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 Quad4(ElasticMaterial2D material)
{
materialsAtGaussPoints = new ElasticMaterial2D[iInt2];
for (int i = 0; i < iInt2; i++)
{
materialsAtGaussPoints[i] = (ElasticMaterial2D)material.Clone();
}
}
public ContinuumElement2D CreateElement(CellType cellType, IReadOnlyList <Node> nodes, double thickness,
ElasticMaterial2D material, DynamicMaterial dynamicProperties)
{
int numGPs = integrationsForStiffness[cellType].IntegrationPoints.Count;
var materialsAtGaussPoints = new ElasticMaterial2D[numGPs];
for (int gp = 0; gp < numGPs; ++gp)
{
materialsAtGaussPoints[gp] = material.Clone();
}
return(CreateElement(cellType, nodes, thickness, materialsAtGaussPoints, dynamicProperties));
}
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 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));
}
}
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));
}