private static void TestConsistentMass0()
{
IQuadrature2D quadratureForMass = TriangleQuadratureSymmetricGaussian.Order4Points6;
var materialsAtGaussPoints = new List <ElasticMaterial2D>();
foreach (GaussPoint gaussPoint in quadratureForMass.IntegrationPoints)
{
materialsAtGaussPoints.Add(material0.Clone());
}
var tri6 = new ContinuumElement2D(thickness, nodeSet0, InterpolationTri6.UniqueInstance,
TriangleQuadratureSymmetricGaussian.Order2Points3, quadratureForMass,
ExtrapolationGaussTriangular3Points.UniqueInstance,
materialsAtGaussPoints, dynamicMaterial);
IMatrix M = tri6.BuildConsistentMassMatrix();
Matrix expectedM = Matrix.CreateFromArray(new double[, ]
{
{ 11.83599396, 0, -1.829621484, 0, -1.968668415, 0, 0.702983761, 0, -6.922261694, 0, 0.623796095, 0, },
{ 0, 11.83599396, 0, -1.829621484, 0, -1.968668415, 0, 0.702983761, 0, -6.922261694, 0, 0.623796095, },
{ -1.829621484, 0, 9.926994738, 0, -1.638252825, 0, -0.618678599, 0, -0.46271906, 0, -7.392556104, 0, },
{ 0, -1.829621484, 0, 9.926994738, 0, -1.638252825, 0, -0.618678599, 0, -0.46271906, 0, -7.392556104, },
{ -1.968668415, 0, -1.638252825, 0, 10.74103411, 0, -7.234180772, 0, 9.35E-02, 0, -0.141678539, 0, },
{ 0, -1.968668415, 0, -1.638252825, 0, 10.74103411, 0, -7.234180772, 0, 9.35E-02, 0, -0.141678539, },
{ 0.702983761, 0, -0.618678599, 0, -7.234180772, 0, 57.86118359, 0, 28.31288493, 0, 29.25347375, 0, },
{ 0, 0.702983761, 0, -0.618678599, 0, -7.234180772, 0, 57.86118359, 0, 28.31288493, 0, 29.25347375, },
{ -6.922261694, 0, -0.46271906, 0, 9.35E-02, 0, 28.31288493, 0, 56.00999156, 0, 28.6296356, 0, },
{ 0, -6.922261694, 0, -0.46271906, 0, 9.35E-02, 0, 28.31288493, 0, 56.00999156, 0, 28.6296356, },
{ 0.623796095, 0, -7.392556104, 0, -0.141678539, 0, 29.25347375, 0, 28.6296356, 0, 58.49121809, 0, },
{ 0, 0.623796095, 0, -7.392556104, 0, -0.141678539, 0, 29.25347375, 0, 28.6296356, 0, 58.49121809, }
}); // from Abaqus
Assert.True(M.Equals(expectedM, 1e-3));
}
public SurfaceLoadElement(ISurfaceLoad surfaceLoad, IIsoparametricInterpolation2D isoparametricInterpolation2D,
IQuadrature2D quadrature2D, IReadOnlyList <Node> nodes)
{
this.surfaceLoad = surfaceLoad;
this.isoparametricInterpolation2D = isoparametricInterpolation2D;
this.quadrature2D = quadrature2D;
this.nodes = nodes;
}
public CohesiveShell8ToHexa20(ICohesiveZoneMaterial3D material, IQuadrature2D quadratureForStiffness)
{
this.QuadratureForStiffness = quadratureForStiffness;
this.nGaussPoints = quadratureForStiffness.IntegrationPoints.Count;
materialsAtGaussPoints = new ICohesiveZoneMaterial3D[nGaussPoints];
for (int i = 0; i < nGaussPoints; i++)
{
materialsAtGaussPoints[i] = material.Clone();
}
}
public IReadOnlyList <Matrix> EvaluateN3ShapeFunctionsReorganized(IQuadrature2D quadrature)
{
bool isCached = cachedN3AtGPs.TryGetValue(quadrature,
out IReadOnlyList <Matrix> N3AtGPs);
if (isCached)
{
return(N3AtGPs);
}
else
{
IReadOnlyList <double[]> N1 = EvaluateFunctionsAtGaussPoints(quadrature);
N3AtGPs = GetN3ShapeFunctionsReorganized(quadrature, N1);
cachedN3AtGPs.Add(quadrature, N3AtGPs);
return(N3AtGPs);
}
}
//private readonly Dictionary<GaussPoint, ThermalMaterial> materialsAtGaussPoints;
public ThermalElement2D(double thickness, IReadOnlyList <Node> nodes, IIsoparametricInterpolation2D interpolation,
IQuadrature2D quadratureForStiffness, IQuadrature2D quadratureForConsistentMass,
IGaussPointExtrapolation2D gaussPointExtrapolation,
ThermalMaterial material)
{
this.material = material;
this.GaussPointExtrapolation = gaussPointExtrapolation;
this.Nodes = nodes;
this.Interpolation = interpolation;
this.QuadratureForConsistentMass = quadratureForConsistentMass;
this.QuadratureForStiffness = quadratureForStiffness;
this.Thickness = thickness;
dofTypes = new IDofType[nodes.Count][];
for (int i = 0; i < interpolation.NumFunctions; ++i)
{
dofTypes[i] = new IDofType[] { ThermalDof.Temperature }
}
;
}
public ContinuumElement2D(double thickness, IReadOnlyList <Node> nodes, IIsoparametricInterpolation2D interpolation,
IQuadrature2D quadratureForStiffness, IQuadrature2D quadratureForConsistentMass,
IGaussPointExtrapolation2D gaussPointExtrapolation,
IReadOnlyList <ElasticMaterial2D> materialsAtGaussPoints, DynamicMaterial dynamicProperties)
{
this.dynamicProperties = dynamicProperties;
this.materialsAtGaussPoints = materialsAtGaussPoints;
this.GaussPointExtrapolation = gaussPointExtrapolation;
this.Nodes = nodes;
this.Interpolation = interpolation;
this.QuadratureForConsistentMass = quadratureForConsistentMass;
this.QuadratureForStiffness = quadratureForStiffness;
this.Thickness = thickness;
dofTypes = new IDofType[nodes.Count][];
for (int i = 0; i < nodes.Count; ++i)
{
dofTypes[i] = new IDofType[] { StructuralDof.TranslationX, StructuralDof.TranslationY };
}
}
/// <summary>
/// See <see cref="IIsoparametricInterpolation2D.EvaluateFunctionsAtGaussPoints(IQuadrature2D)"/>.
/// </summary>
public IReadOnlyList <double[]> EvaluateFunctionsAtGaussPoints(IQuadrature2D quadrature)
{
bool isCached = cachedFunctionsAtGPs.TryGetValue(quadrature,
out IReadOnlyList <double[]> shapeFunctionsAtGPs);
if (isCached)
{
return(shapeFunctionsAtGPs);
}
else
{
int numGPs = quadrature.IntegrationPoints.Count;
var shapeFunctionsAtGPsArray = new double[numGPs][];
for (int gp = 0; gp < numGPs; ++gp)
{
GaussPoint gaussPoint = quadrature.IntegrationPoints[gp];
shapeFunctionsAtGPsArray[gp] = EvaluateAt(gaussPoint.Xi, gaussPoint.Eta);
}
cachedFunctionsAtGPs.Add(quadrature, shapeFunctionsAtGPsArray);
return(shapeFunctionsAtGPsArray);
}
}
/// <summary>
/// See <see cref="IIsoparametricInterpolation2D.EvaluateNaturalGradientsAtGaussPoints(IQuadrature2D)"/>.
/// </summary>
/// <param name="quadrature"></param>
public IReadOnlyList <Matrix> EvaluateNaturalGradientsAtGaussPoints(IQuadrature2D quadrature)
{
bool isCached = cachedNaturalGradientsAtGPs.TryGetValue(quadrature,
out IReadOnlyList <Matrix> naturalGradientsAtGPs);
if (isCached)
{
return(naturalGradientsAtGPs);
}
else
{
int numGPs = quadrature.IntegrationPoints.Count;
var naturalGradientsAtGPsArray = new Matrix[numGPs];
for (int gp = 0; gp < numGPs; ++gp)
{
GaussPoint gaussPoint = quadrature.IntegrationPoints[gp];
naturalGradientsAtGPsArray[gp] = EvaluateGradientsAt(gaussPoint.Xi, gaussPoint.Eta);
}
cachedNaturalGradientsAtGPs.Add(quadrature, naturalGradientsAtGPsArray);
return(naturalGradientsAtGPsArray);
}
}
private static void TestConsistentMass0()
{
IQuadrature2D quadratureForMass = GaussLegendre2D.GetQuadratureWithOrder(3, 3);
var materialsAtGaussPoints = new List <ElasticMaterial2D>();
foreach (GaussPoint gaussPoint in quadratureForMass.IntegrationPoints)
{
materialsAtGaussPoints.Add(material0.Clone());
}
var quad8 = new ContinuumElement2D(thickness, nodeSet0, InterpolationQuad8.UniqueInstance,
GaussLegendre2D.GetQuadratureWithOrder(3, 3), quadratureForMass,
ExtrapolationGaussLegendre3x3.UniqueInstance,
materialsAtGaussPoints, dynamicMaterial);
IMatrix M = quad8.BuildConsistentMassMatrix();
Matrix expectedM = Matrix.CreateFromArray(new double[, ]
{
{ 9.115245555556, 0.000000000000, 1.881383333333, 0.000000000000, 3.914882222222, 0.000000000000, 2.417800000000, 0.000000000000, -7.376906666667, 0.000000000000, -11.056637777778, 0.000000000000, -9.104604444445, 0.000000000000, -7.444940000000, 0.000000000000 },
{ 0.000000000000, 9.115245555556, 0.000000000000, 1.881383333333, 0.000000000000, 3.914882222222, 0.000000000000, 2.417800000000, 0.000000000000, -7.376906666667, 0.000000000000, -11.056637777778, 0.000000000000, -9.104604444445, 0.000000000000, -7.444940000000 },
{ 1.881383333333, 0.000000000000, 9.727545555556, 0.000000000000, 2.239866666667, 0.000000000000, 3.841615555556, 0.000000000000, -6.727973333334, 0.000000000000, -6.701806666667, 0.000000000000, -9.031337777778, 0.000000000000, -11.077571111111, 0.000000000000 },
{ 0.000000000000, 1.881383333333, 0.000000000000, 9.727545555556, 0.000000000000, 2.239866666667, 0.000000000000, 3.841615555556, 0.000000000000, -6.727973333334, 0.000000000000, -6.701806666667, 0.000000000000, -9.031337777778, 0.000000000000, -11.077571111111 },
{ 3.914882222222, 0.000000000000, 2.239866666667, 0.000000000000, 7.681312222222, 0.000000000000, 2.776283333333, 0.000000000000, -11.082804444445, 0.000000000000, -8.784673333334, 0.000000000000, -6.832640000000, 0.000000000000, -11.150837777778, 0.000000000000 },
{ 0.000000000000, 3.914882222222, 0.000000000000, 2.239866666667, 0.000000000000, 7.681312222222, 0.000000000000, 2.776283333333, 0.000000000000, -11.082804444445, 0.000000000000, -8.784673333334, 0.000000000000, -6.832640000000, 0.000000000000, -11.150837777778 },
{ 2.417800000000, 0.000000000000, 3.841615555556, 0.000000000000, 2.776283333333, 0.000000000000, 7.581878888889, 0.000000000000, -11.009537777778, 0.000000000000, -10.983371111111, 0.000000000000, -6.895440000000, 0.000000000000, -8.941673333334, 0.000000000000 },
{ 0.000000000000, 2.417800000000, 0.000000000000, 3.841615555556, 0.000000000000, 2.776283333333, 0.000000000000, 7.581878888889, 0.000000000000, -11.009537777778, 0.000000000000, -10.983371111111, 0.000000000000, -6.895440000000, 0.000000000000, -8.941673333334 },
{ -7.376906666667, 0.000000000000, -6.727973333334, 0.000000000000, -11.082804444445, 0.000000000000, -11.009537777778, 0.000000000000, 45.023413333334, 0.000000000000, 28.692622222223, 0.000000000000, 20.114142222223, 0.000000000000, 28.734488888889, 0.000000000000 },
{ 0.000000000000, -7.376906666667, 0.000000000000, -6.727973333334, 0.000000000000, -11.082804444445, 0.000000000000, -11.009537777778, 0.000000000000, 45.023413333334, 0.000000000000, 28.692622222223, 0.000000000000, 20.114142222223, 0.000000000000, 28.734488888889 },
{ -11.056637777778, 0.000000000000, -6.701806666667, 0.000000000000, -8.784673333334, 0.000000000000, -10.983371111111, 0.000000000000, 28.692622222223, 0.000000000000, 48.215746666667, 0.000000000000, 24.589688888889, 0.000000000000, 22.134208888889, 0.000000000000 },
{ 0.000000000000, -11.056637777778, 0.000000000000, -6.701806666667, 0.000000000000, -8.784673333334, 0.000000000000, -10.983371111111, 0.000000000000, 28.692622222223, 0.000000000000, 48.215746666667, 0.000000000000, 24.589688888889, 0.000000000000, 22.134208888889 },
{ -9.104604444445, 0.000000000000, -9.031337777778, 0.000000000000, -6.832640000000, 0.000000000000, -6.895440000000, 0.000000000000, 20.114142222223, 0.000000000000, 24.589688888889, 0.000000000000, 28.821013333334, 0.000000000000, 24.924622222223, 0.000000000000 },
{ 0.000000000000, -9.104604444445, 0.000000000000, -9.031337777778, 0.000000000000, -6.832640000000, 0.000000000000, -6.895440000000, 0.000000000000, 20.114142222223, 0.000000000000, 24.589688888889, 0.000000000000, 28.821013333334, 0.000000000000, 24.924622222223 },
{ -7.444940000000, 0.000000000000, -11.077571111111, 0.000000000000, -11.150837777778, 0.000000000000, -8.941673333334, 0.000000000000, 28.734488888889, 0.000000000000, 22.134208888889, 0.000000000000, 24.924622222223, 0.000000000000, 49.869480000000, 0.000000000000 },
{ 0.000000000000, -7.444940000000, 0.000000000000, -11.077571111111, 0.000000000000, -11.150837777778, 0.000000000000, -8.941673333334, 0.000000000000, 28.734488888889, 0.000000000000, 22.134208888889, 0.000000000000, 24.924622222223, 0.000000000000, 49.869480000000 }
}); // from Abaqus
Assert.True(M.Equals(expectedM, 1e-10));
}
private static void TestConsistentMass0()
{
// reduced integration rule - bad idea
IQuadrature2D quadratureForMass = GaussLegendre2D.GetQuadratureWithOrder(1, 1);
var materialsAtGaussPoints = new List <ElasticMaterial2D>();
foreach (GaussPoint gaussPoint in quadratureForMass.IntegrationPoints)
{
materialsAtGaussPoints.Add(material0.Clone());
}
var quad4 = new ContinuumElement2D(thickness, nodeSet1, InterpolationQuad4.UniqueInstance,
GaussLegendre2D.GetQuadratureWithOrder(2, 2), quadratureForMass,
ExtrapolationGaussLegendre2x2.UniqueInstance, materialsAtGaussPoints, dynamicMaterial);
IMatrix M = quad4.BuildConsistentMassMatrix();
Matrix expectedM = Matrix.CreateFromArray(new double[, ]
{
{ 1, 0, 1, 0, 1, 0, 1, 0 },
{ 0, 1, 0, 1, 0, 1, 0, 1 },
{ 1, 0, 1, 0, 1, 0, 1, 0 },
{ 0, 1, 0, 1, 0, 1, 0, 1 },
{ 1, 0, 1, 0, 1, 0, 1, 0 },
{ 0, 1, 0, 1, 0, 1, 0, 1 },
{ 1, 0, 1, 0, 1, 0, 1, 0 },
{ 0, 1, 0, 1, 0, 1, 0, 1 }
});
double lengthX = nodeSet1[1].X - nodeSet1[0].X;
double lengthY = nodeSet1[2].Y - nodeSet1[1].Y;
// For some reason , only half the thickness is used for Quad4 elements, as shown in Fig. 31.9. Therefore the
// coefficient 1/16 (full thickness) became 1/32 (half thickness). Here 1/16 is used.
double scalar = dynamicMaterial.Density * thickness * lengthX * lengthY / 16.0;
expectedM.ScaleIntoThis(scalar);
Assert.True(M.Equals(expectedM, 1e-10));
}
private IReadOnlyList <Matrix> GetN3ShapeFunctionsReorganized(IQuadrature2D quadrature, IReadOnlyList <double[]> N1)
{
//TODO reorganize cohesive shell to use only N1 (not reorganised)
int nGaussPoints = quadrature.IntegrationPoints.Count;
var N3 = new Matrix[nGaussPoints]; // shapeFunctionsgpData
for (int npoint = 0; npoint < nGaussPoints; npoint++)
{
double ksi = quadrature.IntegrationPoints[npoint].Xi;
double heta = quadrature.IntegrationPoints[npoint].Eta;
var N3gp = Matrix.CreateZero(3, 24); //8=nShapeFunctions;
for (int l = 0; l < 3; l++)
{
for (int m = 0; m < 8; m++)
{
N3gp[l, l + 3 * m] = N1[npoint][m];
}
}
N3[npoint] = N3gp;
}
return(N3);
}
public Table <INode, IDofType, double> CalculateSurfaceLoad(IIsoparametricInterpolation2D interpolation,
IQuadrature2D integration, IReadOnlyList <Node> nodes)
{
var loadTable = new Table <INode, IDofType, double>();
IReadOnlyList <Matrix> shapeGradientsNatural =
interpolation.EvaluateNaturalGradientsAtGaussPoints(integration);
IReadOnlyList <double[]> shapeFunctionNatural =
interpolation.EvaluateFunctionsAtGaussPoints(integration);
for (int gp = 0; gp < integration.IntegrationPoints.Count; gp++)
{
var jacobianMatrix = Matrix.CreateZero(2, 3);
for (int indexNode = 0; indexNode < nodes.Count; indexNode++)
{
jacobianMatrix[0, 0] += shapeGradientsNatural[gp][indexNode, 0] * nodes[indexNode].X;
jacobianMatrix[0, 1] += shapeGradientsNatural[gp][indexNode, 0] * nodes[indexNode].Y;
jacobianMatrix[0, 2] += shapeGradientsNatural[gp][indexNode, 0] * nodes[indexNode].Z;
jacobianMatrix[1, 0] += shapeGradientsNatural[gp][indexNode, 1] * nodes[indexNode].X;
jacobianMatrix[1, 1] += shapeGradientsNatural[gp][indexNode, 1] * nodes[indexNode].Y;
jacobianMatrix[1, 2] += shapeGradientsNatural[gp][indexNode, 1] * nodes[indexNode].Z;
}
var tangentVector1 = jacobianMatrix.GetRow(0);
var tangentVector2 = jacobianMatrix.GetRow(1);
var normalVector = tangentVector1.CrossProduct(tangentVector2);
Vector surfaceBasisVector1 = Vector.CreateZero(3);
surfaceBasisVector1[0] = jacobianMatrix[0, 0];
surfaceBasisVector1[1] = jacobianMatrix[0, 1];
surfaceBasisVector1[2] = jacobianMatrix[0, 2];
Vector surfaceBasisVector2 = Vector.CreateZero(3);
surfaceBasisVector2[0] = jacobianMatrix[1, 0];
surfaceBasisVector2[1] = jacobianMatrix[1, 1];
surfaceBasisVector2[2] = jacobianMatrix[1, 2];
Vector surfaceBasisVector3 = surfaceBasisVector1.CrossProduct(surfaceBasisVector2);
var jacdet = surfaceBasisVector3.Norm2();
var weightFactor = integration.IntegrationPoints[gp].Weight;
for (int indexNode = 0; indexNode < nodes.Count; indexNode++)
{
var node = nodes[indexNode];
var valueX = _loadX * shapeFunctionNatural[gp][indexNode] * jacdet *
weightFactor;
var valueY = _loadY * shapeFunctionNatural[gp][indexNode] * jacdet *
weightFactor;
var valueZ = _loadZ * shapeFunctionNatural[gp][indexNode] * jacdet *
weightFactor;
if (loadTable.Contains(node, StructuralDof.TranslationX))
{
loadTable[node, StructuralDof.TranslationX] += valueX;
}
else
{
loadTable.TryAdd(node, StructuralDof.TranslationX, valueX);
}
if (loadTable.Contains(node, StructuralDof.TranslationY))
{
loadTable[node, StructuralDof.TranslationY] += valueY;
}
else
{
loadTable.TryAdd(node, StructuralDof.TranslationY, valueY);
}
if (loadTable.Contains(node, StructuralDof.TranslationZ))
{
loadTable[node, StructuralDof.TranslationZ] += valueZ;
}
else
{
loadTable.TryAdd(node, StructuralDof.TranslationZ, valueZ);
}
}
}
return(loadTable);
}
/// <summary>
/// See <see cref="IIsoparametricInterpolation2D.EvaluateAllAtGaussPoints(IReadOnlyList{Node}, IQuadrature2D)"/>.
/// </summary>
public IReadOnlyList <EvalInterpolation2D> EvaluateAllAtGaussPoints(IReadOnlyList <Node> nodes, IQuadrature2D quadrature)
{
// The shape functions and natural derivatives at each Gauss point are probably cached from previous calls
IReadOnlyList <double[]> shapeFunctionsAtGPs = EvaluateFunctionsAtGaussPoints(quadrature);
IReadOnlyList <Matrix> naturalShapeDerivativesAtGPs = EvaluateNaturalGradientsAtGaussPoints(quadrature);
// Calculate the Jacobians and shape derivatives w.r.t. global cartesian coordinates at each Gauss point
int numGPs = quadrature.IntegrationPoints.Count;
var interpolationsAtGPs = new EvalInterpolation2D[numGPs];
for (int gp = 0; gp < numGPs; ++gp)
{
interpolationsAtGPs[gp] = new EvalInterpolation2D(nodes, shapeFunctionsAtGPs[gp],
naturalShapeDerivativesAtGPs[gp], new IsoparametricJacobian2D(nodes, naturalShapeDerivativesAtGPs[gp]));
}
return(interpolationsAtGPs);
}
protected GaussPointExtrapolation2DBase(IQuadrature2D quadrature)
{
this.cachedExtrapolationFunctionsAtNodes = new Dictionary <IIsoparametricInterpolation2D, double[][]>();
this.Quadrature = quadrature;
}
private readonly IDofType[][] standardDofTypes; //TODO: this should not be stored for each element. Instead store it once for each Quad4, Tri3, etc. Otherwise create it on the fly.
public XContinuumElement2D(int id, IReadOnlyList <XNode> nodes, IIsoparametricInterpolation2D interpolation,
IGaussPointExtrapolation2D gaussPointExtrapolation, IQuadrature2D standardQuadrature,
IIntegrationStrategy2D <XContinuumElement2D> integrationStrategy,
IIntegrationStrategy2D <XContinuumElement2D> jIntegralStrategy, IMaterialField2D material)
{
this.id = id;
this.Nodes = nodes;
this.Interpolation = interpolation;
this.GaussPointExtrapolation = gaussPointExtrapolation;
this.StandardQuadrature = standardQuadrature;
this.IntegrationStrategy = integrationStrategy;
this.JintegralStrategy = jIntegralStrategy;
this.Material = material;
this.NumStandardDofs = 2 * nodes.Count;
standardDofTypes = new IDofType[nodes.Count][];
for (int i = 0; i < nodes.Count; ++i)
{
standardDofTypes[i] = new IDofType[] { StructuralDof.TranslationX, StructuralDof.TranslationY };
}
//OBSOLETE: Elements access their enrichments from nodes now.
//this.EnrichmentItems = new List<IEnrichmentItem2D>();
}
private static void TestConsistentMassParametric(IReadOnlyList <Node> nodeSet, IQuadrature2D quadratureForMass,
bool reducedQuadrature)
{
var materialsAtGaussPoints = new List <IContinuumMaterial2D>();
foreach (GaussPoint gaussPoint in quadratureForMass.IntegrationPoints)
{
materialsAtGaussPoints.Add(material0.Clone());
}
var tri3 = new ContinuumElement2D(thickness, nodeSet, InterpolationTri3.UniqueInstance,
TriangleQuadratureSymmetricGaussian.Order1Point1, quadratureForMass,
ExtrapolationGaussTriangular1Point.UniqueInstance,
materialsAtGaussPoints, dynamicMaterial);
IMatrix M = tri3.BuildConsistentMassMatrix();
// Reference: http://kis.tu.kielce.pl/mo/COLORADO_FEM/colorado/IFEM.Ch31.pdf, (eq 31.27)
Matrix expectedM = Matrix.CreateFromArray(new double[, ]
{
{ 2, 0, 1, 0, 1, 0 },
{ 0, 2, 0, 1, 0, 1 },
{ 1, 0, 2, 0, 1, 0 },
{ 0, 1, 0, 2, 0, 1 },
{ 1, 0, 1, 0, 2, 0 },
{ 0, 1, 0, 1, 0, 2 }
});
double area = CalcTriangleArea(nodeSet);
double scalar = dynamicMaterial.Density * thickness * area / 12.0;
expectedM.ScaleIntoThis(scalar);
if (reducedQuadrature)
{
Assert.False(M.Equals(expectedM, 1e-10));
}
else
{
Assert.True(M.Equals(expectedM, 1e-10));
}
}
public Table <INode, IDofType, double> CalculateSurfaceLoad(IIsoparametricInterpolation2D interpolation, IQuadrature2D integration, IReadOnlyList <Node> nodes)
{
int numDofs = nodes.Count;
var stiffness = Vector.CreateZero(numDofs);
IReadOnlyList <double[]> shapeFunctions =
interpolation.EvaluateFunctionsAtGaussPoints(integration);
IReadOnlyList <Matrix> shapeGradientsNatural =
interpolation.EvaluateNaturalGradientsAtGaussPoints(integration);
for (int gp = 0; gp < integration.IntegrationPoints.Count; ++gp)
{
Vector shapeFunctionVector = Vector.CreateFromArray(shapeFunctions[gp]);
Matrix jacobianMatrix = Matrix.CreateZero(2, 3);
for (int k = 0; k < nodes.Count; k++)
{
jacobianMatrix[0, 0] += shapeGradientsNatural[gp][k, 0] * nodes[k].X;
jacobianMatrix[0, 1] += shapeGradientsNatural[gp][k, 0] * nodes[k].Y;
jacobianMatrix[0, 2] += shapeGradientsNatural[gp][k, 0] * nodes[k].Z;
jacobianMatrix[1, 0] += shapeGradientsNatural[gp][k, 1] * nodes[k].X;
jacobianMatrix[1, 1] += shapeGradientsNatural[gp][k, 1] * nodes[k].Y;
jacobianMatrix[1, 2] += shapeGradientsNatural[gp][k, 1] * nodes[k].Z;
}
Vector tangentVector1 = jacobianMatrix.GetRow(0);
Vector tangentVector2 = jacobianMatrix.GetRow(1);
Vector normalVector = tangentVector1.CrossProduct(tangentVector2);
var jacdet = normalVector.Norm2();
double dA = jacdet * integration.IntegrationPoints[gp].Weight;
stiffness.AxpyIntoThis(shapeFunctionVector, dA);
}
var appliedDisplacements = Vector.CreateWithValue(nodes.Count, _flux);
var fluxLoad = stiffness.DoEntrywise(appliedDisplacements, (stiffi, appi) => stiffi * appi);
var table = new Table <INode, IDofType, double>();
for (int i = 0; i < nodes.Count; i++)
{
table.TryAdd(nodes[i], ThermalDof.Temperature, fluxLoad[i]);
}
return(table);
}
public Table <INode, IDofType, double> CalculateSurfaceLoad(IIsoparametricInterpolation2D interpolation, IQuadrature2D integration, IReadOnlyList <Node> nodes)
{
//nodes[0].ElementsDictionary.Values.ToList<>
int numDofs = nodes.Count;
double kappaCoef;
if (numDofs == 4)
{
kappaCoef = 100;
}
else
{
kappaCoef = 1;
}
var stiffness = Matrix.CreateZero(numDofs, numDofs);
IReadOnlyList <double[]> shapeFunctions =
interpolation.EvaluateFunctionsAtGaussPoints(integration);
IReadOnlyList <Matrix> shapeGradientsNatural =
interpolation.EvaluateNaturalGradientsAtGaussPoints(integration);
double[] dist = new double[nodes.Count];
List <INode> neighborNodes = new List <INode>();
for (int i = 0; i < nodes.Count; i++)
{
neighborNodes.Clear();
foreach (var element in nodes[i].ElementsDictionary.Values)
{
neighborNodes.AddRange(element.Nodes);
}
neighborNodes = neighborNodes.Distinct().ToList();
neighborNodes.Remove(nodes[i]);
var minDist = neighborNodes.Select(x => Math.Sqrt(
Math.Pow(nodes[i].X - x.X, 2) +
Math.Pow(nodes[i].Y - x.Y, 2) + Math.Pow(nodes[i].Z - x.Z, 2))).Min();
dist[i] = minDist;
}
//double kappa = kappaCoef * _diffusionCoeff / dist.Min();
//double[] kappa = new double[nodes.Count];
for (int gp = 0; gp < integration.IntegrationPoints.Count; ++gp)
{
//var jacobian = new IsoparametricJacobian3D(Nodes, shapeGradientsNatural[gp]);
var shapeFunctionMatrix = Vector.CreateFromArray(shapeFunctions[gp]);
Matrix jacobianMatrix = Matrix.CreateZero(2, 3);
for (int k = 0; k < nodes.Count; k++)
{
//xGaussPoint += shapeFunctionMatrix[gp, k] * this.Nodes[k].X;
//yGaussPoint += shapeFunctionMatrix[gp, k] * this.Nodes[k].Y;
//zGaussPoint += shapeFunctionMatrix[gp, k] * this.Nodes[k].Z;
jacobianMatrix[0, 0] += shapeGradientsNatural[gp][k, 0] * nodes[k].X;
jacobianMatrix[0, 1] += shapeGradientsNatural[gp][k, 0] * nodes[k].Y;
jacobianMatrix[0, 2] += shapeGradientsNatural[gp][k, 0] * nodes[k].Z;
jacobianMatrix[1, 0] += shapeGradientsNatural[gp][k, 1] * nodes[k].X;
jacobianMatrix[1, 1] += shapeGradientsNatural[gp][k, 1] * nodes[k].Y;
jacobianMatrix[1, 2] += shapeGradientsNatural[gp][k, 1] * nodes[k].Z;
//kappa[k] = _diffusionCoeff / .05 / dist[k];
}
Vector tangentVector1 = jacobianMatrix.GetRow(0);
Vector tangentVector2 = jacobianMatrix.GetRow(1);
Vector normalVector = tangentVector1.CrossProduct(tangentVector2);
var jacdet = normalVector.Norm2();
normalVector.ScaleIntoThis(1 / jacdet);
Matrix jacobianMatrixLeftInverse = jacobianMatrix.Transpose() *
(jacobianMatrix * jacobianMatrix.Transpose()).Invert();
Matrix shapeGradientsCartesian = (shapeGradientsNatural[gp]) * jacobianMatrixLeftInverse.Transpose();
Matrix deformation = shapeGradientsCartesian.Transpose();
Vector deformationNormal = normalVector * deformation;
//Vector deformationX = deformation.GetRow(0);
//Vector deformationY = deformation.GetRow(1);
//Vector deformationZ = deformation.GetRow(2);
//Matrix partial = kappa * shapeFunctionMatrix.TensorProduct(shapeFunctionMatrix)
// -_diffusionCoeff * deformationNormal.TensorProduct(shapeFunctionMatrix);
double kappa = _diffusionCoeff / .05;
Matrix partial = kappa * shapeFunctionMatrix.TensorProduct(shapeFunctionMatrix);
//Vector surfaceBasisVector1 = Vector.CreateZero(3);
//surfaceBasisVector1[0] = jacobianMatrix[0, 0];
//surfaceBasisVector1[1] = jacobianMatrix[0, 1];
//surfaceBasisVector1[2] = jacobianMatrix[0, 2];
//Vector surfaceBasisVector2 = Vector.CreateZero(3);
//surfaceBasisVector2[0] = jacobianMatrix[1, 0];
//surfaceBasisVector2[1] = jacobianMatrix[1, 1];
//surfaceBasisVector2[2] = jacobianMatrix[1, 2];
//Vector surfaceBasisVector3 = surfaceBasisVector1.CrossProduct(surfaceBasisVector2);
//var jacdet = surfaceBasisVector3.Norm2();
double dA = jacdet * integration.IntegrationPoints[gp].Weight;
stiffness.AxpyIntoThis(partial, dA);
}
//var appliedDisplacements=Vector.CreateWithValue(nodes.Count, _magnitude);
var appliedDisplacements = _distribution(nodes);
var weakDirichletForces = stiffness * appliedDisplacements;
var table = new Table <INode, IDofType, double>();
for (int i = 0; i < nodes.Count; i++)
{
table.TryAdd(nodes[i], ThermalDof.Temperature, weakDirichletForces[i]);
}
return(table);
}
