public void GetKMatrixLinearElementTest()
{
// ElasticCoefficient = E / (1 - v^2)
double elasticCoefficient = 2.31E+06;
Node node1 = new Node(0.0, 0.0);
Node node2 = new Node(1.0, 0.0);
LinearElement element1 = new LinearElement(node1, node2);
double[][] dMatrix = MatrixOperations.MatrixCreate(1, 1);
dMatrix[0][0] = elasticCoefficient;
element1.SetDMatrix(dMatrix);
#region Kglobal
FiniteElementMethodModel model = new FiniteElementMethodModel();
model.Nodes.Add(node1);
model.Nodes.Add(node2);
model.Elements.Add(element1);
var kGlobal = model.BuildGlobalKMatrix();
Console.Write(kGlobal.DisplayMatrixToString());
// Setting displacements
double[][] uMatrix = MatrixOperations.MatrixCreate(2, 1);
uMatrix[0][0] = 0.0;
uMatrix[1][0] = 0.001;
// todo improve matrix inverse and determinant
double[][] fMatrix = kGlobal.MatrixProduct(uMatrix);
// With those strains, this is equivalent to a force of 2310 N applying on the free side
Assert.AreEqual(-2310, fMatrix[0][0]);
Assert.AreEqual(2310, fMatrix[1][0]);
#endregion
}
public void GetKMatrixLinearNElementTest()
{
// ElasticCoefficient = E / (1 - v^2)
double elasticCoefficient = 2.31E+06;
Node node1 = new Node(0.0, 0.0);
Node node2 = new Node(0.25, 0.0);
Node node3 = new Node(0.5, 0.0);
Node node4 = new Node(0.75, 0.0);
Node node5 = new Node(1.0, 0.0);
LinearElement element1 = new LinearElement(node1, node2);
LinearElement element2 = new LinearElement(node2, node3);
LinearElement element3 = new LinearElement(node3, node4);
LinearElement element4 = new LinearElement(node4, node5);
double[][] dMatrix = MatrixOperations.MatrixCreate(1, 1);
dMatrix[0][0] = elasticCoefficient;
element1.SetDMatrix(dMatrix);
element2.SetDMatrix(dMatrix);
element3.SetDMatrix(dMatrix);
element4.SetDMatrix(dMatrix);
#region Kglobal
FiniteElementMethodModel model = new FiniteElementMethodModel();
model.Nodes.Add(node1);
model.Nodes.Add(node2);
model.Nodes.Add(node3);
model.Nodes.Add(node4);
model.Nodes.Add(node5);
model.Elements.Add(element1);
model.Elements.Add(element2);
model.Elements.Add(element3);
model.Elements.Add(element4);
var kGlobal = model.BuildGlobalKMatrix();
Console.Write(kGlobal.DisplayMatrixToString());
// Setting displacements
double[][] uMatrix = MatrixOperations.MatrixCreate(5, 1);
uMatrix[0][0] = 0.0;
uMatrix[1][0] = 0.00025;
uMatrix[2][0] = 0.0005;
uMatrix[3][0] = 0.00075;
uMatrix[4][0] = 0.001;
// todo improve matrix inverse and determinant
double[][] fMatrix = kGlobal.MatrixProduct(uMatrix);
// With those strains, this is equivalent to a force of 2310 N applying on the free side
Assert.AreEqual(-2310, fMatrix[0][0]);
Assert.AreEqual(0, fMatrix[1][0]);
Assert.AreEqual(0, fMatrix[2][0]);
Assert.AreEqual(0, fMatrix[3][0]);
Assert.AreEqual(2310, fMatrix[4][0]);
// Let's get the submatrix and get its inverse to solve the problem automatically and compare its results
double[][] subKMatrix = MatrixOperations.MatrixCreate(4, 4);
double[][] subFMatrix = MatrixOperations.MatrixCreate(4, 1);
int i2 = 0;
for (int i1 = 1; i1 < kGlobal.Length; i1++)
{
int j2 = 0;
for (int j1 = 1; j1 < kGlobal[0].Length; j1++)
{
subKMatrix[i2][j2] = kGlobal[i1][j1];
j2++;
}
subFMatrix[i2] = fMatrix[i1];
i2++;
}
double[][] subKInverse = subKMatrix.MatrixInverse();
double[][] newUMatrix = subKInverse.MatrixProduct(subFMatrix);
Assert.IsTrue(Math.Abs(uMatrix[1][0] - newUMatrix[0][0]) < 0.001);
Assert.IsTrue(Math.Abs(uMatrix[2][0] - newUMatrix[1][0]) < 0.001);
Assert.IsTrue(Math.Abs(uMatrix[3][0] - newUMatrix[2][0]) < 0.001);
Assert.IsTrue(Math.Abs(uMatrix[4][0] - newUMatrix[3][0]) < 0.001);
#endregion
}
public void GetKMatrixTest()
{
// E/(1-v^2) = E / ((1-v)*(1+v) = 2,31E+06
// Modulo elastico acero: E = 2,10E+06
// Coeficiente de Poisson Acero: v = E/2G - 1 = 0.3
// Modulo de elasticidad transversal acero: G = E/(2*(1 + v)), este cálculo asume que Tension_tangencial = G * (2 * Deformacion_tangencial)
// La fórmula de arriba es la que aplicaremos para simplificar calculos en la matriz de derivadas, aunque en realidad: G = E /(1 + v)
// ElasticCoefficient = E / (1 - v^2)
double elasticCoefficient = 2.31E+06;
// D matrix: {Stress} = [D] * {Strain}
// | 1 v 0 | | Strain_X |
// [D] = E / (1 - v^2) * | v 1 0 | * | Strain_Y |
// | 0 0 (1-v)/2 | | Strain_XY |, Strain_XY = 2 * Actual_Strain_XY (That's why there is a 2 dividing (1-v).
double[][] cMatrix = MatrixOperations.MatrixCreate(3, 3);
cMatrix[0][0] = 1.0;
cMatrix[0][1] = 0.3;
cMatrix[0][2] = 0.0;
cMatrix[1][0] = 0.3;
cMatrix[1][1] = 1.0;
cMatrix[1][2] = 0.0;
cMatrix[2][0] = 0.0;
cMatrix[2][1] = 0.0;
cMatrix[2][2] = 0.35;
Node node1 = new Node(0.0, 0.0);
Node node2 = new Node(15.0, 0.0);
Node node3 = new Node(0.0, 15.0);
Node node4 = new Node(15.0, 15.0);
// It looks it is important that all elements are set up with the same spin direction
// Check what happens in 3D how does it work
// node1 => node4 => node3
TriangularElement element1 = new TriangularElement(node1, node4, node3);
// node1 => node2 => node4
TriangularElement element2 = new TriangularElement(node1, node2, node4);
var dMatrix = cMatrix.MatrixProductByConstant(elasticCoefficient);
#region Element 1
element1.SetDMatrix(dMatrix);
#endregion
#region Element 2
element2.SetDMatrix(dMatrix);
#endregion
#region Kglobal
FiniteElementMethodModel model = new FiniteElementMethodModel();
model.Nodes.Add(node1);
model.Nodes.Add(node2);
model.Nodes.Add(node3);
model.Nodes.Add(node4);
model.Elements.Add(element1);
model.Elements.Add(element2);
var kGlobal = model.BuildGlobalKMatrix();
// Setting displacements
double[][] uMatrix = MatrixOperations.MatrixCreate(8, 1);
uMatrix[0][0] = 0.0;
uMatrix[1][0] = 0.0;
uMatrix[2][0] = 0.364E-2;
uMatrix[3][0] = 0.742E-3;
uMatrix[4][0] = 0.0;
uMatrix[5][0] = 0.0;
uMatrix[6][0] = 0.316E-2;
uMatrix[7][0] = -0.259E-3;
// Obtaining global matrix
double[][] fMatrix = kGlobal.MatrixProduct(uMatrix);
Console.Write(kGlobal.DisplayMatrixToString());
// Checking for absolute errors
var absErrorF1X = Math.Abs(fMatrix[0][0] - (-3750.0));
var absErrorF1Y = Math.Abs(fMatrix[1][0] - (-1198.0));
var absErrorF2X = Math.Abs(fMatrix[2][0] - (3750));
var absErrorF2Y = Math.Abs(fMatrix[3][0] - (0));
var absErrorF3X = Math.Abs(fMatrix[4][0] - (-3750.0));
var absErrorF3Y = Math.Abs(fMatrix[5][0] - (1198));
var absErrorF4X = Math.Abs(fMatrix[6][0] - (3750.0));
var absErrorF4Y = Math.Abs(fMatrix[7][0] - (0));
// Making sure absolute errors are less than 1%
Assert.IsTrue(absErrorF1X < Math.Abs(fMatrix[0][0] * 0.01));
Assert.IsTrue(absErrorF1Y < Math.Abs(fMatrix[1][0] * 0.01));
Assert.IsTrue(absErrorF2X < Math.Abs(fMatrix[2][0] * 0.01));
Assert.IsTrue(absErrorF2Y < 1.0);
Assert.IsTrue(absErrorF3X < Math.Abs(fMatrix[4][0] * 0.01));
Assert.IsTrue(absErrorF3Y < Math.Abs(fMatrix[5][0] * 0.01));
Assert.IsTrue(absErrorF4X < Math.Abs(fMatrix[6][0] * 0.01));
Assert.IsTrue(absErrorF4Y < 1.0);
#endregion
}
public void GetKMatrix2Test()
{
Node node1 = new Node(0.0, 0.0);
Node node2 = new Node(1.0, 0.0);
Node node3 = new Node(2.0, 0.0);
Node node4 = new Node(2.0, 1.0);
Node node5 = new Node(1.0, 1.0);
Node node6 = new Node(0.0, 1.0);
TriangularElement element1 = new TriangularElement(node1, node2, node5);
TriangularElement element2 = new TriangularElement(node2, node3, node4);
TriangularElement element3 = new TriangularElement(node2, node4, node5);
TriangularElement element4 = new TriangularElement(node1, node5, node6);
double[][] dMatrix = MatrixOperations.MatrixCreate(3, 3);
dMatrix[0][0] = 1.0;
dMatrix[0][1] = 0.5;
dMatrix[0][2] = 0.0;
dMatrix[1][0] = 0.5;
dMatrix[1][1] = 1.0;
dMatrix[1][2] = 0.0;
dMatrix[2][0] = 0.0;
dMatrix[2][1] = 0.0;
dMatrix[2][2] = 1.0;
element1.SetDMatrix(dMatrix);
element2.SetDMatrix(dMatrix);
element3.SetDMatrix(dMatrix);
element4.SetDMatrix(dMatrix);
#region Kglobal
FiniteElementMethodModel model = new FiniteElementMethodModel();
model.Nodes.Add(node1);
model.Nodes.Add(node2);
model.Nodes.Add(node3);
model.Nodes.Add(node4);
model.Nodes.Add(node5);
model.Nodes.Add(node6);
model.Elements.Add(element1);
model.Elements.Add(element2);
model.Elements.Add(element3);
model.Elements.Add(element4);
var kGlobal = model.BuildGlobalKMatrix();
Console.Write(kGlobal.DisplayMatrixToString());
Assert.AreEqual(1.0, kGlobal[0][0]);
Assert.AreEqual(-0.75, kGlobal[0][9]);
Assert.AreEqual(-0.5, kGlobal[0][10]);
Assert.AreEqual(-0.5, kGlobal[1][3]);
Assert.AreEqual(-0.0, kGlobal[1][6]);
Assert.AreEqual(-0.5, kGlobal[1][11]);
Assert.AreEqual(2.0, kGlobal[2][2]);
Assert.AreEqual(0.25, kGlobal[2][5]);
Assert.AreEqual(-0.75, kGlobal[2][7]);
Assert.AreEqual(0.25, kGlobal[3][0]);
Assert.AreEqual(2.0, kGlobal[3][3]);
Assert.AreEqual(-0.0, kGlobal[3][7]);
Assert.AreEqual(0.0, kGlobal[8][0]);
Assert.AreEqual(2.0, kGlobal[8][8]);
Assert.AreEqual(-0.75, kGlobal[8][9]);
#endregion
}