private Matrix CalculateConstitutiveMatrix(TSplineKirchhoffLoveShellElement element, Vector surfaceBasisVector1, Vector surfaceBasisVector2)
{
var auxMatrix1 = Matrix.CreateZero(2, 2);
auxMatrix1[0, 0] = surfaceBasisVector1.DotProduct(surfaceBasisVector1);
auxMatrix1[0, 1] = surfaceBasisVector1.DotProduct(surfaceBasisVector2);
auxMatrix1[1, 0] = surfaceBasisVector2.DotProduct(surfaceBasisVector1);
auxMatrix1[1, 1] = surfaceBasisVector2.DotProduct(surfaceBasisVector2);
(Matrix inverse, double det) = auxMatrix1.InvertAndDeterminant();
var material = ((IContinuumMaterial2D)element.Patch.Material);
var constitutiveMatrix = Matrix.CreateFromArray(new double[3, 3]
{
{
inverse[0, 0] * inverse[0, 0],
material.PoissonRatio * inverse[0, 0] * inverse[1, 1] + (1 - material.PoissonRatio) * inverse[1, 0] * inverse[1, 0],
inverse[0, 0] * inverse[1, 0]
},
{
material.PoissonRatio *inverse[0, 0] * inverse[1, 1] + (1 - material.PoissonRatio) * inverse[1, 0] * inverse[1, 0],
inverse[1, 1] * inverse[1, 1],
inverse[1, 1] * inverse[1, 0]
},
{
inverse[0, 0] * inverse[1, 0],
inverse[1, 1] * inverse[1, 0],
0.5 * (1 - material.PoissonRatio) * inverse[0, 0] * inverse[1, 1] + (1 + material.PoissonRatio) * inverse[1, 0] * inverse[1, 0]
},
});
return(constitutiveMatrix);
}
/// <summary>
/// Calculates knots physical coordinates for post-processing with Paraview.
/// </summary>
/// <param name="element">An <see cref="Element"/> of type <see cref="TSplineKirchhoffLoveShellElement"/>.</param>
/// <returns>A <see cref="double"/> array calculating the coordinates of the element Knots'.
/// The rows of the matrix denote the knot numbering while the columns the displacements for each degree of freedom.</returns>
public double[,] CalculatePointsForPostProcessing(TSplineKirchhoffLoveShellElement element)
{
var localCoordinates = new double[4, 2]
{
{ -1, -1 },
{ -1, 1 },
{ 1, -1 },
{ 1, 1 }
};
var knotParametricCoordinatesKsi = Vector.CreateFromArray(new double[] { -1, 1 });
var knotParametricCoordinatesHeta = Vector.CreateFromArray(new double[] { -1, 1 });
var elementControlPoints = element.ControlPoints.ToArray();
var tsplines = new ShapeTSplines2DFromBezierExtraction(element, elementControlPoints, knotParametricCoordinatesKsi, knotParametricCoordinatesHeta);
var knotDisplacements = new double[4, 3];
var paraviewKnotRenumbering = new int[] { 0, 3, 1, 2 };
for (int j = 0; j < localCoordinates.GetLength(0); j++)
{
for (int i = 0; i < elementControlPoints.Length; i++)
{
knotDisplacements[paraviewKnotRenumbering[j], 0] += tsplines.TSplineValues[i, j] * elementControlPoints[i].X;
knotDisplacements[paraviewKnotRenumbering[j], 1] += tsplines.TSplineValues[i, j] * elementControlPoints[i].Y;
knotDisplacements[paraviewKnotRenumbering[j], 2] += tsplines.TSplineValues[i, j] * elementControlPoints[i].Z;
}
}
return(knotDisplacements);
}
private IList <GaussLegendrePoint3D> CreateElementGaussPoints(TSplineKirchhoffLoveShellElement element)
{
GaussQuadrature gauss = new GaussQuadrature();
return(gauss.CalculateElementGaussPoints(element.DegreeKsi, element.DegreeHeta, new List <Knot>
{
new Knot()
{
ID = 0, Ksi = -1, Heta = -1, Zeta = 0
},
new Knot()
{
ID = 1, Ksi = -1, Heta = 1, Zeta = 0
},
new Knot()
{
ID = 2, Ksi = 1, Heta = -1, Zeta = 0
},
new Knot()
{
ID = 3, Ksi = 1, Heta = 1, Zeta = 0
}
}));
}
