private static Model CreateModel(int numElementsX, int numElementsY)
{
// Create mesh
var meshGenerator = new UniformMeshGenerator2D(0, 0, length, height, numElementsX, numElementsY);
(Node[] nodes, Element[] elements) = meshGenerator.CreateMesh();
// Create model and add the nodes
var model = new Model();
foreach (Node node in nodes)
{
model.NodesDictionary.Add(node.ID, node);
}
// Find nodes on the left side and constrain their displacement
var leftNodes = model.FindNodesWithX(0);
foreach (Node node in leftNodes)
{
node.Constraints.AddRange(new[] { DOFType.X, DOFType.Y });
}
// Find nodes on the right side and apply load
var rightNodes = model.FindNodesWithX(length);
double loadPerNode = totalLoad / rightNodes.Count;
foreach (Node node in rightNodes)
{
model.Loads.Add(new Load()
{
Amount = loadPerNode, Node = node, DOF = DOFType.Y
});
}
// Create Quad4 elements and their material
var material = new ElasticMaterial2D(StressState2D.PlaneStress)
{
YoungModulus = youngModulus,
PoissonRatio = poissonRatio
};
foreach (Element element in elements)
{
element.ElementType = new Quad4(material)
{
Thickness = thickness
};
model.ElementsDictionary.Add(element.ID, element);
}
// Finalize model creation
model.ConnectDataStructures();
return(model);
}
private static Model CreateModel(int numElementsX, int numElementsY)
{
// Create mesh
var meshGenerator = new UniformMeshGenerator2D(0, 0, length, height, numElementsX, numElementsY);
(Node[] nodes, Element[] elements) = meshGenerator.CreateMesh();
// Create model and add the nodes
var model = new Model();
foreach (Node node in nodes)
{
model.NodesDictionary.Add(node.ID, node);
}
// Create Quad4 elements and their material
var material = new ElasticMaterial2D(StressState2D.PlaneStress)
{
YoungModulus = youngModulus,
PoissonRatio = poissonRatio
};
foreach (Element element in elements)
{
element.ElementType = new Quad4(material)
{
Thickness = thickness
};
model.ElementsDictionary.Add(element.ID, element);
}
// Boundary conditions:
// *******************************************************************************************
// *******************************************************************************************
// Excercise: Write your own boundary conditions for simply supported beam
// *******************************************************************************************
// *******************************************************************************************
ApplyCantileverBoundaryConditions(model);
// Finalize model creation
model.ConnectDataStructures();
return(model);
}
private static void AddHostElements(Model model)
{
// Material
double density = 1.0;
double c = 1.0;
double h = 0;
// Generate mesh
var meshGenerator = new UniformMeshGenerator2D <Node>(minX, minY, maxX, maxY, numElementsX, numElementsY);
(IReadOnlyList <Node> vertices, IReadOnlyList <CellConnectivity <Node> > cells) =
meshGenerator.CreateMesh((id, x, y, z) => new Node(id: id, x: x, y: y, z: z));
// Add nodes to the model
for (int n = 0; n < vertices.Count; ++n)
{
model.NodesDictionary.Add(n, vertices[n]);
}
// Add the elements to the model
var elementFactory = new ThermalElement2DFactory(1.0, new ThermalMaterial(density, c, conductivityMatrix, h));
for (int e = 0; e < cells.Count; ++e)
{
ThermalElement2D element = elementFactory.CreateElement(cells[e].CellType, cells[e].Vertices);
var elementWrapper = new Element()
{
ID = e + hostElementsIDStart, ElementType = element
};
foreach (Node node in element.Nodes)
{
elementWrapper.AddNode(node);
}
model.ElementsDictionary.Add(elementWrapper.ID, elementWrapper);
model.SubdomainsDictionary[subdomainID].Elements.Add(elementWrapper);
}
}
private static (IReadOnlyList <Node> nodes, IReadOnlyList <CellConnectivity <Node> > elements) GenerateUniformMesh()
{
var meshGen = new UniformMeshGenerator2D <Node>(0.0, 0.0, length, height, 4, 20);
return(meshGen.CreateMesh((id, x, y, z) => new Node(id: id, x: x, y: y, z: z)));
}
public CantileverBeam BuildWithQuad4Elements(int numElementsAlongLength, int numElementsAlongHeight)
{
// Material and section properties
double thickness = Width;
var material = new ElasticMaterial2D(StressState2D.PlaneStress)
{
YoungModulus = this.YoungModulus,
PoissonRatio = this.PoissonRatio
};
var dynamicProperties = new DynamicMaterial(1.0, 0.0, 0.0);
// Model with 1 subdomain
var model = new Model();
model.SubdomainsDictionary.Add(subdomainID, new Subdomain(subdomainID));
// Generate mesh
var meshGenerator = new UniformMeshGenerator2D <Node>(0.0, 0.0, Length, Height,
numElementsAlongLength, numElementsAlongHeight);
(IReadOnlyList <Node> vertices, IReadOnlyList <CellConnectivity <Node> > cells) =
meshGenerator.CreateMesh((id, x, y, z) => new Node(id: id, x: x, y: y, z: z));
// Add nodes to the model
for (int n = 0; n < vertices.Count; ++n)
{
model.NodesDictionary.Add(n, vertices[n]);
}
// Add Quad4 elements to the model
var factory = new ContinuumElement2DFactory(thickness, material, dynamicProperties);
for (int e = 0; e < cells.Count; ++e)
{
ContinuumElement2D element = factory.CreateElement(cells[e].CellType, cells[e].Vertices);
var elementWrapper = new Element()
{
ID = e, ElementType = element
};
foreach (Node node in element.Nodes)
{
elementWrapper.AddNode(node);
}
model.ElementsDictionary.Add(e, elementWrapper);
model.SubdomainsDictionary[subdomainID].Elements.Add(elementWrapper);
}
// Clamp boundary condition at one end
double tol = 1E-10; //TODO: this should be chosen w.r.t. the element size along X
foreach (var node in model.Nodes.Where(node => Math.Abs(node.X) <= tol))
{
node.Constraints.Add(new Constraint()
{
DOF = StructuralDof.TranslationX, Amount = 0.0
});
node.Constraints.Add(new Constraint()
{
DOF = StructuralDof.TranslationY, Amount = 0.0
});
}
// Apply concentrated load at the other end
Node[] loadedNodes = model.Nodes.Where(node => Math.Abs(node.X - Length) <= tol).ToArray();
foreach (var node in loadedNodes)
{
model.Loads.Add(new Load()
{
Amount = EndPointLoad / loadedNodes.Length, Node = node, DOF = StructuralDof.TranslationY
});
}
return(new CantileverBeam(Length, Height, Width, EndPointLoad, YoungModulus, model, loadedNodes));
}
public static void WriteStiffnessOfContinuum2DStructure()
{
// ____ ____
// | | |
// |____|____|
// | | |
// |____|____|
// Model with 1 subdomain
var model = new Model();
model.SubdomainsDictionary.Add(subdomainID, new Subdomain(subdomainID));
// Material
double thickness = 1.0;
var material = new ElasticMaterial2D(StressState2D.PlaneStress)
{
YoungModulus = 2.1E7,
PoissonRatio = 0.3
};
var dynamicProperties = new DynamicMaterial(1.0, 0.0, 0.0, true);
// Generate mesh
double domainLength = 2.0;
double domainHeight = 2.4;
var meshGenerator = new UniformMeshGenerator2D <Node>(0.0, 0.0, domainLength, domainHeight, 10, 10);
(IReadOnlyList <Node> vertices, IReadOnlyList <CellConnectivity <Node> > cells) =
meshGenerator.CreateMesh((id, x, y, z) => new Node(id: id, x: x, y: y, z: z));
// Add nodes to the model
for (int n = 0; n < vertices.Count; ++n)
{
model.NodesDictionary.Add(n, vertices[n]);
}
// Add Quad4 elements to the model
var factory = new ContinuumElement2DFactory(thickness, material, dynamicProperties);
for (int e = 0; e < cells.Count; ++e)
{
ContinuumElement2D element = factory.CreateElement(cells[e].CellType, cells[e].Vertices);
var elementWrapper = new Element()
{
ID = e, ElementType = element
};
foreach (Node node in element.Nodes)
{
elementWrapper.AddNode(node);
}
model.ElementsDictionary.Add(e, elementWrapper);
model.SubdomainsDictionary[subdomainID].Elements.Add(elementWrapper);
}
// Solver
var solverBuilder = new SkylineSolver.Builder();
SkylineSolver solver = solverBuilder.BuildSolver(model);
// Structural problem provider
var provider = new ProblemStructural(model, solver);
// Linear static analysis
var childAnalyzer = new LinearAnalyzer(model, solver, provider);
var parentAnalyzer = new StaticAnalyzer(model, solver, provider, childAnalyzer);
// Run the analysis to build the stiffness matrix
parentAnalyzer.Initialize();
parentAnalyzer.BuildMatrices();
// Print the stiffness matrix
//var writer = new MatlabWriter();
var writer = new RawArraysWriter();
writer.WriteToMultipleFiles((SkylineMatrix)solver.LinearSystems[subdomainID].Matrix,
outputDirectory + @"\quad4_20x20_stiffness.txt");
}
public void CreateModel(int numElementsX, int numElementsY, double jIntegralRadiusRatio)
{
var model = new XModel();
model.Subdomains[subdomainID] = new XSubdomain(subdomainID);
this.Model = model;
// Mesh generation
var meshGenerator = new UniformMeshGenerator2D <XNode>(0.0, 0.0, beamLength, beamHeight, numElementsX, numElementsY);
(IReadOnlyList <XNode> nodes, IReadOnlyList <CellConnectivity <XNode> > elementConnectivities) =
meshGenerator.CreateMesh((id, x, y, z) => new XNode(id, x, y, z));
// Nodes
foreach (XNode node in nodes)
{
model.Nodes.Add(node);
}
// Elements
var factory = new XContinuumElement2DFactory(integration, jIntegration, material);
var cells = new XContinuumElement2D[elementConnectivities.Count];
for (int e = 0; e < elementConnectivities.Count; ++e)
{
XContinuumElement2D element = factory.CreateElement(e, CellType.Quad4, elementConnectivities[e].Vertices);
cells[e] = element;
model.Elements.Add(element);
model.Subdomains[subdomainID].Elements.Add(model.Elements[e]);
}
// Mesh
var mesh = new BidirectionalMesh2D <XNode, XContinuumElement2D>(model.Nodes,
model.Elements.Select(e => (XContinuumElement2D)e).ToArray(), beamBoundary);
// Boundary conditions
double tol = 1E-6;
double L = DoubleCantileverBeam.beamLength;
double H = DoubleCantileverBeam.beamHeight;
XNode topRight = model.Nodes.Where(n => Math.Abs(n.X - L) <= tol && Math.Abs(n.Y - H) <= tol).First();
XNode bottomRight = model.Nodes.Where(n => Math.Abs(n.X - L) <= tol && Math.Abs(n.Y) <= tol).First();
topRight.Constraints.Add(new Constraint()
{
DOF = StructuralDof.TranslationY, Amount = +0.05
});
bottomRight.Constraints.Add(new Constraint()
{
DOF = StructuralDof.TranslationY, Amount = -0.05
});
foreach (XNode node in model.Nodes.Where(n => Math.Abs(n.X) <= tol))
{
node.Constraints.Add(new Constraint()
{
DOF = StructuralDof.TranslationX, Amount = 0.0
});
node.Constraints.Add(new Constraint()
{
DOF = StructuralDof.TranslationY, Amount = 0.0
});
}
// Create crack
double elementSizeX = beamLength / numElementsX;
double elementSizeY = beamHeight / numElementsY;
CreateCrack(Math.Max(elementSizeX, elementSizeY), model, mesh, jIntegralRadiusRatio);
}
private static void TestCantileverBeamGeneral()
{
// Define the materials
double thickness = 1.0;
var material = new ElasticMaterial2D(StressState2D.PlaneStress)
{
YoungModulus = youngModulus, PoissonRatio = 0.3
};
var dynamicProperties = new DynamicMaterial(1.0, 0.0, 0.0, true);
// Model with 1 subdomain
var model = new Model();
model.SubdomainsDictionary.Add(subdomainID, new Subdomain(subdomainID));
// Generate mesh
int numElementsX = 32, numElementsY = 20;
double lengthX = numElementsX;
double depthY = numElementsY;
var mesher = new UniformMeshGenerator2D <Node>(0, 0, lengthX, depthY, numElementsX, numElementsY);
(IReadOnlyList <Node> nodes, IReadOnlyList <CellConnectivity <Node> > connectivity) =
mesher.CreateMesh((id, x, y, z) => new Node(id: id, x: x, y: y, z: z));
// Add nodes to the model
for (int n = 0; n < nodes.Count; ++n)
{
model.NodesDictionary.Add(n, nodes[n]);
}
// Add Quad4 elements to the model
var factory = new ContinuumElement2DFactory(thickness, material, dynamicProperties);
for (int e = 0; e < connectivity.Count; ++e)
{
ContinuumElement2D element = factory.CreateElement(connectivity[e].CellType, connectivity[e].Vertices);
var elementWrapper = new Element()
{
ID = e, ElementType = element
};
foreach (Node node in element.Nodes)
{
elementWrapper.AddNode(node);
}
model.ElementsDictionary.Add(e, elementWrapper);
model.SubdomainsDictionary[subdomainID].Elements.Add(elementWrapper);
}
// Clamp boundary condition at left edge
double tol = 1E-10; //TODO: this should be chosen w.r.t. the element size along X
foreach (var node in model.Nodes.Where(node => Math.Abs(node.X) <= tol))
{
node.Constraints.Add(new Constraint()
{
DOF = StructuralDof.TranslationX, Amount = 0.0
});
node.Constraints.Add(new Constraint()
{
DOF = StructuralDof.TranslationY, Amount = 0.0
});
}
// Apply concentrated load at the bottom right corner
double load = 1.0;
var cornerNode = model.Nodes.Where(
node => (Math.Abs(node.X - lengthX) <= tol) && (Math.Abs(node.Y - depthY) <= tol));
Assert.True(cornerNode.Count() == 1);
model.Loads.Add(new Load()
{
Amount = load, Node = cornerNode.First(), DOF = StructuralDof.TranslationY
});
// Define the solver
SkylineSolver solver = (new SkylineSolver.Builder()).BuildSolver(model);
// Define the fem analysis and the filter
double filterAreaRadius = 1.2;
var fem = new LinearFemAnalysis2DGeneral(model, solver);
var filter = new ProximityDensityFilter2D(model, filterAreaRadius);
// Run the test
TestCantileverBeam(fem, filter);
}
