private static void TestMbbBeam(ILinearFemAnalysis fem, IDensityFilter filter)
{
// Parameters
double volumeFraction = 0.5, penalty = 3.0;
// Define the optimization
var materialInterpolation = new PowerLawMaterialInterpolation(youngModulus, penalty, 1E-3);
var simp = new TopologySimpLinear2D(fem, optimAlgorithmBuilder, filter, materialInterpolation, volumeFraction);
var logger = new ObjectiveFunctionLogger();
simp.Logger = logger;
// Run the optimization
simp.Initialize();
(double compliance, Vector densities) = simp.Optimize();
// Check the history of the compliance (objective function)
var expectedCompliances = Vector.CreateFromArray(TopologySimp99LinesTests.ComplianceHistoryForMbbBeam);
Assert.True(expectedCompliances.Equals(
Vector.CreateFromArray(logger.ObjectiveFunctionValues.ToArray()),
1E-10));
// Check the optimum element densities (design variables).
string densitiesPath = Directory.GetParent(Directory.GetCurrentDirectory()).Parent.Parent.FullName
+ @"\Resources\topology99lines_MBBbeam_densities.txt";
var reader = new FullMatrixReader(false, ',');
Vector densitiesExpected = reader.ReadFile(densitiesPath).Reshape(false);
Assert.True(densitiesExpected.Equals(densities, 1E-8));
}
private static void TestCantileverBeamWith2LoadCasesHardCoded()
{
// Parameters
int numElementsX = 30, numElementsY = 30;
double filterAreaRadius = 1.2, volumeFraction = 0.4, penalty = 3.0;
// Define the optimization
var material = new ElasticMaterial2D(StressState2D.PlaneStress)
{
YoungModulus = youngModulus, PoissonRatio = 0.3
};
var fem = new LinearFemAnalysis2DUniformHardcoded(numElementsX, numElementsY, material,
LinearFemAnalysis2DUniformHardcoded.BoundaryConditions.Cantilever2LoadCases);
var filter = new MeshIndependentSensitivityFilter2DUniform(numElementsX, numElementsY, filterAreaRadius);
var materialInterpolation = new PowerLawMaterialInterpolation(youngModulus, penalty, 1E-3);
var simp = new TopologySimpLinear2D(fem, optimAlgorithmBuilder, filter, materialInterpolation, volumeFraction);
var logger = new ObjectiveFunctionLogger();
simp.Logger = logger;
// Run the optimization
simp.Initialize();
(double compliance, Vector densities) = simp.Optimize();
// Check the history of the compliance (objective function)
var expectedCompliances = Vector.CreateFromArray(
TopologySimp99LinesTests.ComplianceHistoryForCantileverWith2LoadCases);
Assert.True(expectedCompliances.Equals(
Vector.CreateFromArray(logger.ObjectiveFunctionValues.ToArray()),
1E-11));
// Check the optimum element densities (design variables).
string densitiesPath = Directory.GetParent(Directory.GetCurrentDirectory()).Parent.Parent.FullName
+ @"\Resources\topology99lines_cantilever_loadcases_densities.txt";
var reader = new FullMatrixReader(false, ',');
Vector densitiesExpected = reader.ReadFile(densitiesPath).Reshape(false);
Assert.True(densitiesExpected.Equals(densities, 1E-11));
}
public (double compliance, Matrix densities, ObjectiveFunctionLogger logger) TopologyOptimization()
{
// Initialize
var x = Matrix.CreateWithValue(nely, nelx, volfrac); // design variables: element densities
bool[,] passive = applyPassiveElements(x); // extension for passive elements
var dc = Matrix.CreateZero(nely, nelx); // compliance sensitivities
int loop = 0;
double change = 1.0;
double c = double.MaxValue;
var logger = new ObjectiveFunctionLogger();
// Start iterations
while (change > 0.01)
{
++loop;
Matrix xold = x.Copy();
// FE analysis
IList <Vector> U = feAnalysis(x);
// Objective function and sensitivity analysis
Matrix Ke = ElementStiffness(); // common for all elements
c = 0.0;
for (int ely = 1; ely <= nely; ++ely)
{
for (int elx = 1; elx <= nelx; ++elx)
{
int n1 = (nely + 1) * (elx - 1) + ely;
int n2 = (nely + 1) * elx + ely;
dc[ely - 1, elx - 1] = 0.0;
int[] elementDofs = GetElementDofs(elx, ely);
foreach (Vector Ui in U)
{
Vector Ue = Ui.GetSubvector(elementDofs);
double unitCompliance = Ue * (Ke * Ue);
double xe = x[ely - 1, elx - 1];
c += Math.Pow(xe, penal) * unitCompliance;
dc[ely - 1, elx - 1] -= Math.Pow(xe, penal - 1) * unitCompliance * penal;
}
}
}
// Filtering of sensitivities
dc = MeshIndependencyFilter(x, dc);
// Design update by the optimality criteria method
x = OptimalityCriteriaUpdate(x, dc, passive);
change = (x - xold).MaxAbsolute();
// Print results
Console.WriteLine($"Iteration = {loop}, Compliance = {c}, Volume = {x.Sum() / (nelx*nely)}, Change = {change}");
//Console.WriteLine("Densities:");
//var writer = new FullMatrixWriter();
//writer.WriteToConsole(x);
//Console.WriteLine("-----------------------------------");
logger.Log(c);
}
return(c, x, logger);
}
