public double[] FindDisplacementsAt(double x, double y)
{
Element element = FindElementThatContains(x, y);
Quad4 quad4 = (Quad4)element.ElementType;
Node[] nodes = element.Nodes.ToArray();
// Calculate shape functions
var inverseInterpolation = new InverseInterpolationQuad4(nodes);
double[] naturalCoords = inverseInterpolation.TransformPointCartesianToNatural(new double[] { x, y });
//double[] naturalCoords = quad4.GetNaturalCoordinates(element, new Node() { X = x, Y = y });
double[] shapeFunctions = quad4.CalcQ4Shape(naturalCoords[0], naturalCoords[1]);
// Interpolate nodal displacements
double ux = 0.0, uy = 0.0;
for (int i = 0; i < nodes.Length; i++)
{
int nodeID = nodes[i].ID;
double N = shapeFunctions[i];
ux += N * nodalDisplacements[nodeID][0];
uy += N * nodalDisplacements[nodeID][1];
}
return(new double[] { ux, uy });
}
private Bilinear(double[,] result, Quad4 srcQuad, Quad4 dstQuad)
{
rc00 = result[0, 0];
rc10 = result[1, 0];
rc20 = result[2, 0];
rc30 = result[3, 0];
rc01 = result[0, 1];
rc11 = result[1, 1];
rc21 = result[2, 1];
rc31 = result[3, 1];
_valid = true;
_srcQuad = srcQuad;
_dstQuad = dstQuad;
}
public void TestQuad4LinearCantileverExample()
{
// Model and node creation
var model = new Model();
model.NodesDictionary.Add(1, new Node {
ID = 1, X = 0.0, Y = 0.0, Z = 0.0
});
model.NodesDictionary.Add(2, new Node {
ID = 2, X = 10.0, Y = 0.0, Z = 0.0
});
model.NodesDictionary.Add(3, new Node {
ID = 3, X = 10.0, Y = 10.0, Z = 0.0
});
model.NodesDictionary.Add(4, new Node {
ID = 4, X = 0.0, Y = 10.0, Z = 0.0
});
// Constrain bottom nodes of the model and add loads
model.NodesDictionary[1].Constraints.AddRange(new[] { DOFType.X, DOFType.Y });
model.NodesDictionary[4].Constraints.AddRange(new[] { DOFType.X, DOFType.Y });
model.Loads.Add(new Load()
{
Amount = 500, Node = model.NodesDictionary[2], DOF = DOFType.X
});
model.Loads.Add(new Load()
{
Amount = 500, Node = model.NodesDictionary[3], DOF = DOFType.X
});
// Create Quad4 element and its material
var material = new ElasticMaterial2D(StressState2D.PlaneStress)
{
YoungModulus = 3.76, PoissonRatio = 0.3779
};
var quad = new Quad4(material)
{
Thickness = 1
};
// Create the element connectivity
var element = new Element()
{
ID = 1, ElementType = quad
};
element.AddNode(model.NodesDictionary[1]);
element.AddNode(model.NodesDictionary[2]);
element.AddNode(model.NodesDictionary[3]);
element.AddNode(model.NodesDictionary[4]);
// Add quad element to the element and subdomains dictionary of the model
model.ElementsDictionary.Add(element.ID, element);
model.ConnectDataStructures();
// Setup
var linearSystem = new SkylineLinearSystem(model.Forces);
var solver = new SolverSkyline(linearSystem);
var provider = new ProblemStructural(model);
var childAnalyzer = new LinearAnalyzer(solver);
var parentAnalyzer = new StaticAnalyzer(provider, childAnalyzer, linearSystem);
parentAnalyzer.BuildMatrices();
parentAnalyzer.Initialize();
parentAnalyzer.Solve();
var expectedSolution = new double[] { 253.13237596153559, 66.567582057178811, 253.13237596153553, -66.567582057178811 };
for (int i = 0; i < expectedSolution.Length; i++)
{
Assert.Equal(expectedSolution[i], linearSystem.Solution[i], 12);
}
}
