public IMatrix2D <double> MassMatrix(Element element)
{
double x2 = Math.Pow(element.Nodes[1].X - element.Nodes[0].X, 2);
double y2 = Math.Pow(element.Nodes[1].Y - element.Nodes[0].Y, 2);
double z2 = Math.Pow(element.Nodes[1].Z - element.Nodes[0].Z, 2);
double L = 1d / Math.Sqrt(x2 + y2 + z2);
//double halfMass = 0.5 * Density * SectionArea * L;
//var massMatrix = new SymmetricMatrix2D<double>(new double[] { halfMass, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
// halfMass, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
// halfMass, 0, 0, 0, 0, 0, 0, 0, 0, 0,
// halfMass, 0, 0, 0, 0, 0, 0, 0, 0,
// halfMass, 0, 0, 0, 0, 0, 0, 0,
// halfMass, 0, 0, 0, 0, 0, 0,
// halfMass, 0, 0, 0, 0, 0,
// halfMass, 0, 0, 0, 0,
// halfMass, 0, 0, 0,
// halfMass, 0, 0,
// halfMass, 0,
// halfMass
//});
double halfMass = Density * SectionArea / L / 6d;
var massMatrix = new SymmetricMatrix2D <double>(new double[] { halfMass, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
halfMass, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
halfMass, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0,
halfMass, 0, 0, 0, 0, 0,
halfMass, 0, 0, 0, 0,
halfMass, 0, 0, 0,
0, 0, 0,
0, 0,
0 });
var refx = new double[] { 1, 1, 1 };
var beamTransformation = new Matrix2D <double>(12, 12);
beamTransformation[0, 0] = (element.Nodes[1].X - element.Nodes[0].X) * L;
beamTransformation[0, 1] = (element.Nodes[1].Y - element.Nodes[0].Y) * L;
beamTransformation[0, 2] = (element.Nodes[1].Z - element.Nodes[0].Z) * L;
beamTransformation[1, 0] = refx[1] * beamTransformation[0, 2] - refx[2] * beamTransformation[0, 1];
beamTransformation[1, 1] = refx[2] * beamTransformation[0, 0] - refx[0] * beamTransformation[0, 2];
beamTransformation[1, 2] = refx[0] * beamTransformation[0, 1] - refx[1] * beamTransformation[0, 0];
double dn = 1.0 / Math.Sqrt(beamTransformation[1, 0] * beamTransformation[1, 0] + beamTransformation[1, 1] * beamTransformation[1, 1] + beamTransformation[1, 2] * beamTransformation[1, 2]);
beamTransformation[1, 0] = beamTransformation[1, 0] * dn;
beamTransformation[1, 1] = beamTransformation[1, 1] * dn;
beamTransformation[1, 2] = beamTransformation[1, 2] * dn;
beamTransformation[2, 0] = beamTransformation[0, 1] * beamTransformation[1, 2] - beamTransformation[0, 2] * beamTransformation[1, 1];
beamTransformation[2, 1] = beamTransformation[0, 2] * beamTransformation[1, 0] - beamTransformation[0, 0] * beamTransformation[1, 2];
beamTransformation[2, 2] = beamTransformation[0, 0] * beamTransformation[1, 1] - beamTransformation[0, 1] * beamTransformation[1, 0];
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
beamTransformation[i + 3, j + 3] = beamTransformation[i, j];
beamTransformation[i + 6, j + 6] = beamTransformation[i, j];
beamTransformation[i + 9, j + 9] = beamTransformation[i, j];
}
}
CalculateRotTranformation(element);
return(dofEnumerator.GetTransformedMatrix(new SymmetricMatrix2D <double>(rotTransformation.Transpose() * beamTransformation.Transpose() * massMatrix.ToMatrix2D() * beamTransformation * rotTransformation)));
}
private IMatrix2D <double> StiffnessMatrixPure(Element element)
{
//var m = (material as IFiniteElementMaterial3D);//TODO remove material
double x2 = Math.Pow(element.Nodes[1].X - element.Nodes[0].X, 2);
double y2 = Math.Pow(element.Nodes[1].Y - element.Nodes[0].Y, 2);
double z2 = Math.Pow(element.Nodes[1].Z - element.Nodes[0].Z, 2);
double L = 1 / Math.Sqrt(x2 + y2 + z2);
double L2 = L * L;
double L3 = L2 * L;
//double EIx = m.YoungModulus * MomentOfInertiaX;
/* deprecated calculations after the removal of the material class as input
* double EIy = m.YoungModulus * MomentOfInertiaY;
* double EIz = m.YoungModulus * MomentOfInertiaZ;
* double GJL = m.YoungModulus * L * MomentOfInertiaPolar / (2 * (1 + m.PoissonRatio));
* double EAL = m.YoungModulus * SectionArea * L;
*/
double EIy = this.youngModulus * MomentOfInertiaY;
double EIz = this.youngModulus * MomentOfInertiaZ;
double GJL = this.youngModulus * L * MomentOfInertiaPolar / (2 * (1 + this.poissonRatio));
double EAL = this.youngModulus * SectionArea * L;
var stiffnessMatrix = new SymmetricMatrix2D <double>(new double[] { EAL, 0, 0, 0, 0, 0, -EAL, 0, 0, 0, 0, 0,
12 * EIz * L3, 0, 0, 0, 6 * EIz * L2, 0, -12 * EIz * L3, 0, 0, 0, 6 * EIz * L2,
12 * EIy * L3, 0, -6 * EIy * L2, 0, 0, 0, -12 * EIy * L3, 0, -6 * EIy * L2, 0,
GJL, 0, 0, 0, 0, 0, -GJL, 0, 0,
4 * EIy * L, 0, 0, 0, 6 * EIy * L2, 0, 2 * EIy * L, 0,
4 * EIz * L, 0, -6 * EIz * L2, 0, 0, 0, 2 * EIz * L,
EAL, 0, 0, 0, 0, 0,
12 * EIz * L3, 0, 0, 0, -6 * EIz * L2,
12 * EIy * L3, 0, 6 * EIy * L2, 0,
GJL, 0, 0,
4 * EIy * L, 0,
4 * EIz * L });
var refx = new double[] { 1, 1, 1 };
var beamTransformation = new Matrix2D <double>(12, 12);
beamTransformation[0, 0] = (element.Nodes[1].X - element.Nodes[0].X) * L;
beamTransformation[0, 1] = (element.Nodes[1].Y - element.Nodes[0].Y) * L;
beamTransformation[0, 2] = (element.Nodes[1].Z - element.Nodes[0].Z) * L;
//beamTransformation[2, 0] = refx[0];
//beamTransformation[2, 1] = refx[1];
//beamTransformation[2, 2] = refx[2];
//beamTransformation[1, 0] = beamTransformation[2, 1] * beamTransformation[0, 2] - beamTransformation[2, 2] * beamTransformation[0, 1];
//beamTransformation[1, 1] = beamTransformation[2, 2] * beamTransformation[0, 0] - beamTransformation[2, 0] * beamTransformation[0, 2];
//beamTransformation[1, 2] = beamTransformation[2, 0] * beamTransformation[0, 1] - beamTransformation[2, 1] * beamTransformation[0, 0];
beamTransformation[1, 0] = refx[1] * beamTransformation[0, 2] - refx[2] * beamTransformation[0, 1];
beamTransformation[1, 1] = refx[2] * beamTransformation[0, 0] - refx[0] * beamTransformation[0, 2];
beamTransformation[1, 2] = refx[0] * beamTransformation[0, 1] - refx[1] * beamTransformation[0, 0];
double dn = 1.0 / Math.Sqrt(beamTransformation[1, 0] * beamTransformation[1, 0] + beamTransformation[1, 1] * beamTransformation[1, 1] + beamTransformation[1, 2] * beamTransformation[1, 2]);
beamTransformation[1, 0] = beamTransformation[1, 0] * dn;
beamTransformation[1, 1] = beamTransformation[1, 1] * dn;
beamTransformation[1, 2] = beamTransformation[1, 2] * dn;
beamTransformation[2, 0] = beamTransformation[0, 1] * beamTransformation[1, 2] - beamTransformation[0, 2] * beamTransformation[1, 1];
beamTransformation[2, 1] = beamTransformation[0, 2] * beamTransformation[1, 0] - beamTransformation[0, 0] * beamTransformation[1, 2];
beamTransformation[2, 2] = beamTransformation[0, 0] * beamTransformation[1, 1] - beamTransformation[0, 1] * beamTransformation[1, 0];
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
beamTransformation[i + 3, j + 3] = beamTransformation[i, j];
beamTransformation[i + 6, j + 6] = beamTransformation[i, j];
beamTransformation[i + 9, j + 9] = beamTransformation[i, j];
}
}
return(new SymmetricMatrix2D <double>(beamTransformation.Transpose() * stiffnessMatrix.ToMatrix2D() * beamTransformation));
////if (element.Nodes.Count(n => n.EmbeddedInElement != null) == 0) return stiffnessMatrix;
//stiffnessMatrix = new SymmetricMatrix2D<double>(beamTransformation.Transpose() * stiffnessMatrix.ToMatrix2D() * beamTransformation);
//if (embeddedNodes.Count == 0) return stiffnessMatrix;
////var hostElements = element.Nodes.Select(x => x.EmbeddedInElement).Distinct();
//var size = GetElementDOFTypes(element).SelectMany(x => x).Count();
//transformation = new Matrix2D<double>(dofs.SelectMany(d => d).Count(), size);
//isNodeEmbedded = new bool[element.Nodes.Count];
////TODO : SEPARATE FROM ELEMENT!!
////TODO: Must match DOFs of host with embedded element
//int row = 0;
//int col = 0;
//hostElementList = new List<Element>();
//for (int i = 0; i < element.Nodes.Count; i++)
//{
// var node = element.Nodes[i];
// var embeddedNode = embeddedNodes.Where(x => x.Node == node).FirstOrDefault();
// //var hostElement = node.EmbeddedInElement;
// Element hostElement = embeddedNode == null ? null : embeddedNode.EmbeddedInElement;
// if (hostElement == null)
// {
// isNodeEmbedded[i] = false;
// for (int j = 0; j < dofs[i].Length; j++)
// {
// transformation[row, col] = 1;
// row++;
// col++;
// }
// }
// else
// {
// isNodeEmbedded[i] = true;
// //double[] hostShapeFunctions = ((IEmbeddedHostElement)hostElement.ElementType).GetShapeFunctionsForNode(hostElement, node);
// double[] hostShapeFunctions = ((IEmbeddedHostElement)hostElement.ElementType).GetShapeFunctionsForNode(hostElement, embeddedNode);
// if (hostElementList.IndexOf(hostElement) < 0)
// hostElementList.Add(hostElement);
// else
// col -= hostShapeFunctions.Length * hostDofsPerNode;
// for (int j = 0; j < commonDofsPerNode; j++)
// {
// for (int k = 0; k < hostShapeFunctions.Length; k++)
// transformation[row, hostDofsPerNode * k + col + j] = hostShapeFunctions[k];
// row++;
// }
// row += embeddedDofsPerNode - commonDofsPerNode;
// col += hostShapeFunctions.Length * hostDofsPerNode;
// }
//}
//// Add identity matrix
//int index = 0;
//if (isNodeEmbedded[0])
//{
// transformation[3, col] = 1;
// transformation[4, col + 1] = 1;
// transformation[5, col + 2] = 1;
// index += 3;
//}
//if (isNodeEmbedded[1])
//{
// transformation[9, col + index] = 1;
// transformation[10, col + index + 1] = 1;
// transformation[11, col + index + 2] = 1;
//}
//var transformedMatrix = new SymmetricMatrix2D<double>(transformation.Transpose() * stiffnessMatrix.ToMatrix2D() * transformation);
////var sw = File.CreateText(@"d:\BeamTransformed.txt");
////for (int i = 0; i < 54; i++)
////{
//// var s = string.Empty;
//// for (int j = 0; j < 54; j++)
//// s += transformedMatrix[i, j].ToString() + ";";
//// sw.WriteLine(s);
////}
////sw.Close();
//return transformedMatrix;
}