private IList <Vector> FEAnalysisCantilever2LoadCases(Matrix x)
{
int numLoadCases = 2;
int numAllDofs = 2 * (nelx + 1) * (nely + 1);
var K = DokSymmetric.CreateEmpty(numAllDofs);
var F = new Vector[] { Vector.CreateZero(numAllDofs), Vector.CreateZero(numAllDofs) };
var U = new Vector[] { Vector.CreateZero(numAllDofs), Vector.CreateZero(numAllDofs) };
Matrix Ke = ElementStiffness();
int numElementDofs = Ke.NumRows;
int[] elementDofsLocal = Enumerable.Range(0, numElementDofs).ToArray();
// Global stiffness matrix assembly
for (int ely = 1; ely <= nely; ++ely)
{
for (int elx = 1; elx <= nelx; ++elx)
{
int[] elementDofsGlobal = GetElementDofs(elx, ely);
double density = Math.Pow(x[ely - 1, elx - 1], penal);
K.AddSubmatrixSymmetric(density * Ke, elementDofsLocal, elementDofsGlobal);
}
}
// Define supports for cantilever beam
IEnumerable <int> fixedDofs = Enumerable.Range(0, 2 * (nely + 1));
int[] freeDofs = Enumerable.Range(0, numAllDofs).Except(fixedDofs).ToArray();
// Load case 1: unit load towards -y at bottom right corner
F[0][2 * (nelx + 1) * (nely + 1) - 1] = -1.0;
// Load case 2: unit load towards +y at top right corner
F[1][2 * (nelx) * (nely + 1) + 1] = 1.0;
// Solve linear system
CholeskyCSparseNet factorizedKf = CholeskyCSparseNet.Factorize(
K.GetSubmatrix(freeDofs).BuildSymmetricCscMatrix(true)); // only factorize the matrix once
for (int c = 0; c < numLoadCases; ++c)
{
Vector Ff = F[c].GetSubvector(freeDofs);
Vector Uf = factorizedKf.SolveLinearSystem(Ff);
for (int i = 0; i < freeDofs.Length; ++i)
{
U[c][freeDofs[i]] = Uf[i];
}
//U[c].CopyNonContiguouslyFrom(freeDofs, Uf, Enumerable.Range(0, freeDofs.Length).ToArray()); // alternative way, but probably slower.
//foreach (int i in fixedDofs) U[c][i] = 0.0; // They are 0 by default
}
return(U);
}
private static void TestSystemSolution()
{
int order = SparsePosDef10by10.Order;
var skyline = SkylineMatrix.CreateFromArrays(order, SparsePosDef10by10.SkylineValues,
SparsePosDef10by10.SkylineDiagOffsets, true, true);
var dok = DokSymmetric.CreateFromSparseMatrix(skyline);
var b = Vector.CreateFromArray(SparsePosDef10by10.Rhs);
var xExpected = Vector.CreateFromArray(SparsePosDef10by10.Lhs);
(double[] cscValues, int[] cscRowIndices, int[] cscColOffsets) = dok.BuildSymmetricCscArrays(true);
var factor = CholeskyCSparseNet.Factorize(order, cscValues.Length, cscValues, cscRowIndices, cscColOffsets);
Vector xComputed = factor.SolveLinearSystem(b);
comparer.AssertEqual(xExpected, xComputed);
}
private IList <Vector> FEAnalysisHalfMbbBeam(Matrix x)
{
int numAllDofs = 2 * (nelx + 1) * (nely + 1);
var K = DokSymmetric.CreateEmpty(numAllDofs);
var F = Vector.CreateZero(numAllDofs);
var U = Vector.CreateZero(numAllDofs);
Matrix Ke = ElementStiffness();
int numElementDofs = Ke.NumRows;
int[] elementDofsLocal = Enumerable.Range(0, numElementDofs).ToArray();
// Global stiffness matrix assembly
for (int ely = 1; ely <= nely; ++ely)
{
for (int elx = 1; elx <= nelx; ++elx)
{
int[] elementDofsGlobal = GetElementDofs(elx, ely);
double density = Math.Pow(x[ely - 1, elx - 1], penal);
K.AddSubmatrixSymmetric(density * Ke, elementDofsLocal, elementDofsGlobal);
}
}
// Define loads and supports for half MBB beam
F[1] = -1.0;
var fixedDofs = new HashSet <int>(); //TODO: Use LINQ to simplify this
for (int i = 0; i < 2 * (nely + 1); i += 2)
{
fixedDofs.Add(i);
}
fixedDofs.Add(numAllDofs - 1);
int[] freeDofs = Enumerable.Range(0, numAllDofs).Except(fixedDofs).ToArray();
// Solve linear system
DokSymmetric Kf = K.GetSubmatrix(freeDofs);
Vector Ff = F.GetSubvector(freeDofs);
Vector Uf = CholeskyCSparseNet.Factorize(Kf.BuildSymmetricCscMatrix(true)).SolveLinearSystem(Ff);
for (int i = 0; i < freeDofs.Length; ++i)
{
U[freeDofs[i]] = Uf[i];
}
//U.CopyNonContiguouslyFrom(freeDofs, Uf, Enumerable.Range(0, freeDofs.Length).ToArray()); // alternative way, but probably slower.
//foreach (int i in fixedDofs) U[i] = 0.0; // They are 0 by default
return(new Vector[] { U });
}
public void UpdateModelAndAnalyze(IVectorView youngModuli)
{
this.youngModuli = youngModuli;
// Global stiffness matrix assembly
int numAllDofs = 2 * (numElementsX + 1) * (numElementsY + 1);
var K = DokSymmetric.CreateEmpty(numAllDofs);
for (int e = 0; e < NumElements; ++e)
{
int[] elementDofsGlobal = GetElementDofs(e);
K.AddSubmatrixSymmetric(unitStiffness.Scale(youngModuli[e]), elementDofsLocal, elementDofsGlobal);
}
// Apply boundary conditions
(int[] freeDofs, Vector[] Fs) = ApplyBoundaryConditions();
int numLoadCases = Fs.Length;
globalDisplacements = new Vector[numLoadCases];
// Solve linear system
DokSymmetric Kf = K.GetSubmatrix(freeDofs);
var factor = CholeskyCSparseNet.Factorize(Kf.BuildSymmetricCscMatrix(true));
for (int c = 0; c < numLoadCases; ++c)
{
Vector Ff = Fs[c].GetSubvector(freeDofs);
Vector Uf = factor.SolveLinearSystem(Ff);
var U = Vector.CreateZero(numAllDofs);
for (int i = 0; i < freeDofs.Length; ++i)
{
U[freeDofs[i]] = Uf[i];
}
globalDisplacements[c] = U;
//U.CopyNonContiguouslyFrom(freeDofs, Uf, Enumerable.Range(0, freeDofs.Length).ToArray()); // alternative way, but probably slower.
}
}
