/// <inheritdoc />
public override Matrix GetGlobalStifnessMatrix()
{
int[] newOrder;
UpdateGeoMatrix();
var E = GetConstitutive();
var b = GetB(out newOrder);
var V = Math.Abs(det) / 6;
var buf = b.Transpose() * E * b;
buf.MultiplyByConstant(V);
var currentOrder = new Elo[12];
for (var i = 0; i < 4; i++)
{
currentOrder[3 * i + 0] = new Elo(newOrder[i], DoF.Dx);
currentOrder[3 * i + 1] = new Elo(newOrder[i], DoF.Dy);
currentOrder[3 * i + 2] = new Elo(newOrder[i], DoF.Dz);
}
var bufEx = ElementPermuteHelper.FullyExpand(buf, currentOrder, 4);
return(bufEx);
}
public override Matrix GetGlobalStifnessMatrix()
{
if (nodes[0].Location.Equals(nodes[1].Location))
{
var kl = new Matrix(6, 6);
kl[0, 0] = kl[1, 1] = kl[2, 2] = kl[3, 3] =
kl[4, 4] = kl[5, 5] = _k;
kl[1, 0] = kl[0, 1] =
kl[2, 3] = kl[3, 2] =
kl[4, 5] = kl[5, 4] = -_k;
var currentOrder = new ElementPermuteHelper.ElementLocalDof[]
{
new ElementPermuteHelper.ElementLocalDof(0, DoF.Dx),
new ElementPermuteHelper.ElementLocalDof(1, DoF.Dx),
new ElementPermuteHelper.ElementLocalDof(0, DoF.Dy),
new ElementPermuteHelper.ElementLocalDof(1, DoF.Dy),
new ElementPermuteHelper.ElementLocalDof(0, DoF.Dz),
new ElementPermuteHelper.ElementLocalDof(1, DoF.Dz),
};
var kle = ElementPermuteHelper.FullyExpand(kl, currentOrder, 2);
return(kle);
}
else
{
var kl = new Matrix(12, 12);//.FromRowColCoreArray(12, 12, baseArr);
kl[0, 0] = kl[6, 6] = _k;
kl[6, 0] = kl[0, 6] = -_k;
var t = CalcUtil.Get2NodeElementTransformationMatrix(EndNode.Location - StartNode.Location);
return(t.Transpose() * kl * t);
}
throw new NotImplementedException();
}
/// <inheritdoc />
public override Matrix GetGlobalStifnessMatrix()
{
//step 1 : get points in local system
//step 2 : get local stiffness matrix
//step 3 : expand local stiffness matrix
//step 4 : get global stiffness matrix
//step 1
var ls = GetLocalPoints();
var xs = new double[] { ls[0].X, ls[1].X, ls[2].X };
var ys = new double[] { ls[0].Y, ls[1].Y, ls[2].Y };
//step 2
var kl = DktElement.GetStiffnessMatrix(xs, ys, this._thickness, this.ElasticModulus, this.PoissonRatio);
//step 3
var currentOrder = new ElementPermuteHelper.ElementLocalDof[]
{
new ElementPermuteHelper.ElementLocalDof(0, DoF.Dz),
new ElementPermuteHelper.ElementLocalDof(0, DoF.Rx),
new ElementPermuteHelper.ElementLocalDof(0, DoF.Ry),
new ElementPermuteHelper.ElementLocalDof(1, DoF.Dz),
new ElementPermuteHelper.ElementLocalDof(1, DoF.Rx),
new ElementPermuteHelper.ElementLocalDof(1, DoF.Ry),
new ElementPermuteHelper.ElementLocalDof(2, DoF.Dz),
new ElementPermuteHelper.ElementLocalDof(2, DoF.Rx),
new ElementPermuteHelper.ElementLocalDof(2, DoF.Ry),
};
var kle = ElementPermuteHelper.FullyExpand(kl, currentOrder, 3);
var lambda = GetTransformationMatrix();
var t = Matrix.DiagonallyRepeat(lambda.Transpose(), 6); // eq. 5-16 page 78 (87 of file)
//step 4 : get global stiffness matrix
var buf = t.Transpose() * kle * t; //eq. 5-15 p77
return(buf);
}
public Matrix GetLocalPlateBendingStiffnessMatrix()
{
//dkt
//step 1 : get points in local system
//step 2 : get local stiffness matrix
//step 3 : expand local stiffness matrix
//step 4 : get global stiffness matrix
//step 1
var ls = GetLocalPoints();
var xs = new double[] { ls[0].X, ls[1].X, ls[2].X };
var ys = new double[] { ls[0].Y, ls[1].Y, ls[2].Y };
//step 2
var kl = DktElement.GetStiffnessMatrix(xs, ys, this._thickness, this.ElasticModulus, this.PoissonRatio);
//step 3
var currentOrder = new ElementPermuteHelper.ElementLocalDof[]
{
new ElementPermuteHelper.ElementLocalDof(0, DoF.Dz),
new ElementPermuteHelper.ElementLocalDof(0, DoF.Rx),
new ElementPermuteHelper.ElementLocalDof(0, DoF.Ry),
new ElementPermuteHelper.ElementLocalDof(1, DoF.Dz),
new ElementPermuteHelper.ElementLocalDof(1, DoF.Rx),
new ElementPermuteHelper.ElementLocalDof(1, DoF.Ry),
new ElementPermuteHelper.ElementLocalDof(2, DoF.Dz),
new ElementPermuteHelper.ElementLocalDof(2, DoF.Rx),
new ElementPermuteHelper.ElementLocalDof(2, DoF.Ry),
};
var kle = ElementPermuteHelper.FullyExpand(kl, currentOrder, 3);
return(kle);
}
private Matrix GetLocalMembraneStiffnessMatrix()
{
//cst
//step 1 : get points in local system
//step 2 : get local stiffness matrix
//step 3 : expand local stiffness matrix
//step 4 : get global stiffness matrix
//step 1
var ls = GetLocalPoints();
var xs = new[] { ls[0].X, ls[1].X, ls[2].X };
var ys = new[] { ls[0].Y, ls[1].Y, ls[2].Y };
//step 2
var kl = CstElement.GetStiffnessMatrix(xs, ys, this._thickness, this.ElasticModulus, this.PoissonRatio,
this._formulationType);
//step 3
var currentOrder = new[]
{
new ElementPermuteHelper.ElementLocalDof(0, DoF.Dx),
new ElementPermuteHelper.ElementLocalDof(0, DoF.Dy),
new ElementPermuteHelper.ElementLocalDof(1, DoF.Dx),
new ElementPermuteHelper.ElementLocalDof(1, DoF.Dy),
new ElementPermuteHelper.ElementLocalDof(2, DoF.Dx),
new ElementPermuteHelper.ElementLocalDof(2, DoF.Dy),
};
var kle = ElementPermuteHelper.FullyExpand(kl, currentOrder, 3);
return(kle);
}
public Matrix GetGlobalStifnessMatrix_old()
{
//Code ported from D3_TETRAH.m from fem_toolbox
UpdateGeoMatrix();
var J = new Matrix(4, 4);
for (var i = 0; i < 4; i++)
{
J[0, i] = 1;
J[1, i] = nodes[i].Location.X;
J[2, i] = nodes[i].Location.Y;
J[3, i] = nodes[i].Location.Z;
}
var detJ = J.Determinant();
var V = detJ / 6;
var Q = detJ * J.Inverse();
double a1 = a[0]; double b1 = b[0]; double c1 = c[0]; double d1 = d[0];
double a2 = a[1]; double b2 = b[1]; double c2 = c[1]; double d2 = d[1];
double a3 = a[2]; double b3 = b[2]; double c3 = c[2]; double d3 = d[2];
double a4 = a[3]; double b4 = b[3]; double c4 = c[3]; double d4 = d[3];
var B = new Matrix(6, 12);//transpose of b
B.FillMatrixRowise(
b1, 0, 0, b2, 0, 0, b3, 0, 0, b4, 0, 0,
0, c1, 0, 0, c2, 0, 0, c3, 0, 0, c4, 0,
0, 0, d1, 0, 0, d2, 0, 0, d3, 0, 0, d4,
c1, b1, 0, c2, b2, 0, c3, b3, 0, c4, b4, 0,
0, d1, c1, 0, d2, c2, 0, d3, c3, 0, d4, c4,
d1, 0, b1, d2, 0, b2, d3, 0, b3, d4, 0, b4);
B.MultiplyByConstant(1 / (2 * V));
var miu = this.Nu;
var s = (1 - miu);
var E = new Matrix(6, 6);
E.FillMatrixRowise(1, miu / s, miu / s, 0, 0, 0, miu / s, 1, miu / s, 0, 0, 0, miu / s, miu / s, 1, 0, 0, 0, 0, 0, 0,
(1 - 2 * miu) / (2 * s), 0, 0, 0, 0, 0, 0, (1 - 2 * miu) / (2 * s), 0, 0, 0, 0, 0, 0, (1 - 2 * miu) / (2 * s));
E.MultiplyByConstant(this.E * (1 - miu) / ((1 + miu) * (1 - 2 * miu)));
var buf = B.Transpose() * E * B;
buf.MultiplyByConstant(V);
var currentOrder = new Elo[12];
for (var i = 0; i < 4; i++)
{
currentOrder[3 * i + 0] = new Elo(i, DoF.Dx);
currentOrder[3 * i + 1] = new Elo(i, DoF.Dy);
currentOrder[3 * i + 2] = new Elo(i, DoF.Dz);
}
var bufEx = ElementPermuteHelper.FullyExpand(buf, currentOrder, 4);
var tmp2 = GetGlobalStifnessMatrix_old();
return(tmp2);
}