public StrainTensor GetBendingInternalStrain(double localX, double localY, LoadCombination cmb)
{
//step 1 : get transformation matrix
//step 2 : convert globals points to locals
//step 3 : convert global displacements to locals
//step 4 : calculate B matrix
//step 5 : e=B*U
//Note : Steps changed...
var trans = this.GetTransformationMatrix();
var lp = GetLocalPoints();
var g2l = new Func <Vector, Vector>(glob => (trans.Transpose() * glob.ToMatrix()).ToVector());
//var l2g = new Func<Vector, Vector>(local => (trans*local.ToMatrix()).ToPoint());
var d1g = this.nodes[0].GetNodalDisplacement(cmb);
var d2g = this.nodes[1].GetNodalDisplacement(cmb);
var d3g = this.nodes[2].GetNodalDisplacement(cmb);
//step 3
var d1l = new Displacement(g2l(d1g.Displacements), g2l(d1g.Rotations));
var d2l = new Displacement(g2l(d2g.Displacements), g2l(d2g.Rotations));
var d3l = new Displacement(g2l(d3g.Displacements), g2l(d3g.Rotations));
var uDkt =
new Matrix(new[]
{ d1l.DZ, d1l.RX, d1l.RY, /**/ d2l.DZ, d2l.RX, d2l.RY, /**/ d3l.DZ, d3l.RX, d3l.RY });
var b = DktElement.GetBMatrix(localX, localY,
lp.Select(i => i.X).ToArray(),
lp.Select(i => i.Y).ToArray());
var mDkt = b * uDkt;
var buf = new StrainTensor();
buf.S11 = mDkt[0, 0];
buf.S22 = mDkt[1, 0];
buf.S12 = mDkt[2, 0];
return(buf);
}
private MembraneStressTensor GetMembraneInternalForce(LoadCombination combination)
{
//Note: membrane internal force is constant
//step 1 : get transformation matrix
//step 2 : convert globals points to locals
//step 3 : convert global displacements to locals
//step 4 : calculate B matrix and D matrix
//step 5 : M=D*B*U
//Note : Steps changed...
var trans = this.GetTransformationMatrix();
var lp = GetLocalPoints();
var g2l = new Func <Vector, Vector>(glob => (trans.Transpose() * glob.ToMatrix()).ToVector());
//var l2g = new Func<Vector, Vector>(local => (trans*local.ToMatrix()).ToPoint());
var d1g = this.nodes[0].GetNodalDisplacement(combination);
var d2g = this.nodes[1].GetNodalDisplacement(combination);
var d3g = this.nodes[2].GetNodalDisplacement(combination);
//step 3
var d1l = new Displacement(g2l(d1g.Displacements), g2l(d1g.Rotations));
var d2l = new Displacement(g2l(d2g.Displacements), g2l(d2g.Rotations));
var d3l = new Displacement(g2l(d3g.Displacements), g2l(d3g.Rotations));
var uCst =
new Matrix(new[]
{ d1l.DX, d1l.DY, d2l.DX, d2l.DY, /**/ d3l.DX, d3l.DY });
var dbCst = CstElement.GetDMatrix(_elasticModulus, _poissonRatio, _formulationType);
var bCst = CstElement.GetBMatrix(lp.Select(i => i.X).ToArray(),
lp.Select(i => i.Y).ToArray());
var sCst = dbCst * bCst * uCst;
var buf = new MembraneStressTensor();
buf.Sx = sCst[0, 0];
buf.Sy = sCst[1, 0];
buf.Txy = sCst[2, 0];
return(buf);
}
private PlateBendingStressTensor GetBendingInternalForce(double localX, double localY, LoadCombination cmb)
{
//step 1 : get transformation matrix
//step 2 : convert globals points to locals
//step 3 : convert global displacements to locals
//step 4 : calculate B matrix and D matrix
//step 5 : M=D*B*U
//Note : Steps changed...
var trans = this.GetTransformationMatrix();
var lp = GetLocalPoints();
var g2l = new Func <Vector, Vector>(glob => (trans.Transpose() * glob.ToMatrix()).ToVector());
//var l2g = new Func<Vector, Vector>(local => (trans*local.ToMatrix()).ToPoint());
var d1g = this.nodes[0].GetNodalDisplacement(cmb);
var d2g = this.nodes[1].GetNodalDisplacement(cmb);
var d3g = this.nodes[2].GetNodalDisplacement(cmb);
//step 3
var d1l = new Displacement(g2l(d1g.Displacements), g2l(d1g.Rotations));
var d2l = new Displacement(g2l(d2g.Displacements), g2l(d2g.Rotations));
var d3l = new Displacement(g2l(d3g.Displacements), g2l(d3g.Rotations));
var uDkt =
new Matrix(new[]
{ d1l.DZ, d1l.RX, d1l.RY, /**/ d2l.DZ, d2l.RX, d2l.RY, /**/ d3l.DZ, d3l.RX, d3l.RY });
var dbDkt = DktElement.GetDMatrix(this._thickness, this._elasticModulus, this._poissonRatio);
var b = DktElement.GetBMatrix(localX, localY,
lp.Select(i => i.X).ToArray(),
lp.Select(i => i.Y).ToArray());
var mDkt = dbDkt * b * uDkt; //eq. 32, batoz article
var buf = new PlateBendingStressTensor();
buf.Mx = mDkt[0, 0];
buf.My = mDkt[1, 0];
buf.Mxy = mDkt[2, 0];
return(buf);
}