// See slides p.44
public void GetLocalNodeCoordinates(out Matrix xel, out Matrix Tg)
{
Vector3D v1 = Nodes[1].Pos - Nodes[0].Pos;
Vector3D _v2 = Nodes[2].Pos - Nodes[0].Pos;
Vector3D v3 = Vector3D.CrossProduct(v1, _v2);
Vector3D v2 = Vector3D.CrossProduct(v3, v1);
if (v1.IsZeroVector() || v2.IsZeroVector() || v3.IsZeroVector())
{
throw new Exception("Bad element, ID: " + this.Id.ToString());
}
Vector3D e1 = v1.Normalize(false);
Vector3D e2 = v2.Normalize(false);
Vector3D e3 = v3.Normalize(false);
Matrix xeg = new Matrix(3, 3);
xeg.SetRow(v1.ToMatrix().Transpose(), 1);
xeg.SetRow(_v2.ToMatrix().Transpose(), 2);
Matrix T = new Matrix(3, 3);
T.SetCol(e1.ToMatrix(), 0);
T.SetCol(e2.ToMatrix(), 1);
T.SetCol(e3.ToMatrix(), 2);
xel = xeg * T;
Tg = new Matrix(18, 18);
int[] pos1 = SF.intSrs(0, 2);
int[] pos2 = SF.intSrs(3, 5);
int[] pos3 = SF.intSrs(6, 8);
int[] pos4 = SF.intSrs(9, 11);
int[] pos5 = SF.intSrs(12, 14);
int[] pos6 = SF.intSrs(15, 17);
Tg[pos1, pos1] = T;
Tg[pos2, pos2] = T;
Tg[pos3, pos3] = T;
Tg[pos4, pos4] = T;
Tg[pos5, pos5] = T;
Tg[pos6, pos6] = T;
}
//Calculate principal tresses for all the elements
public void CalcStresses()
{
//Folllowing plants in MATlab, each element 15 dofs
//the 15 active dofs used in each element (with 18 dofs in total)
int[] activeDofs = new int[] { 0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16 };
PrincipalStresses = new List <Vector3D>();
stresses = new List <Matrix>();
PrincipalAngles = new List <double>();
vonMises = new List <double>();
for (int i = 0; i < elements.Count; i++)
{
//Get all the 18 element dofs from the global
int[] dofsFull = elements[i].GetElementDofs();
//Take the deformations from the element dofs
Matrix aTrans = new Matrix(18, 1);
for (int j = 0; j < dofsFull.Count(); j++)
{
aTrans[j] = a[dofsFull[j]];
}
//Transform the local coordinates to global
aTrans = elements[i].Te.Invert() * aTrans;
//Take the 15 active dofs that should be used from the transformed defrormations
Matrix ed = new Matrix(1, 15);
for (int j = 0; j < activeDofs.Count(); j++)
{
ed[0, j] = aTrans[activeDofs[j]];
}
//Stresses (D*B*a)
// Matrix ss = elements[i].DBe * ed[0, SF.intSrs(0, 14)].Transpose();
// stresses.Add(ss);
double theta = 0;
Vector3D vMax = new Vector3D();
//for every layer
for (int j = 0; j < elements[i].DBe.Count; j++)
{
Matrix ss = new Matrix(6, 1);
ed[3] *= elements[i].zs[j];
ed[4] *= elements[i].zs[j];
ed[8] *= elements[i].zs[j];
ed[9] *= elements[i].zs[j];
ed[13] *= elements[i].zs[j];
ed[14] *= elements[i].zs[j];
ss = elements[i].DBe[j] * ed[0, SF.intSrs(0, 14)].Transpose();
//Make sure there is no errors when this is changed
// theta = 0.5 * Math.Atan(2 * ss[2] / (ss[0] - ss[1]));
// if (ss[0] < ss[1]) theta = theta + Math.PI / 2;
//PrincipalAngles.Add(theta);
//Principle stresses
double p1 = (ss[0] + ss[1]) / 2.0 + Math.Sqrt(Math.Pow((ss[0] - ss[1]) / 2, 2) + Math.Pow(ss[2], 2));
double p2 = (ss[0] + ss[1]) / 2.0 - Math.Sqrt(Math.Pow((ss[0] - ss[1]) / 2, 2) + Math.Pow(ss[2], 2));
Vector3D v = new Vector3D(p1, p2, 0);
if (v.Length > vMax.Length)
{
vMax = v;
theta = 0.5 * Math.Atan(2 * ss[2] / (ss[0] - ss[1]));
if (ss[0] < ss[1])
{
theta = theta + Math.PI / 2;
}
}
}
// PrincipalStresses.Add(new Vector3D(p1, p2, 0));
PrincipalStresses.Add(vMax);
// vonMises.Add(Math.Sqrt(p1 * p1 - p1 * p2 + p2 * p2));
vonMises.Add(Math.Sqrt(vMax.X * vMax.X - vMax.X * vMax.Y + vMax.Y * vMax.Y));
PrincipalAngles.Add(theta);
}
}
