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BESO2D.cs
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BESO2D.cs
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using System;
using System.Collections.Generic;
using System.Linq;
using System.Diagnostics;
using System.Text;
using System.Threading.Tasks;
using System.Runtime.InteropServices;
using System.IO;
namespace BESO
{
public class BESO2D
{
#region Resolution
public int nelx;
public int nely;
#endregion
#region FE varialbes
private double[] U;
private int[] ik;
private int[] jk;
private double[] vk;
#endregion
#region BESO Parameters
/// <summary>
/// Filter radius
/// </summary>
public double rmin;
/// <summary>
/// Volume fraction
/// </summary>
public double vf;
/// <summary>
/// Penalty exponent
/// </summary>
public double p;
/// <summary>
/// Evolution rate
/// </summary>
public double ert;
/// <summary>
/// The maximum iteration
/// </summary>
public int maxIter;
#endregion
#region BESO variables
/// <summary>
/// Design variables
/// </summary>
public double[] Xe;
public double[] dc;
public double[] dc_old;
/// <summary>
/// Elemental stiffness matrix
/// </summary>
private double[] Ke;
/// <summary>
/// The minimum design variable
/// </summary>
private double Xmin = 0.001;
/// <summary>
/// The isovalue for extracting isosurface.
/// </summary>
public List<double> isovalues = new List<double>();
/// <summary>
/// The iterative history of the global compliance
/// </summary>
private List<double> HistoryC = new List<double>();
public int[] free_dofs;
public double Compliance = 0.0;
public double vol = 1.0;
public double delta = 1.0;
public int iter = 0;
public bool convergence = false;
public string info = null;
public StringBuilder initInfo;
public StringBuilder optInfo;
#endregion
#region Flt variables
public int[] ih;
public int[] jh;
public double[] vh;
public double[] sh;
#endregion
private Stopwatch stopwatch;
#region Settings
public bool parallel = true;
public bool changeSupports = true;
#endregion
public BESO2D() { }
public BESO2D(double rmin, double vf, double ert = 0.02, double p = 3.0, int maxIter = 100)
{
if (rmin <= 0.0)
throw new Exception("Rmin must be large than 0.");
if (!(vf > 0.0 && vf < 1.0))
throw new Exception("Vt must be large than 0 and be less than 1.");
this.vf = vf;
this.p = p;
this.ert = ert;
this.maxIter = maxIter;
this.rmin = rmin;
}
public void Initialize(int nelx, int nely)
{
initInfo = new StringBuilder("====================== Launch BESO ======================" + '\n');
this.nelx = nelx;
this.nely = nely;
dc = new double[nely * nelx];
dc_old = new double[nely * nelx];
Xe = new double[nely* nelx];
Array.Fill(Xe, 1.0);
GetKe();
ik = new int[nelx * nely * 8 * 8];
jk = new int[nelx * nely * 8 * 8];
Wrapper.PreFE(nelx, nely, ik, jk);
PreFlt();
}
public void Optimize()
{
if (delta > 0.001 && iter < maxIter)
{
iter += 1;
vol = Math.Max(vf, vol * (1.0 - ert));
FE();
GetDc();
HistoryC.Add(Compliance);
Wrapper.Flt(dc.Length, dc, sh);
if (iter > 1)
for (int j = 0; j < nely; j++)
{
for (int i = 0; i < nelx; i++)
{
dc[i * nely + j] = (dc[i * nely + j] + dc_old[i * nely + j]) * 0.5;
}
}
// Record the sensitiveies in each step
dc_old = (double[])dc.Clone();
ADD_DEL(vol);
// Check convergence
if (iter > 10)
{
var newV = 0.0;
var lastV = 0.0;
for (int i = 1; i < 6; i++)
{
newV += HistoryC[HistoryC.Count - i];
lastV += HistoryC[HistoryC.Count - 5 - i];
}
delta = Math.Abs((newV - lastV) / lastV);
}
info = "It.: " + iter.ToString() + ", Obj.: " + Compliance.ToString() +
", Vol.: " + vol.ToString() + ", ch.: " + delta.ToString();
}
else
{
convergence = true;
}
}
private void PreFlt()
{
int rminf = (int)Math.Floor(rmin);
ih = new int[(int)(nelx * nely * Math.Pow((2 * rminf + 1), 2))];
jh = new int[ih.Length];
vh = new double[ih.Length];
sh = new double[nelx * nely];
int sum = 0;
for (int i = 0; i < nelx; i++)
{
for (int j = 0; j < nely; j++)
{
var e1 = i * nely + j + 1;
for (int k = Math.Max(i - rminf, 0); k < Math.Min(i + rminf + 1, nelx); k++)
{
for (int l = Math.Max(j - rminf, 0); l < Math.Min(j + rminf + 1, nely); l++)
{
var e2 = k * nely + l + 1;
ih[sum] = e1 - 1;
jh[sum] = e2 - 1;
vh[sum] = Math.Max(0.0, rminf - Math.Sqrt((i - k) * (i - k) + (j - l) * (j - l)));
sum++;
}
}
}
}
Wrapper.GetRowSum(sum, nelx * nely, ih, jh, vh, sh);
}
private void ADD_DEL(double volfra)
{
double lowest = dc.Min();
double highest = dc.Max();
double th = 0.0;
double vol = volfra * nelx * nely;
while (((highest - lowest) / highest) > 1e-5)
{
th = (highest + lowest) * 0.5;
double sum = 0.0;
for (int j = 0; j < nely; j++)
{
for (int i = 0; i < nelx; i++)
{
Xe[j*nelx+ i] = dc[i * nely + j] > th ? 1.0 : Xmin;
sum += Xe[j * nelx + i];
}
}
if (sum - vol > 0.0) lowest = th;
else highest = th;
}
isovalues.Add(th);
}
private void GetDc()
{
Compliance = 0.0;
double[] C = new double[nelx * nely];
Parallel.For(0, nely, ely=>
{
for (int elx = 0; elx < nelx; elx++)
{
var n1 = (nely + 1) * elx + ely + 1;
var n2 = (nely + 1) * (elx + 1) + ely + 1;
double[] Ue = { U[2 * n1 - 2], U[2 * n1 - 1], U[2 * n2 - 2], U[2 * n2 - 1],
U[2 * n2], U[2 * n2 + 1], U[2 * n1], U[2 * n1 + 1]};
double v = Wrapper.TransposeMultiply(8, 8, Ke, Ue);
C[elx * nely + ely] = 0.5 * Math.Pow(Xe[ely*nelx + elx], p) * v;
dc[elx * nely + ely] = 0.5 * Math.Pow(Xe[ely* nelx + elx], p - 1) * v;
}
});
Compliance = C.Sum();
}
private void FE()
{
int num_allDofs = 2 * (nelx + 1) * (nely + 1);
int num_fixedDofs = 2 * (nely + 1);
int num_freeDofs = num_allDofs - num_fixedDofs;
// Assemble stiffness matrix with all DOFs
vk = new double[64 * nelx * nely];
Parallel.For(0, nelx, i =>
{
for (int j = 0; j < nely; j++)
{
var ex = Math.Pow(Xe[j * nelx + i], p);
for (int a = 0; a < 8; a++)
{
for (int b = 0; b < 8; b++)
{
vk[i * nely * 64 + j * 64 + a * 8 + b] = ex * Ke[a * 8 + b];
}
}
}
});
var F = new double[num_allDofs];
U = new double[num_allDofs];
// Define force vector
F[2 * (nelx + 1) * (nely + 1) - nely - 1] = -1.0;
if (changeSupports)
{
// Define fixed dofs
var fixed_dofs = new int[num_fixedDofs];
for (int i = 0; i < num_fixedDofs; i++)
fixed_dofs[i] = i;
var all_dofs = new int[num_allDofs];
for (int i = 0; i < num_allDofs; i++)
all_dofs[i] = i;
// Obtain free dofs
free_dofs = all_dofs.Except(fixed_dofs).ToArray();
changeSupports = false;
}
var U_freedof = new double[num_freeDofs];
Wrapper.Assembly_Solve(1, parallel, num_freeDofs, num_allDofs, ik.Length, free_dofs, ik, jk, vk, F, U_freedof);
for (int i = 0; i < num_freeDofs; i++)
{
U[free_dofs[i]] = U_freedof[i];
}
}
private void GetKe()
{
var E = 1.0;
var nu = 0.3;
var w = E / (1 - nu * nu);
var k = new double[8]
{
w * (0.5-nu/6.0), w * (0.125+nu/8.0), w * (-0.25-nu/12.0), w * (-0.125+3*nu/8.0),
w * (-0.25+nu/12.0), w * (-0.125-nu/8.0), w * (nu/6.0), w * (0.125-3*nu/8.0)
};
Ke = new double[64]{
k[0],k[1],k[2],k[3],k[4],k[5],k[6],k[7],
k[1],k[0],k[7],k[6],k[5],k[4],k[3],k[2],
k[2],k[7],k[0],k[5],k[6],k[3],k[4],k[1],
k[3],k[6],k[5],k[0],k[7],k[2],k[1],k[4],
k[4],k[5],k[6],k[7],k[0],k[1],k[2],k[3],
k[5],k[4],k[3],k[2],k[1],k[0],k[7],k[6],
k[6],k[3],k[4],k[1],k[2],k[7],k[0],k[5],
k[7],k[2],k[1],k[4],k[3],k[6],k[5],k[0]};
}
#region Debug Methods
public StringBuilder ModelInfo()
{
StringBuilder report = new StringBuilder("=================== Model Info ===================" + '\n');
report.Append("Disp Nodes: " + ((nelx + 1) * (nely + 1)).ToString() + '\n');
report.Append("Disp Elements: " + (nelx * nely).ToString() + '\n');
report.Append('\n');
report.Append("Opt Nodes: " + ((nelx + 1) * (nely + 1)).ToString() + '\n');
report.Append("Opt Elements: " + (nelx * nely).ToString() + '\n');
report.Append('\n');
report.Append("=================== Parameters Info ===================" + '\n');
report.Append("xCount: " + nelx.ToString() + '\n');
report.Append("yCount: " + nely.ToString() + '\n');
return report;
}
public void WriteXe(string path)
{
string output = path + '\\' + "Xe2.txt";
StreamWriter sw = new StreamWriter(output);
for (int i = 0; i < nelx; i++)
{
for (int j = 0; j < nely; j++)
{
sw.WriteLine(Xe[j * nelx + i].ToString());
}
}
sw.Flush();
sw.Close();
sw.Dispose();
}
#endregion
}
}