private void CreateLinearShell(int elementDegreeKsi, int elementDegreeHeta, Matrix extractionOperator,
int[] connectivity)
{
Element element = new TSplineKirchhoffLoveShellElement()
{
ID = elementIDCounter,
Patch = _model.PatchesDictionary[0],
ElementType = new TSplineKirchhoffLoveShellElement(),
DegreeKsi = elementDegreeKsi,
DegreeHeta = elementDegreeHeta,
ExtractionOperator = extractionOperator
};
for (int cp = 0; cp < connectivity.Length; cp++)
{
element.AddControlPoint(_model.ControlPointsDictionary[connectivity[cp]]);
}
_model.ElementsDictionary.Add(elementIDCounter++, element);
_model.PatchesDictionary[0].Elements.Add(element);
}
/// <summary>
/// Two-dimensional T-spline shape functions from Bezier extraction for <see cref="TSplineKirchhoffLoveShellElement"/>.
/// </summary>
/// <param name="element">An <see cref="Element"/> of type <see cref="TSplineKirchhoffLoveShellElement"/>.</param>
/// <param name="controlPoints">A <see cref="List{T}"/> containing the control points of the element.</param>
public ShapeTSplines2DFromBezierExtraction(TSplineKirchhoffLoveShellElement element, ControlPoint[] controlPoints)
{
GaussQuadrature gauss = new GaussQuadrature();
IList <GaussLegendrePoint3D> gaussPoints = 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
}
});
var parametricGaussPointKsi = Vector.CreateZero(element.DegreeKsi + 1);
for (int i = 0; i < element.DegreeKsi + 1; i++)
{
parametricGaussPointKsi[i] = gaussPoints[i * (element.DegreeHeta + 1)].Ksi;
}
var parametricGaussPointHeta = Vector.CreateZero(element.DegreeHeta + 1);
for (int i = 0; i < element.DegreeHeta + 1; i++)
{
parametricGaussPointHeta[i] = gaussPoints[i].Heta;
}
Vector knotValueVectorKsi = Vector.CreateZero((element.DegreeKsi + 1) * 2);
Vector knotValueVectorHeta = Vector.CreateZero((element.DegreeHeta + 1) * 2);
for (int i = 0; i < element.DegreeKsi + 1; i++)
{
knotValueVectorKsi[i] = -1;
knotValueVectorKsi[element.DegreeKsi + 1 + i] = 1;
}
for (int i = 0; i < element.DegreeHeta + 1; i++)
{
knotValueVectorHeta[i] = -1;
knotValueVectorHeta[element.DegreeHeta + 1 + i] = 1;
}
BSPLines1D bernsteinKsi = new BSPLines1D(element.DegreeKsi, knotValueVectorKsi, parametricGaussPointKsi);
BSPLines1D bernsteinHeta = new BSPLines1D(element.DegreeHeta, knotValueVectorHeta, parametricGaussPointHeta);
bernsteinKsi.calculateBSPLinesAndDerivatives();
bernsteinHeta.calculateBSPLinesAndDerivatives();
int supportKsi = element.DegreeKsi + 1;
int supportHeta = element.DegreeHeta + 1;
var bKsi = MatrixPart(supportKsi, bernsteinKsi.BSPLineValues);
var bdKsi = MatrixPart(supportKsi, bernsteinKsi.BSPLineDerivativeValues);
var bddKsi = MatrixPart(supportKsi, bernsteinKsi.BSPLineSecondDerivativeValues);
var bheta = MatrixPart(supportHeta, bernsteinHeta.BSPLineValues);
var bdheta = MatrixPart(supportHeta, bernsteinHeta.BSPLineDerivativeValues);
var bddheta = MatrixPart(supportHeta, bernsteinHeta.BSPLineSecondDerivativeValues);
var bernsteinShapeFunctions = KroneckerProduct(bKsi, bheta);
Matrix bernsteinShapeFunctionDerivativesKsi = KroneckerProduct(bheta, bdKsi);
Matrix bernsteinShapeFunctionDerivativesHeta = KroneckerProduct(bdheta, bKsi);
Matrix bernsteinShapeFunctionSecondDerivativesKsi = KroneckerProduct(bheta, bddKsi);
Matrix bernsteinShapeFunctionSecondDerivativesHeta = KroneckerProduct(bddheta, bKsi);
Matrix bernsteinShapeFunctionSecondDerivativesKsiHeta = KroneckerProduct(bdheta, bdKsi);
Matrix rationalTSplines = element.ExtractionOperator * bernsteinShapeFunctions;
Matrix rationalTSplineDerivativesKsi = element.ExtractionOperator * bernsteinShapeFunctionDerivativesKsi;
Matrix rationalTSplineDerivativesHeta = element.ExtractionOperator * bernsteinShapeFunctionDerivativesHeta;
Matrix rationalTSplineSecondDerivativesKsi = element.ExtractionOperator * bernsteinShapeFunctionSecondDerivativesKsi;
Matrix rationalTSplineSecondDerivativesHeta = element.ExtractionOperator * bernsteinShapeFunctionSecondDerivativesHeta;
Matrix rationalTSplineSecondDerivativesKsiHeta = element.ExtractionOperator * bernsteinShapeFunctionSecondDerivativesKsiHeta;
TSplineValues = Matrix.CreateZero(controlPoints.Length, supportKsi * supportHeta);
TSplineDerivativeValuesKsi = Matrix.CreateZero(controlPoints.Length, supportKsi * supportHeta);
TSplineDerivativeValuesHeta = Matrix.CreateZero(controlPoints.Length, supportKsi * supportHeta);
TSplineSecondDerivativesValueKsi = Matrix.CreateZero(controlPoints.Length, supportKsi * supportHeta);
TSplineSecondDerivativesValueHeta = Matrix.CreateZero(controlPoints.Length, supportKsi * supportHeta);
TSplineSecondDerivativesValueKsiHeta = Matrix.CreateZero(controlPoints.Length, supportKsi * supportHeta);
for (int i = 0; i < supportKsi; i++)
{
for (int j = 0; j < supportHeta; j++)
{
double sumKsiHeta = 0;
double sumdKsiHeta = 0;
double sumKsidHeta = 0;
double sumdKsidKsi = 0;
double sumdHetadHeta = 0;
double sumdKsidHeta = 0;
var index = i * supportHeta + j;
for (int k = 0; k < controlPoints.Length; k++)
{
sumKsiHeta += rationalTSplines[k, index] * controlPoints[k].WeightFactor;
sumdKsiHeta += rationalTSplineDerivativesKsi[k, index] * controlPoints[k].WeightFactor;
sumKsidHeta += rationalTSplineDerivativesHeta[k, index] * controlPoints[k].WeightFactor;
sumdKsidKsi += rationalTSplineSecondDerivativesKsi[k, index] * controlPoints[k].WeightFactor;
sumdHetadHeta += rationalTSplineSecondDerivativesHeta[k, index] * controlPoints[k].WeightFactor;
sumdKsidHeta += rationalTSplineSecondDerivativesKsiHeta[k, index] * controlPoints[k].WeightFactor;
}
for (int k = 0; k < controlPoints.Length; k++)
{
TSplineValues[k, index] = rationalTSplines[k, index] * controlPoints[k].WeightFactor / sumKsiHeta;
TSplineDerivativeValuesKsi[k, index] = (rationalTSplineDerivativesKsi[k, index] * sumKsiHeta -
rationalTSplines[k, index] * sumdKsiHeta) /
Math.Pow(sumKsiHeta, 2) * controlPoints[k].WeightFactor;
TSplineDerivativeValuesHeta[k, index] = (rationalTSplineDerivativesHeta[k, index] * sumKsiHeta -
rationalTSplines[k, index] * sumKsidHeta) /
Math.Pow(sumKsiHeta, 2) * controlPoints[k].WeightFactor;
TSplineSecondDerivativesValueKsi[k, index] = (rationalTSplineSecondDerivativesKsi[k, index] / sumKsiHeta -
2 * rationalTSplineDerivativesKsi[k, index] * sumdKsiHeta /
Math.Pow(sumKsiHeta, 2) -
rationalTSplines[k, index] * sumdKsidKsi / Math.Pow(sumKsiHeta, 2) +
2 * rationalTSplines[k, index] * Math.Pow(sumdKsiHeta, 2) /
Math.Pow(sumKsiHeta, 3)) * controlPoints[k].WeightFactor;
TSplineSecondDerivativesValueHeta[k, index] = (rationalTSplineSecondDerivativesHeta[k, index] / sumKsiHeta -
2 * rationalTSplineDerivativesHeta[k, index] * sumKsidHeta /
Math.Pow(sumKsiHeta, 2) -
rationalTSplines[k, index] * sumdHetadHeta /
Math.Pow(sumKsiHeta, 2) +
2 * rationalTSplines[k, index] * Math.Pow(sumKsidHeta, 2) /
Math.Pow(sumKsiHeta, 3)) * controlPoints[k].WeightFactor;
TSplineSecondDerivativesValueKsiHeta[k, index] = (rationalTSplineSecondDerivativesKsiHeta[k, index] / sumKsiHeta -
rationalTSplineDerivativesKsi[k, index] * sumKsidHeta /
Math.Pow(sumKsiHeta, 2) -
rationalTSplineDerivativesHeta[k, index] * sumdKsiHeta /
Math.Pow(sumKsiHeta, 2) -
rationalTSplines[k, index] * sumdKsidHeta /
Math.Pow(sumKsiHeta, 2) +
2 * rationalTSplines[k, index] * sumdKsiHeta * sumKsidHeta /
Math.Pow(sumKsiHeta, 3)) *
controlPoints[k].WeightFactor;
}
}
}
}
/// <summary>
/// Two-dimensional T-spline shape functions from Bezier extraction for <see cref="TSplineKirchhoffLoveShellElement"/>.
/// </summary>
/// <param name="element">An <see cref="Element"/> of type <see cref="TSplineKirchhoffLoveShellElement"/>.</param>
/// <param name="controlPoints">A <see cref="List{T}"/> containing the control points of the element.</param>
/// <param name="parametricGaussPointKsi">An <see cref="IVector"/> containing Gauss points of axis Ksi.</param>
/// <param name="parametricGaussPointHeta">An <see cref="IVector"/> containing Gauss points of axis Heta.</param>
public ShapeTSplines2DFromBezierExtraction(TSplineKirchhoffLoveShellElement element, ControlPoint[] controlPoints, Vector parametricGaussPointKsi, Vector parametricGaussPointHeta)
{
Vector knotValueVectorKsi = Vector.CreateZero((element.DegreeKsi + 1) * 2);
Vector knotValueVectorHeta = Vector.CreateZero((element.DegreeHeta + 1) * 2);
for (int i = 0; i < element.DegreeKsi + 1; i++)
{
knotValueVectorKsi[i] = -1;
knotValueVectorKsi[element.DegreeKsi + 1 + i] = 1;
}
for (int i = 0; i < element.DegreeHeta + 1; i++)
{
knotValueVectorHeta[i] = -1;
knotValueVectorHeta[element.DegreeHeta + 1 + i] = 1;
}
BSPLines1D bernsteinKsi = new BSPLines1D(element.DegreeKsi, knotValueVectorKsi, parametricGaussPointKsi);
BSPLines1D bernsteinHeta = new BSPLines1D(element.DegreeHeta, knotValueVectorHeta, parametricGaussPointHeta);
bernsteinKsi.calculateBSPLinesAndDerivatives();
bernsteinHeta.calculateBSPLinesAndDerivatives();
int supportElementKsi = element.DegreeKsi + 1;
int supportElementHeta = element.DegreeHeta + 1;
int supportKsi = parametricGaussPointKsi.Length;
int supportHeta = parametricGaussPointHeta.Length;
var bKsi = MatrixPart(supportElementKsi, supportKsi, bernsteinKsi.BSPLineValues);
var bdKsi = MatrixPart(supportElementKsi, supportKsi, bernsteinKsi.BSPLineDerivativeValues);
var bddKsi = MatrixPart(supportElementKsi, supportKsi, bernsteinKsi.BSPLineSecondDerivativeValues);
var bheta = MatrixPart(supportElementHeta, supportHeta, bernsteinHeta.BSPLineValues);
var bdheta = MatrixPart(supportElementHeta, supportHeta, bernsteinHeta.BSPLineDerivativeValues);
var bddheta = MatrixPart(supportElementHeta, supportHeta, bernsteinHeta.BSPLineSecondDerivativeValues);
var bernsteinShapeFunctions = KroneckerProduct(bKsi, bheta);
Matrix bernsteinShapeFunctionDerivativesKsi = KroneckerProduct(bheta, bdKsi);
Matrix bernsteinShapeFunctionDerivativesHeta = KroneckerProduct(bdheta, bKsi);
Matrix bernsteinShapeFunctionSecondDerivativesKsi = KroneckerProduct(bheta, bddKsi);
Matrix bernsteinShapeFunctionSecondDerivativesHeta = KroneckerProduct(bddheta, bKsi);
Matrix bernsteinShapeFunctionSecondDerivativesKsiHeta = KroneckerProduct(bdheta, bdKsi);
Matrix rationalTSplines = element.ExtractionOperator * bernsteinShapeFunctions;
Matrix rationalTSplineDerivativesKsi = element.ExtractionOperator * bernsteinShapeFunctionDerivativesKsi;
Matrix rationalTSplineDerivativesHeta = element.ExtractionOperator * bernsteinShapeFunctionDerivativesHeta;
Matrix rationalTSplineSecondDerivativesKsi = element.ExtractionOperator * bernsteinShapeFunctionSecondDerivativesKsi;
Matrix rationalTSplineSecondDerivativesHeta = element.ExtractionOperator * bernsteinShapeFunctionSecondDerivativesHeta;
Matrix rationalTSplineSecondDerivativesKsiHeta = element.ExtractionOperator * bernsteinShapeFunctionSecondDerivativesKsiHeta;
TSplineValues = Matrix.CreateZero(controlPoints.Length, supportKsi * supportHeta);
TSplineDerivativeValuesKsi = Matrix.CreateZero(controlPoints.Length, supportKsi * supportHeta);
TSplineDerivativeValuesHeta = Matrix.CreateZero(controlPoints.Length, supportKsi * supportHeta);
TSplineSecondDerivativesValueKsi = Matrix.CreateZero(controlPoints.Length, supportKsi * supportHeta);
TSplineSecondDerivativesValueHeta = Matrix.CreateZero(controlPoints.Length, supportKsi * supportHeta);
TSplineSecondDerivativesValueKsiHeta = Matrix.CreateZero(controlPoints.Length, supportKsi * supportHeta);
for (int i = 0; i < supportKsi; i++)
{
for (int j = 0; j < supportHeta; j++)
{
double sumKsiHeta = 0;
double sumdKsiHeta = 0;
double sumKsidHeta = 0;
double sumdKsidKsi = 0;
double sumdHetadHeta = 0;
double sumdKsidHeta = 0;
var index = i * supportHeta + j;
for (int k = 0; k < controlPoints.Length; k++)
{
sumKsiHeta += rationalTSplines[k, index] * controlPoints[k].WeightFactor;
sumdKsiHeta += rationalTSplineDerivativesKsi[k, index] * controlPoints[k].WeightFactor;
sumKsidHeta += rationalTSplineDerivativesHeta[k, index] * controlPoints[k].WeightFactor;
sumdKsidKsi += rationalTSplineSecondDerivativesKsi[k, index] * controlPoints[k].WeightFactor;
sumdHetadHeta += rationalTSplineSecondDerivativesHeta[k, index] * controlPoints[k].WeightFactor;
sumdKsidHeta += rationalTSplineSecondDerivativesKsiHeta[k, index] * controlPoints[k].WeightFactor;
}
for (int k = 0; k < controlPoints.Length; k++)
{
TSplineValues[k, index] = rationalTSplines[k, index] * controlPoints[k].WeightFactor / sumKsiHeta;
TSplineDerivativeValuesKsi[k, index] = (rationalTSplineDerivativesKsi[k, index] * sumKsiHeta -
rationalTSplines[k, index] * sumdKsiHeta) /
Math.Pow(sumKsiHeta, 2) * controlPoints[k].WeightFactor;
TSplineDerivativeValuesHeta[k, index] = (rationalTSplineDerivativesHeta[k, index] * sumKsiHeta -
rationalTSplines[k, index] * sumKsidHeta) /
Math.Pow(sumKsiHeta, 2) * controlPoints[k].WeightFactor;
TSplineSecondDerivativesValueKsi[k, index] = (rationalTSplineSecondDerivativesKsi[k, index] / sumKsiHeta -
2 * rationalTSplineDerivativesKsi[k, index] * sumdKsiHeta /
Math.Pow(sumKsiHeta, 2) -
rationalTSplines[k, index] * sumdKsidKsi / Math.Pow(sumKsiHeta, 2) +
2 * rationalTSplines[k, index] * Math.Pow(sumdKsiHeta, 2) /
Math.Pow(sumKsiHeta, 3)) * controlPoints[k].WeightFactor;
TSplineSecondDerivativesValueHeta[k, index] = (rationalTSplineSecondDerivativesHeta[k, index] / sumKsiHeta -
2 * rationalTSplineDerivativesHeta[k, index] * sumKsidHeta /
Math.Pow(sumKsiHeta, 2) -
rationalTSplines[k, index] * sumdHetadHeta /
Math.Pow(sumKsiHeta, 2) +
2 * rationalTSplines[k, index] * Math.Pow(sumKsidHeta, 2) /
Math.Pow(sumKsiHeta, 3)) * controlPoints[k].WeightFactor;
TSplineSecondDerivativesValueKsiHeta[k, index] = (rationalTSplineSecondDerivativesKsiHeta[k, index] / sumKsiHeta -
rationalTSplineDerivativesKsi[k, index] * sumKsidHeta /
Math.Pow(sumKsiHeta, 2) -
rationalTSplineDerivativesHeta[k, index] * sumdKsiHeta /
Math.Pow(sumKsiHeta, 2) -
rationalTSplines[k, index] * sumdKsidHeta /
Math.Pow(sumKsiHeta, 2) +
2 * rationalTSplines[k, index] * sumdKsiHeta * sumKsidHeta /
Math.Pow(sumKsiHeta, 3)) *
controlPoints[k].WeightFactor;
}
}
}
}
