeMatrix) * uOnElement;
Matrix derivativeUMatrix = new Matrix(4, 4);
derivativeUMatrix[0, 0] = derivativeUMatrix[2, 2] = uDerivative[0];
derivativeUMatrix[1, 1] = derivativeUMatrix[3, 3] = uDerivative[1];
derivativeUMatrix[3, 0] = derivativeUMatrix[1, 2] = uDerivative[2];
derivativeUMatrix[2, 1] = derivativeUMatrix[0, 3] = uDerivative[3];
return(derivativeUMatrix);
}
protected Matrix GetLocalDerivativeMatrix(IFiniteElement element, double eta)
{
int n = 12;
Matrix LocalDerivativeMatrix = new Matrix(n, n);
int m = 0;
for (int j = 0; j < n; j++)
{
if (j % 2 == 0)
{
LocalDerivativeMatrix[j, m] = (1 - eta) / 2;
LocalDerivativeMatrix[j, m + 6] = (1 + eta) / 2;
}
else
{
LocalDerivativeMatrix[j, m] = 1 / (element[0].Point.X - element[1].Point.X);
LocalDerivativeMatrix[j, m + 6] = 1 / (element[1].Point.X - element[0].Point.X);
m += 1;
}
}
return(LocalDerivativeMatrix);
}
public Vector DU(double ksi, double eta, IFiniteElement element)
{
Vector uElement = GetUByElement(element);
return(uElement * GetLocalDerivativeMatrix(element, ksi, eta));
}
private Matrix GetLocalStiffnessMatrix(IFiniteElement element)
{
elementCurrent = element;
Matrix localStiffnessMatrix = Integration.GaussianIntegrationMatrix(LocalStiffnessMatrixFunction);
return localStiffnessMatrix;
}
private Matrix GetLocalMassMatrixMatrix(IFiniteElement element)
{
elementCurrent = element;
Matrix localMassMatrix = _model.Material.Rho * Integration.GaussianIntegrationMatrix(LocalMassMatrixFunction);
return localMassMatrix;
}
private Matrix GetLocalUDerivativeMatrix(Vector previousU, IFiniteElement elementCurrent, double ksi, double eta)
{
Matrix derivativeMatrix = GetLocalDerivativeMatrix(elementCurrent, ksi, eta);
Vector uOnElement = new Vector(8);
if (previousU != null)
{
for (int i = 0; i < elementCurrent.Count; i++)
{
uOnElement[2 * i] = previousU[2 * elementCurrent[i].Index];
uOnElement[2 * i + 1] = previousU[2 * elementCurrent[i].Index + 1];
}
}
Vector uDerivative = Matrix.Transpose(derivativeMatrix) * uOnElement;
Matrix derivativeUMatrix = new Matrix(4, 4);
derivativeUMatrix[0, 0] = derivativeUMatrix[2, 2] = uDerivative[0];
derivativeUMatrix[1, 1] = derivativeUMatrix[3, 3] = uDerivative[1];
derivativeUMatrix[3, 0] = derivativeUMatrix[1, 2] = uDerivative[2];
derivativeUMatrix[2, 1] = derivativeUMatrix[0, 3] = uDerivative[3];
return derivativeUMatrix;
}
private Matrix GetLocalNonlinearMatrix(IFiniteElement element, Vector u)
{
elementCurrent = element;
previousU = u;
Matrix localMassMatrix = Integration.GaussianIntegrationMatrix(LocalNonlinearMatrixFunction);
return localMassMatrix;
}
private double UIJ(double alfa1, int shift)
{
IFiniteElement e = FindElement(alfa1);
return(U[6 * e[0].Index + shift] * (e[1].Point.X - alfa1) / (e[1].Point.X - e[0].Point.X) + U[6 * e[1].Index + shift] * (alfa1 - e[0].Point.X) / (e[1].Point.X - e[0].Point.X));
}
public void Setup()
{
mocks = new MockRepository();
node1 = mocks.StrictMock<IFiniteElementNode>();
node2 = mocks.StrictMock<IFiniteElementNode>();
node3 = mocks.StrictMock<IFiniteElementNode>();
spring1 = mocks.StrictMock<IFiniteElement>();
spring2 = mocks.StrictMock<IFiniteElement>();
spring1Calculator = mocks.StrictMock<IElementStiffnessCalculator>();
spring2Calculator = mocks.StrictMock<IElementStiffnessCalculator>();
constraintProvider = mocks.StrictMock<IModelConstraintProvider>();
topologyQueryable = mocks.StrictMock<ITopologyQueryable>();
elementStiffnessMatrixBuilderFactory = mocks.StrictMock<IElementStiffnessMatrixBuilderFactory>();
Expect.Call(elementStiffnessMatrixBuilderFactory.Create(spring1))
.Return(spring1Calculator);
Expect.Call(elementStiffnessMatrixBuilderFactory.Create(spring2))
.Return(spring2Calculator);
SUT = new GlobalModelStiffnessMatrixBuilder(topologyQueryable, constraintProvider, elementStiffnessMatrixBuilderFactory);
}
protected Matrix GetLocalMassMatrix(IFiniteElement element)
{
elementCurrent = element;
//_model.Material.Rho *
Matrix localMassMatrix = Integration.GaussianIntegrationMatrix(LocalMassMatrixFunction);
return localMassMatrix;
}
protected Matrix GetLocalDerivativeMatrix(IFiniteElement element, double eta)
{
int n = 12;
Matrix LocalDerivativeMatrix = new Matrix(n, n);
int m = 0;
for (int j = 0; j < n; j++)
{
if (j % 2 == 0)
{
LocalDerivativeMatrix[j, m] = (1 - eta) / 2;
LocalDerivativeMatrix[j, m + 6] = (1 + eta) / 2;
}
else
{
LocalDerivativeMatrix[j, m] = 1 / (element[0].Point.X - element[1].Point.X);
LocalDerivativeMatrix[j, m + 6] = 1 / (element[1].Point.X - element[0].Point.X);
m += 1;
}
}
return LocalDerivativeMatrix;
}
private Matrix GetNonlinearLocalTotalVector(IFiniteElement element)
{
elementCurrent = element;
Matrix NonlinearLocalTotalVector = Integration.GaussianIntegrationMatrix(LocalVectorFunction);
return NonlinearLocalTotalVector;
}
private Matrix GetVariableVectorOnElement(IFiniteElement element, double ksi, double eta)
{
Matrix VariableVector = new Matrix(4, 1);
Vector du = previousRes.DU(ksi, eta, element);
double d1u1 = du[0];
double d3u3 = du[1];
double d3u1 = du[2];
double d1u3 = du[3];
VariableVector[0, 0] = 0.5 * M1 * d1u1 * d1u1 + 0.5 * M1 * d1u3 * d1u3 + 0.5 * M2 * d3u1 * d3u1 + 0.5 * M2 * d3u3 * d3u3;
VariableVector[1, 0] = 0.5 * M2 * d1u1 * d1u1 + 0.5 * M2 * d1u3 * d1u3 + 0.5 * M3 * d3u1 * d3u1 + 0.5 * M3 * d3u3 * d3u3;
VariableVector[2, 0] = G13 * (d1u1 * d3u1 + d1u3 * d3u3);
VariableVector[3, 0] = G13 * (d1u1 * d3u1 + d1u3 * d3u3);
return VariableVector;
}
protected Matrix GetLocalUDerivativeMatrix(Vector previousU, IFiniteElement elementCurrent, double ksi, double eta)
{
Matrix derivativeMatrix = GetLocalDerivativeMatrix(elementCurrent, ksi, eta);
Vector uOnElement = new Vector(8);
if (previousU != null)
{
for (int i = 0; i < elementCurrent.Count; i++)
{
uOnElement[2 * i] = previousU[2 * elementCurrent[i].Index];
uOnElement[2 * i + 1] = previousU[2 * elementCurrent[i].Index + 1];
}
}
Vector uDerivative = Matrix.Transpose(derivativeMatrix) * uOnElement;
double d1u1 = uDerivative[0];
double d3u3 = uDerivative[1];
Matrix derivativeUMatrix = new Matrix(4, 4);
/*derivativeUMatrix[0, 0] = derivativeUMatrix[2, 2] = uDerivative[0];
derivativeUMatrix[1, 1] = derivativeUMatrix[3, 3] = uDerivative[1];
derivativeUMatrix[3, 0] = derivativeUMatrix[1, 2] = uDerivative[2];
derivativeUMatrix[2, 1] = derivativeUMatrix[0, 3] = uDerivative[3];*/
derivativeUMatrix[0, 0] = (M1 * d1u1 + M2 * d3u3) * 0.5;
derivativeUMatrix[1, 1] = (M2 * d1u1 + M3 * d3u3) * 0.5;
derivativeUMatrix[2, 2] = (M2 * d1u1 + M3 * d3u3) * 0.5 + G13 * d1u1;
derivativeUMatrix[3, 3] = (M1 * d1u1 + M2 * d3u3) * 0.5 + G13 * d3u3;
derivativeUMatrix[2, 3] = G13 * d3u3;
derivativeUMatrix[3, 2] = G13 * d1u1;
return derivativeUMatrix;
}
public Vector DU(double ksi, double eta, IFiniteElement element)
{
Vector uElement = GetUByElement(element);
return uElement * GetLocalDerivativeMatrix(element, ksi, eta);
}
/// <summary>
///
/// </summary>
/// <param name="element"></param>
/// <returns></returns>
private IElementStiffnessCalculator GetElementStiffnessProvider(IFiniteElement element)
{
int elementHash = element.GetHashCode();
// check the cache, and retrieve if available
if (this.elementStiffnessProviderCache.ContainsKey(elementHash))
{
return (IElementStiffnessCalculator)this.elementStiffnessProviderCache[elementHash];
}
IElementStiffnessCalculator builder = this.stiffnessMatrixBuilderFactory.Create(element);
// store in the cache
this.elementStiffnessProviderCache.Add(elementHash, builder);
return builder;
}