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 }