public static GaussianIntegrator CreateFor1DProblem(Func <double, Matrix> function, double x0, double x1,
int sampling)
{
var buf = new GaussianIntegrator();
buf.A1 = x0;
buf.A2 = x1;
buf.F1 = gama => 0;
buf.F2 = gama => 1;
buf.G1 = (eta, gama) => 0;
buf.G2 = (eta, gama) => 1;
buf.GammaPointCount = sampling;
buf.XiPointCount = buf.EtaPointCount = 1;
buf.H = new FunctionMatrixFunction((xi, eta, gama) => function(gama));
return(buf);
}
/// <inheritdoc/>
public Matrix CalcLocalStiffnessMatrix(Element targetElement)
{
var intg = new BriefFiniteElementNet.Integration.GaussianIntegrator();
var tri = targetElement as TriangleElement;
intg.A2 = 1;
intg.A1 = 0;
intg.F2 = (gama => 1);
intg.F1 = (gama => 0);
intg.G2 = ((eta, gama) => 1 - eta);
intg.G1 = ((eta, gama) => 0);
intg.XiPointCount = intg.EtaPointCount = 3;
intg.GammaPointCount = 1;
intg.H = new FunctionMatrixFunction((xi, eta, gamma) =>
{
var b = GetBMatrixAt(targetElement, xi, eta);
var d = this.GetDMatrixAt(targetElement, xi, eta);
var j = GetJMatrixAt(targetElement, xi, eta);
var detJ = j.Determinant();
var ki = b.Transpose() * d * b;
ki.Scale(Math.Abs(j.Determinant()));
//eq 3.27: thickness* bT * d * b;
ki.Scale(tri.Section.GetThicknessAt(new double[] { xi, eta }));
return(ki);
});
var res = intg.Integrate();
return(res);
}
public Matrix CalcLocalStiffnessMatrix(Element targetElement)
{
var intg = new BriefFiniteElementNet.Integration.GaussianIntegrator(); // using eq. 3.50 [1] / eq 8 [3]
var quad = targetElement as QuadrilaturalElement;
intg.A2 = 1.0;
intg.A1 = 0.0;
intg.F2 = (gama => + 1.0);
intg.F1 = (gama => - 1.0);
intg.G2 = (eta, gama) => + 1.0;
intg.G1 = (eta, gama) => - 1.0;
intg.XiPointCount = intg.EtaPointCount = 3; // ref [2]
intg.GammaPointCount = 1;
intg.H = new FunctionMatrixFunction((xi, eta, gamma) =>
{
var b = GetBMatrixAt(targetElement, xi, eta);
var d = this.GetDMatrixAt(targetElement, xi, eta);
var j = GetJMatrixAt(targetElement, xi, eta);
var detJ = j.Determinant();
var ki = b.Transpose() * d * b;
ki.Scale(Math.Abs(j.Determinant()));
ki.Scale(quad.Section.GetThicknessAt(new double[] { xi, eta }));
return(ki);
});
var res = intg.Integrate();
return(res);
}
/// <inheritdoc/>
public Matrix CalcLocalStiffnessMatrix(Element targetElement)
{
var intg = new BriefFiniteElementNet.Integration.GaussianIntegrator();
intg.A2 = 1;
intg.A1 = 0;
intg.F2 = (gama => 1);
intg.F1 = (gama => 0);
intg.G2 = ((eta, gama) => 1 - eta);
intg.G1 = ((eta, gama) => 0);
intg.XiPointCount = intg.EtaPointCount = 3;
intg.GammaPointCount = 1;
intg.H = new FunctionMatrixFunction((xi, eta, gamma) =>
{
var b = GetBMatrixAt(targetElement, xi, eta);
var d = this.GetDMatrixAt(targetElement, xi, eta);
var j = GetJMatrixAt(targetElement, xi, eta);
var detJ = j.Determinant();
var ki = b.Transpose() * d * b;
ki.MultiplyByConstant(Math.Abs(j.Determinant()));
return(ki);
});
var res = intg.Integrate();
return(res);
}
