public static void Test6() { Console.WriteLine("Example 13: I Beam With Flat Shell, BFE vs SAP2000"); var magic = 0; //example #13 p175 #region creating model var model = new Model(); var l = UnitConverter.In2M(40); var w = UnitConverter.In2M(10); var h = UnitConverter.In2M(5); var t = UnitConverter.In2M(0.25); var e = UnitConverter.Ksi2Pas(10000); //10'000 ksi var no = 0.3; var n = 9; var xSpan = l / (n - 1); var nodes = new Node[n][]; for (var i = 0; i < n; i++) { var x = i * xSpan; nodes[i] = new Node[7]; nodes[i][0] = new Node(x, 0, 0); nodes[i][1] = new Node(x, w / 2, 0); nodes[i][2] = new Node(x, w, 0); nodes[i][3] = new Node(x, w / 2, h / 2); nodes[i][4] = new Node(x, 0, h); nodes[i][5] = new Node(x, w / 2, h); nodes[i][6] = new Node(x, w, h); model.Nodes.AddRange(nodes[i]); } var pairs = new int[6][]; pairs[0] = new int[] { 0, 1 }; pairs[1] = new int[] { 1, 2 }; pairs[2] = new int[] { 1, 3 }; pairs[3] = new int[] { 3, 5 }; pairs[4] = new int[] { 4, 5 }; pairs[5] = new int[] { 5, 6 }; for (var i = 0; i < n - 1; i++) { for (int j = 0; j < 6; j++) { var n11 = nodes[i][pairs[j][0]]; var n12 = nodes[i][pairs[j][1]]; var n21 = nodes[i + 1][pairs[j][0]]; var n22 = nodes[i + 1][pairs[j][1]]; { var elm1 = new TriangleFlatShell() { Thickness = t, PoissonRatio = no, ElasticModulus = e }; elm1.Nodes[0] = n11; elm1.Nodes[1] = n12; elm1.Nodes[2] = n21; model.Elements.Add(elm1); var elm2 = new TriangleFlatShell() { Thickness = t, PoissonRatio = no, ElasticModulus = e }; elm2.Nodes[0] = n21; elm2.Nodes[1] = n22; elm2.Nodes[2] = n12; model.Elements.Add(elm2); } } } //loading nodes.Last()[0].Loads.Add(new NodalLoad(new Force(0, UnitConverter.Kip2N(1.6), 0, 0, 0, 0))); nodes.Last()[6].Loads.Add(new NodalLoad(new Force(0, -UnitConverter.Kip2N(1.6), 0, 0, 0, 0))); nodes[0].ToList().ForEach(i => i.Constraints = Constraint.Fixed); #endregion model.Trace.Listeners.Add(new BriefFiniteElementNet.ConsoleTraceListener()); new ModelWarningChecker().CheckModel(model); //ModelVisualizerControl.VisualizeInNewWindow(model); model.Solve(); var A = nodes.Last()[2]; var B = nodes.Last()[4]; var C = nodes.First()[1]; var D = nodes.First()[0]; var E = nodes.Last()[6]; /* * for (int i = 0; i < nodes.Last().Length; i++) * { * nodes.Last()[i].Label = i.ToString(); * } */ /**/ A.Label = "A"; B.Label = "B"; C.Label = "C"; D.Label = "D"; E.Label = "E"; /**/ var da = 1 / 0.0254 * A.GetNodalDisplacement().Displacements; // [inch] var db = 1 / 0.0254 * B.GetNodalDisplacement().Displacements; // [inch] var sap2000Da = new Vector(-0.014921, 0.085471, 0.146070); //tbl 7.14 var sap2000Db = new Vector(-0.014834, -0.085475, -0.144533); //tbl 7.14 Console.WriteLine("Err at A against Sap2000 (displacement): {0:0.0}%", GetError(da, sap2000Da)); Console.WriteLine("Err at B against Sap2000 (displacement): {0:0.0}%", GetError(db, sap2000Db)); { //stresses var cElms = model.Elements.Cast <TriangleFlatShell>().Where(i => i.Nodes.Contains(C)).ToArray(); var DElms = model.Elements.Cast <TriangleFlatShell>().Where(i => i.Nodes.Contains(D)).ToArray(); var EElms = model.Elements.Cast <TriangleFlatShell>().Where(i => i.Nodes.Contains(E)).ToArray(); var globTensor = new Func <TriangleFlatShell, MembraneStressTensor>(elm => { var tns = elm.GetInternalForce(0, 0, LoadCombination.DefaultLoadCombination); var rt = elm.RotateTensor(tns.MembraneTensor, Plane.YZPlane); return(rt); }); var cSy = cElms.Select(i => globTensor(i)) .Select(i => MembraneStressTensor.Multiply(i, UnitConverter.Pas2Psi(1) / 1000)) .Max(i => Math.Abs(i.Sy)); var dSx = DElms.Select(i => globTensor(i)) .Select(i => MembraneStressTensor.Multiply(i, UnitConverter.Pas2Psi(1) / 1000)) .Max(i => Math.Abs(i.Sx)); var eTxy = EElms.Select(i => globTensor(i)) .Select(i => MembraneStressTensor.Multiply(i, UnitConverter.Pas2Psi(1) / 1000)) .Max(i => Math.Abs(i.Txy)); Console.WriteLine("S11 at C against Sap2000 (stress tensor): {0:0.0}%", GetError(cSy, 5.441)); Console.WriteLine("S22 at D against Sap2000 (stress tensor): {0:0.0}%", GetError(dSx, 2.009)); Console.WriteLine("S21 at E against Sap2000 (stress tensor): {0:0.0}%", GetError(eTxy, 1.450)); } }
public static void Test6_2() { Console.WriteLine("Example 13: I Beam With Flat Shell, BFE vs ABAQUS"); var magic = 0; //example #13 p175 #region creating model var model = new Model(); var l = UnitConverter.In2M(40); var w = UnitConverter.In2M(10); var h = UnitConverter.In2M(5); var t = UnitConverter.In2M(0.25); var e = UnitConverter.Ksi2Pas(10000); //10'000 ksi var no = 0.3; var n = 9; var xSpan = l / (n - 1); var nodes = new Node[n][]; for (var i = 0; i < n; i++) { var x = i * xSpan; nodes[i] = new Node[7]; nodes[i][0] = new Node(x, 0, 0); nodes[i][1] = new Node(x, w / 2, 0); nodes[i][2] = new Node(x, w, 0); nodes[i][3] = new Node(x, w / 2, h / 2); nodes[i][4] = new Node(x, 0, h); nodes[i][5] = new Node(x, w / 2, h); nodes[i][6] = new Node(x, w, h); model.Nodes.AddRange(nodes[i]); } var pairs = new int[6][]; pairs[0] = new int[] { 0, 1 }; pairs[1] = new int[] { 1, 2 }; pairs[2] = new int[] { 1, 3 }; pairs[3] = new int[] { 3, 5 }; pairs[4] = new int[] { 4, 5 }; pairs[5] = new int[] { 5, 6 }; for (var i = 0; i < n - 1; i++) { for (int j = 0; j < 6; j++) { var n11 = nodes[i][pairs[j][0]]; var n12 = nodes[i][pairs[j][1]]; var n21 = nodes[i + 1][pairs[j][0]]; var n22 = nodes[i + 1][pairs[j][1]]; { var elm1 = new TriangleFlatShell() { Thickness = t, PoissonRatio = no, ElasticModulus = e }; elm1.Nodes[0] = n11; elm1.Nodes[1] = n12; elm1.Nodes[2] = n21; model.Elements.Add(elm1); var elm2 = new TriangleFlatShell() { Thickness = t, PoissonRatio = no, ElasticModulus = e }; elm2.Nodes[0] = n21; elm2.Nodes[1] = n22; elm2.Nodes[2] = n12; model.Elements.Add(elm2); } } } //loading nodes.Last()[0].Loads.Add(new NodalLoad(new Force(0, UnitConverter.Kip2N(1.6), 0, 0, 0, 0))); nodes.Last()[6].Loads.Add(new NodalLoad(new Force(0, -UnitConverter.Kip2N(1.6), 0, 0, 0, 0))); nodes[0].ToList().ForEach(i => i.Constraints = Constraint.Fixed); #endregion model.Trace.Listeners.Add(new BriefFiniteElementNet.ConsoleTraceListener()); new ModelWarningChecker().CheckModel(model); //ModelVisualizerControl.VisualizeInNewWindow(model); model.Solve(); var A = nodes.Last()[2]; var B = nodes.Last()[4]; var C = nodes.First()[1]; var D = nodes.First()[0]; var E = nodes.Last()[6]; /* * for (int i = 0; i < nodes.Last().Length; i++) * { * nodes.Last()[i].Label = i.ToString(); * } */ /**/ A.Label = "A"; B.Label = "B"; C.Label = "C"; D.Label = "D"; E.Label = "E"; /**/ for (int i = 0; i < model.Elements.Count; i++) { model.Elements[i].Label = i.ToString(); } var da = 1 / 0.0254 * A.GetNodalDisplacement().Displacements; // [inch] var db = 1 / 0.0254 * B.GetNodalDisplacement().Displacements; // [inch] var abaqusDa = new Vector(-15.4207E-03, 88.2587E-03, 150.910E-03); var abaqusDb = new Vector(-15.3246E-03, -88.2629E-03, -148.940E-03); Console.WriteLine("Err at A against ABAQUS (displacement): {0:0.000}%", GetError(da, abaqusDa)); Console.WriteLine("Err at B against ABAQUS (displacement): {0:0.000}%", GetError(db, abaqusDb)); { var abaqusElms = new int[] { 96, 89, 57, 41 }; var bfeElms = new[] { 0, 37, 40, 42 }.Select(i => model.Elements[i]).Cast <TriangleFlatShell>().ToArray(); var bfeTensors = bfeElms.Select(i => i.GetInternalForce(0, 0, LoadCombination.DefaultLoadCombination).MembraneTensor).ToArray(); var abaqusTensors = new MembraneStressTensor[] { new MembraneStressTensor() //elm 96 { Sx = Avg(7.36164, 6.88581, 7.48463 /**/, 8.14348, 8.61931, 8.02049 /**/), Sy = Avg(2.16196, 2.01921, 2.05925 /**/, 2.48958, 2.63233, 2.59229 /**/), Txy = Avg(2.27915, 2.33284, 2.49939 /**/, 2.01766, 1.96396, 1.79742 /**/) }, new MembraneStressTensor() //elm 89 { Sx = Avg(-230.883E-03, -268.773E-03, -226.600E-03, -157.940E-03, -120.050E-03, -162.222E-03), Sy = Avg(-646.591E-03, -591.701E-03, -523.641E-03, -278.264E-03, -333.154E-03, -401.214E-03), Txy = -Avg(676.247E-03, 663.707E-03, 701.730E-03, -1.09379, -1.08125, -1.11928) }, new MembraneStressTensor() { Sx = Avg(-398.693E-03, -205.937E-03, -124.743E-03, 280.574E-03, 87.8183E-03, 6.62372E-03), Sy = Avg(-634.569E-03, -402.618E-03, -100.092E-03, 612.059E-03, 380.109E-03, 77.5826E-03), Txy = Avg(838.081E-03, 925.471E-03, 871.566E-03, -881.344E-03, -968.735E-03, -914.829E-03) }, new MembraneStressTensor() { Sx = Avg(-18.7201E-03, 127.473E-03, 288.131E-03, 4.04619E-03, -142.147E-03, -302.805E-03), Sy = Avg(11.1952E-03, 174.315E-03, 540.586E-03, -37.4831E-03, -200.603E-03, -566.874E-03), Txy = Avg(842.951E-03, 956.823E-03, 865.886E-03, -882.801E-03, -996.674E-03, -905.736E-03) }, }; var globTensor = new Func <TriangleFlatShell, MembraneStressTensor>(elm => { var tns = elm.GetInternalForce(0, 0, LoadCombination.DefaultLoadCombination); var rt = elm.RotateTensor(tns.MembraneTensor, Plane.XZPlane); return(rt); }); for (int i = 0; i < bfeTensors.Length; i++) { var bfeTensor = bfeTensors[i]; bfeTensor = globTensor(bfeElms[i]); bfeTensor = MembraneStressTensor.Multiply(bfeTensor, -UnitConverter.Pas2Psi(1) / 1000); var abaqusTensor = abaqusTensors[i]; Console.WriteLine("Err against ABAQUS (AVG stress tensor) @ elm {1}: {0:0.000}%", GetError(bfeTensor, abaqusTensor), abaqusElms[i]); } } }
public static void Test3() { //example #2 p118 Console.WriteLine("Example 2: CST element Test"); #region creating model var model = new Model(); var l = 48 * 0.0254; //in [m] var b = 12 * 0.0254; // var t = 1 * 0.0254; var e = 206842772603; //30000 ksi var no = 0.25; //Poisson ratio var n = 9; var m = 3; var span = l / (n - 1); var nodes = new Node[n][]; for (var i = 0; i < n; i++) { nodes[i] = new Node[m]; for (var j = 0; j < m; j++) { model.Nodes.Add(nodes[i][j] = new Node(i * span, j * span, 0)); if (i == 0) { nodes[i][j].Constraints = Constraint.Fixed; } var newCns = new Constraint( DofConstraint.Released, DofConstraint.Released, DofConstraint.Fixed, DofConstraint.Fixed, DofConstraint.Fixed, DofConstraint.Fixed); nodes[i][j].Constraints = nodes[i][j].Constraints & newCns; } } var tp = MembraneFormulation.PlaneStress; for (var i = 0; i < n - 1; i++) { for (var j = 0; j < m - 1; j++) { var elm1 = new TriangleFlatShell() { ElasticModulus = e, PoissonRatio = no, Thickness = t, Behavior = FlatShellBehaviour.Membrane, MembraneFormulationType = tp }; elm1.Nodes[2] = nodes[i][j + 1]; elm1.Nodes[1] = nodes[i + 1][j + 1]; elm1.Nodes[0] = nodes[i + 1][j]; model.Elements.Add(elm1); var elm2 = new TriangleFlatShell() { ElasticModulus = e, PoissonRatio = no, Thickness = t, Behavior = FlatShellBehaviour.Membrane, MembraneFormulationType = tp }; elm2.Nodes[2] = nodes[i][j]; elm2.Nodes[1] = nodes[i][j + 1]; elm2.Nodes[0] = nodes[i + 1][j]; model.Elements.Add(elm2); } } var pt = 177928.864; //40 kips nodes.Last()[0].Loads.Add(new NodalLoad(new Force(0, pt / 6, 0, 0, 00, 0))); nodes.Last()[1].Loads.Add(new NodalLoad(new Force(0, 4 * pt / 6, 0, 0, 00, 0))); nodes.Last()[2].Loads.Add(new NodalLoad(new Force(0, pt / 6, 0, 0, 00, 0))); #endregion model.Trace.Listeners.Add(new BriefFiniteElementNet.ConsoleTraceListener()); new ModelWarningChecker().CheckModel(model); model.Solve(); var d8 = 1 / 0.0254 * nodes[4].Last().GetNodalDisplacement().Displacements; var d10 = 1 / 0.0254 * nodes.Last().Last().GetNodalDisplacement().Displacements; var sap2000D8 = new Vector(-0.025605, 0.062971, 0); var sap2000D10 = new Vector(-0.034271, 0.194456, 0); Console.WriteLine("Err at A against Sap2000 (displacement): {0:0.0}%", GetError(d8, sap2000D8)); Console.WriteLine("Err at B against Sap2000 (displacement): {0:0.0}%", GetError(d10, sap2000D10)); { //write internal forces var targetNode = nodes.First().First(); //stress at support node var targetElement = model.Elements.FirstOrDefault(i => i.Nodes.Contains(targetNode)); var localS = (targetElement as TriangleFlatShell).GetInternalForce(0, 0, LoadCombination.DefaultLoadCombination); //tensor in local coordinate system var globalS = (targetElement as TriangleFlatShell).RotateTensor(localS.MembraneTensor, Plane.XZPlane); //tensor in global coordinate system var s6 = MembraneStressTensor.Multiply(globalS, UnitConverter.Pas2Psi(1) / 1000); var sap2000S6 = new MembraneStressTensor() { Sx = -41.493, Sy = -10.37, Txy = 11.84 }; Console.WriteLine("Err at node 6 against Sap2000 (stress): {0:0.0}%", GetError(s6, sap2000S6)); } }