public static ResultFEM Solve(Matrix <double> K, Matrix <double> f, int[] bc, double[] bcVal)
{
// Create dof array:
int ndof = f.RowCount;
// Initialize displacement vector
Matrix u = new DenseMatrix(ndof, 1);
int[] dof = new int[ndof];
for (int i = 0; i < ndof; i++)
{
dof[i] = i;
}
// Create the free dofs:
int[] fdof = dof.Except(bc).ToArray();
int nfdof = fdof.Length; // Number of free dofs.
int nbdof = ndof - nfdof; //Constrained dofs
// Create the permutation array which puts the constrained dofs last:
int[] permute = bc.Union(fdof).ToArray();
Permutation perm = new Permutation(permute);
Permutation invPerm = perm.Inverse();
Matrix <double> KPermuted = DenseMatrix.OfMatrix(K);
KPermuted.PermuteRows(invPerm);
KPermuted.PermuteColumns(invPerm);
// Split K:::
Matrix <double> Kff = KPermuted.SubMatrix(nbdof, nfdof, nbdof, nfdof);
System.Console.WriteLine(Kff); //Down right corner of matrix
Matrix <double> Kfp = KPermuted.SubMatrix(nbdof, nfdof, 0, nbdof); //Down left corner of matrix
// Split F:::
Matrix <double> fPermuted = DenseMatrix.OfMatrix(f);
fPermuted.PermuteRows(invPerm);
Matrix <double> ff = fPermuted.SubMatrix(nbdof, nfdof, 0, 1);
// Split displacements:::
for (int i = 0; i < nbdof; i++)
{
u[i, 0] = bcVal[i];
}
Matrix <double> up = u.SubMatrix(0, nbdof, 0, 1); // Must set up to constrained values in bc.
// Solve for the unknown displacements:::
Matrix <double> s = Kff.Solve(ff.Subtract(Kfp.Multiply(up)));
u.SetSubMatrix(nbdof, 0, s); // Set displacements back.
System.Console.WriteLine(u);
// Permute back u
u.PermuteRows(perm);
System.Console.WriteLine("U after permut");
System.Console.WriteLine(K);
System.Console.WriteLine(u);
System.Console.WriteLine(f);
// Get reaction forces:
Matrix <double> Q = K.Multiply(u).Subtract(f);
ResultFEM result = new ResultFEM(u, Q);
return(result);
}
public static ResultFEM Solve(Matrix<double> K, Matrix<double> f, int[] bc)
{
// Create dof array:
int ndof = f.RowCount;
// Initialize displacement vector
Matrix u = new DenseMatrix(ndof, 1);
int[] dof = new int[ndof];
for (int i = 0; i < ndof; i++)
{
dof[i] = i;
}
// Create the free dofs:
int[] fdof = dof.Except(bc).ToArray();
int nfdof = fdof.Length; // Number of free dofs.
int nbdof = ndof - nfdof; //Constrained dofs
// Create the permutation array which puts the constrained dofs last:
int[] permute = bc.Union(fdof).ToArray();
Permutation perm = new Permutation(permute);
Permutation invPerm = perm.Inverse();
Matrix<double> KPermuted = DenseMatrix.OfMatrix(K);
KPermuted.PermuteRows(invPerm);
KPermuted.PermuteColumns(invPerm);
// Split K:::
Matrix<double> Kff = KPermuted.SubMatrix(nbdof, nfdof, nbdof, nfdof);
System.Console.WriteLine(Kff); //Down right corner of matrix
Matrix<double> Kfp = KPermuted.SubMatrix(nbdof, nfdof, 0, nbdof); //Down left corner of matrix
// Split F:::
Matrix<double> fPermuted = DenseMatrix.OfMatrix(f);
fPermuted.PermuteRows(invPerm);
Matrix<double> ff = fPermuted.SubMatrix(nbdof, nfdof, 0, 1);
Matrix<double> up = u.SubMatrix(0, nbdof, 0, 1); // Must set up to constrained values in bc.
// Solve for the unknown displacements:::
Matrix<double> s = Kff.Solve(ff.Subtract(Kfp.Multiply(up)));
u.SetSubMatrix(nbdof, 0, s); // Set displacements back.
System.Console.WriteLine(u);
// Permute back u
u.PermuteRows(perm);
System.Console.WriteLine("U after permut");
System.Console.WriteLine(K);
System.Console.WriteLine(u);
System.Console.WriteLine(f);
// Get reaction forces:
Matrix<double> Q = K.Multiply(u).Subtract(f);
ResultFEM result = new ResultFEM(u, Q);
return result;
}