public double[] Modal(int nelx,
int nely,
double[] x,
double p,
double q,
out double[,] V)
{
var ke = K_Plain_strain(1e10, 0.3);
var me = M_Plain_strain(1000, 1);
int N = 2 * (nelx + 1) * (nely + 1);
double[][] K = new double[N][];
double[][] M = new double[N][];
for (int i = 0; i < N; i++)
{
K[i] = new double[N];
M[i] = new double[N];
}
for (int elx = 0; elx < nelx; elx++)
{
for (int ely = 0; ely < nely; ely++)
{
int n1 = (nely + 1) * elx + ely;
int n2 = (nely + 1) * (elx + 1) + ely;
var edof = np.array(2 * n1, 2 * n1 + 1, 2 * n2, 2 * n2 + 1, 2 * n2 + 2, 2 * n2 + 3, 2 * n1 + 2, 2 * n1 + 3);
for (int i = 0; i < edof.size; i++)
{
for (int j = 0; j < edof.size; j++)
{
K[edof[i]][edof[j]] = K[edof[i]][edof[j]] + Math.Pow(x[ely + elx * (nely)], p) * ke[i][j];
M[edof[i]][edof[j]] = M[edof[i]][edof[j]] + Math.Pow(x[ely + elx * (nely)], q) * me[i][j];
}
}
}
}
int[] inds = new int[4 * (nely + 1)];
//left and right border fix
for (int i = 0; i < 2 * (nely + 1); i++)
{
inds[i] = i;
inds[i + 2 * (nely + 1)] = N - 2 * (nely + 1) + i - 1;
}
double[,] Kmm = MatrixMath.To2D <double>(K);
double[,] Mmm = MatrixMath.To2D <double>(M);
Kmm = MatrixMath.CrossOut(Kmm, inds);
Mmm = MatrixMath.CrossOut(Mmm, inds);
int reducedN = Kmm.GetLength(0);
double[] wr = new double[reducedN];
//solve
alglib.smatrixgevd(Kmm, reducedN, false, Mmm, false, 1, 1, out wr, out V);
for (int i = 0; i < V.GetLength(0); i++)
{
for (int j = 0; j < V.GetLength(1); j++)
{
V[i, j] = Math.Cos(wr[i]) * V[i, j];
}
}
V = MatrixMath.FillOnWeird(V, inds);
return(wr);
}
public double[] FE_inded(int nelx, int nely, double[] x, Dictionary <int, double> f_map, double p)
{
var ke = KE;
int N = 2 * (nelx + 1) * (nely + 1);
double[][] K_m = new double[N][];
for (int i = 0; i < N; i++)
{
K_m[i] = new double[N];
}
for (int elx = 0; elx < nelx; elx++)
{
for (int ely = 0; ely < nely; ely++)
{
int n1 = (nely + 1) * elx + ely;
int n2 = (nely + 1) * (elx + 1) + ely;
var edof = np.array(2 * n1, 2 * n1 + 1, 2 * n2, 2 * n2 + 1, 2 * n2 + 2, 2 * n2 + 3, 2 * n1 + 2, 2 * n1 + 3);
for (int i = 0; i < edof.size; i++)
{
for (int j = 0; j < edof.size; j++)
{
K_m[edof[i]][edof[j]] = K_m[edof[i]][edof[j]] + Math.Pow(x[ely + elx * (nely)], p) * ke[i][j]; //?diagonal
}
}
}
}
int[] inds = new int[2 * (nely + 1)];
//left and right border fix
for (int i = 0; i < 2 * (nely + 1); i++)
{
inds[i] = i;
}
Random r = new Random(123);
double[,] Kmm = MatrixMath.To2D <double>(K_m);
Kmm = MatrixMath.CrossOut(Kmm, inds);
int reducedN = Kmm.GetLength(0);
List <double> F_full = Enumerable.Repeat(0.0, N).ToList();
double[] X = new double[N];
double[] F = new double[reducedN];
//index crossout
int c = 0;
foreach (var q in f_map)
{
F_full[q.Key] = q.Value;
}
for (int i = 0; i < N; i++)
{
if (c < inds.Length && inds[c] == i)
{
c++;
}
else
{
F[i - c] = F_full[i];
}
}
// F[reducedN -1] = -1e6;
alglib.rmatrixsolvefast(Kmm, reducedN, ref F, out _);
//index backfill
c = 0;
for (int i = 0; i < N; i++)
{
if (c < inds.Length && inds[c] == i)
{
X[i] = 0;
c++;
}
else
{
X[i] = F[i - c];
}
}
return(X);
}
public double[] FE(int nelx, int nely, double[] x, double p)
{
var ke = KE;
int N = 2 * (nelx + 1) * (nely + 1);
double[][] K_m = new double[N][];
for (int i = 0; i < N; i++)
{
K_m[i] = new double[N];
}
for (int elx = 0; elx < nelx; elx++)
{
for (int ely = 0; ely < nely; ely++)
{
int n1 = (nely + 1) * elx + ely;
int n2 = (nely + 1) * (elx + 1) + ely;
var edof = np.array(2 * n1, 2 * n1 + 1, 2 * n2, 2 * n2 + 1, 2 * n2 + 2, 2 * n2 + 3, 2 * n1 + 2, 2 * n1 + 3);
for (int i = 0; i < edof.size; i++)
{
for (int j = 0; j < edof.size; j++)
{
K_m[edof[i]][edof[j]] = K_m[edof[i]][edof[j]] + Math.Pow(x[ely + elx * (nely)], p) * ke[i][j]; //?diagonal
}
}
}
}
int[] inds = new int[2 * (nely + 1)];
//left and right border fix
for (int i = 0; i < 2 * (nely + 1); i++)
{
inds[i] = i;
}
Random r = new Random(123);
double[,] Kmm = MatrixMath.To2D <double>(K_m);
Kmm = MatrixMath.CrossOut(Kmm, inds);
int reducedN = Kmm.GetLength(0);
double[] F = new double[reducedN];
double[] X = new double[N];
for (int i = 0; i < nely; i++)
{
F[(2 * nely + 1) * nelx + i * 2 - 1] = -1;
}
F[reducedN - nely - 1] = r.NextDouble();
alglib.rmatrixsolvefast(Kmm, reducedN, ref F, out _);
int c = 0;
for (int i = 0; i < N; i++)
{
if (c < inds.Length && inds[c] == i)
{
X[i] = 0;
c++;
}
else
{
X[i] = F[i - c];
}
}
return(X);
}
public double[] Harmonic(int nelx, int nely, double[] x, double p, double q, double wmega)
{
var ke = K_Plain_strain(1e10, 0.3);
var me = M_Plain_strain(1000, 1);
int N = 2 * (nelx + 1) * (nely + 1);
double[][] K = new double[N][];
double[][] M = new double[N][];
for (int i = 0; i < N; i++)
{
K[i] = new double[N];
M[i] = new double[N];
}
for (int elx = 0; elx < nelx; elx++)
{
for (int ely = 0; ely < nely; ely++)
{
int n1 = (nely + 1) * elx + ely;
int n2 = (nely + 1) * (elx + 1) + ely;
var edof = np.array(2 * n1, 2 * n1 + 1, 2 * n2, 2 * n2 + 1, 2 * n2 + 2, 2 * n2 + 3, 2 * n1 + 2, 2 * n1 + 3);
for (int i = 0; i < edof.size; i++)
{
for (int j = 0; j < edof.size; j++)
{
K[edof[i]][edof[j]] = K[edof[i]][edof[j]] + Math.Pow(x[ely + elx * (nely)], p) * ke[i][j];
M[edof[i]][edof[j]] = M[edof[i]][edof[j]] + Math.Pow(x[ely + elx * (nely)], q) * me[i][j];
}
}
}
}
int[] inds = new int[2 * (nely + 1)];
//left border fix
for (int i = 0; i < 2 * (nely + 1); i++)
{
inds[i] = i;
}
double[,] Kmm = MatrixMath.To2D <double>(K);
double[,] Mmm = MatrixMath.To2D <double>(M);
Kmm = MatrixMath.CrossOut(Kmm, inds);
Mmm = MatrixMath.CrossOut(Mmm, inds);
List <double> X = new List <double>();
int reducedN = Kmm.GetLength(0);
double[,] DSW = new double[reducedN, reducedN];
for (int ik = 0; ik < Kmm.GetLength(0); ik++)
{
for (int jk = 0; jk < Kmm.GetLength(1); jk++)
{
double l = wmega * 2 * Math.PI;
l = l * l;
DSW[ik, jk] = Kmm[ik, jk] - l * Mmm[ik, jk];
}
}
double[] F = new double[reducedN];
double[] U = new double[reducedN];
F[reducedN - 1] = -1e6;
alglib.rmatrixsolve(DSW, reducedN, F, out _, out _, out U);
int c = 0;
for (int i = 0; i < N; i++)
{
if (c < inds.Length && inds[c] == i)
{
X.Add(0);
c++;
}
else
{
X.Add(U[i - c]);
}
}
return(X.ToArray());
}
