public static void TestSingleElement()
{
var model = new Model();
var elm = new TriangleElement();
var arr = new[]
{
new Node(1, 1, 0),
new Node(3.25, 0.5, 0),
new Node(3.733, 1.92, 0),
};
arr.CopyTo(elm.Nodes, 0);
model.Nodes.AddRange(arr);
model.Elements.Add(elm);
model.Nodes[2].Loads.Add(new NodalLoad(new Force(1, 1, 1, 1, 1, 1) * -5000));
model.Nodes[0].Constraints =
model.Nodes[1].Constraints =
Constraints.Fixed;
elm.Behavior = TriangleElementBehaviours.Shell;
elm.MembraneFormulation = MembraneFormulation.PlaneStress;
elm.Material = new UniformIsotropicMaterial(2100, 0.3);
elm.Section = new UniformParametric2DSection(0.2);
model.Solve();
Console.WriteLine(model.Nodes[2].GetNodalDisplacement().ToString(5));
//var force = elm.GetLocalInternalForceAt(LoadCase.DefaultLoadCase, -0.57735, -0.57735);
}
private static void TestTriangle()
{
var t = 0.01;
var e = 210e9;
var nu = 0.2;
var n1 = new Node(new Point(0, 0, 0));
var n2 = new Node(new Point(3, 5, 7));
var n3 = new Node(new Point(1, -5, 4));
var dkt = new TriangleFlatShell()
{
Behavior = PlaneElementBehaviour.ThinPlate,
PoissonRatio = nu,
ElasticModulus = e,
Thickness = t
};
dkt.Nodes[0] = n1;
dkt.Nodes[1] = n2;
dkt.Nodes[2] = n3;
var tri = new TriangleElement();
tri.Behavior = PlateElementBehaviours.Shell;
tri.Section = new UniformParametric2DSection()
{
T = t
};
tri.Material = new UniformIsotropicMaterial(e, nu);// {E = e, Nu = nu};
tri.Nodes[0] = n1;
tri.Nodes[1] = n2;
tri.Nodes[2] = n3;
var kTri = tri.GetLocalStifnessMatrix();
var kDkt = dkt.GetLocalPlateBendingStiffnessMatrix();
var d = kTri - kDkt;
var xi = 0.162598494;
var eta = 0.284984989;
var b1 = new DktHelper().GetBMatrixAt(tri, xi, eta);
var lpts = dkt.GetLocalPoints();
var b2 = DktElement.GetBMatrix(xi, eta,
new[] { lpts[0].X, lpts[1].X, lpts[2].X },
new[] { lpts[0].Y, lpts[1].Y, lpts[2].Y });
// new DktHelper().GetBMatrixAt(tri, tri.GetTransformationMatrix(), xi, eta);
tri.GetLocalStifnessMatrix();
//GC.Collect();
var db = b1 - b2;
}
/// <summary>
/// Reads an element from an Abaqus input file
/// </summary>
/// <param name="elementline">A line with the element props</param>
/// <param name="delimiter">The separator char</param>
/// <param name="nodes">A list of nodes - starts at 0 -> = node-1</param>
/// <returns>An element</returns>
private static TriangleElement ReadTriangleElement(string elementline, char delimiter, NodeCollection nodes)
{
var elm = new TriangleElement();
string[] split;
int elementNr;//, nodeNr1, nodeNr2, nodeNr3, nodeNr4;
try
{
split = elementline.Split(delimiter);
elementNr = Convert.ToInt32(split[0]);
//subtract 1. The nodes are numbered from 1-> end and are stored as 0-> end-1
elm.Nodes[0] = nodes[Convert.ToInt32(split[1]) - 1];
elm.Nodes[1] = nodes[Convert.ToInt32(split[2]) - 1];
elm.Nodes[2] = nodes[Convert.ToInt32(split[3]) - 1];
elm.label = elementNr.ToString();
}
catch (Exception ex)
{
throw new Exception("Something went wrong with reading the nodes! Error with line: " + elementline);
}
return(elm);
}
public void Dkt_GetBMatrix()
{
var element = new TriangleElement();
element.Nodes[0] = new Node(1, 2, 3);
element.Nodes[1] = new Node(4, 5, 6);
element.Nodes[2] = new Node(7, 8, 9);
var helper = new DktHelper();
var b = helper.GetBMatrixAt(element, 0, 0, 0);
var exact = new Matrix(3, 6);
}
public static Model Generate3DTriangleElementGridTest(int m, int n, int l)
{
var buf = new Model();
var dx = 0.15;
var dy = 0.15;
var dz = 0.15;
var nodes = new Node[m, n, l];
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
for (int k = 0; k < l; k++)
{
var pos = new Point(j * dx, i * dy, k * dz);
var nde = new Node()
{
Location = pos
};
buf.Nodes.Add(nde);
nodes[i, j, k] = nde;
}
}
}
//elements parallel to XZ
for (int j = 0; j < n; j++)
{
for (int i = 0; i < m - 1; i++)
{
for (int k = 0; k < l - 1; k++)
{
{
var elm2 = new TriangleElement();
elm2.Nodes[0] = nodes[i, j, k];
elm2.Nodes[1] = nodes[i, j, k + 1];
elm2.Nodes[2] = nodes[i + 1, j, k];
buf.Elements.Add(elm2);
}
{
var elm2 = new TriangleElement();
elm2.Nodes[0] = nodes[i + 1, j, k + 1];
elm2.Nodes[1] = nodes[i, j, k + 1];
elm2.Nodes[2] = nodes[i + 1, j, k];
buf.Elements.Add(elm2);
}
}
}
}
//elements parallel to YZ
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n - 1; j++)
{
for (int k = 0; k < l - 1; k++)
{
{
var elm2 = new TriangleElement();
elm2.Nodes[0] = nodes[i, j, k];
elm2.Nodes[1] = nodes[i, j, k + 1];
elm2.Nodes[2] = nodes[i, j + 1, k];
buf.Elements.Add(elm2);
}
{
var elm2 = new TriangleElement();
elm2.Nodes[0] = nodes[i, j + 1, k + 1];
elm2.Nodes[1] = nodes[i, j, k + 1];
elm2.Nodes[2] = nodes[i, j + 1, k];
buf.Elements.Add(elm2);
}
}
}
}
//elements parallel to XY
for (int k = 0; k < l; k++)
{
for (int j = 0; j < n - 1; j++)
{
for (int i = 0; i < m - 1; i++)
{
{
var elm2 = new TriangleElement();
elm2.Nodes[0] = nodes[i, j, k];
elm2.Nodes[1] = nodes[i + 1, j, k];
elm2.Nodes[2] = nodes[i, j + 1, k];
buf.Elements.Add(elm2);
}
{
var elm2 = new TriangleElement();
elm2.Nodes[0] = nodes[i + 1, j + 1, k];
elm2.Nodes[1] = nodes[i + 1, j, k];
elm2.Nodes[2] = nodes[i, j + 1, k];
buf.Elements.Add(elm2);
}
}
}
}
foreach (var elm in buf.Elements)
{
var triElm = elm as TriangleElement;
if (triElm == null)
{
continue;
}
triElm.Behavior = PlateElementBehaviours.Shell;
var h = 0.03;
var w = 0.003;
var e = 210e9;
var nu = 0.3;
var sec = (Sections.UniformParametric2DSection)(triElm.Section = new Sections.UniformParametric2DSection());
var mat = triElm.Material = Materials.UniformIsotropicMaterial.CreateFromYoungPoisson(e, nu);
sec.T = 0.003;
}
for (int i = 0; i < m; i++)
{
nodes[i, 0, 0].Constraints = Constraint.Fixed;
}
for (int i = 0; i < m; i++)
{
nodes[i, n - 1, 0].Loads.Add(new NodalLoad(new Force(1500, 0, 0, 0, 0, 0), LoadCase.DefaultLoadCase));
}
return(buf);
}
/// <summary>
///
/// </summary>
/// <param name="m">number of levels in X direction</param>
/// <param name="n">number of levels in Y direction</param>
/// <param name="l">number of levels in Z direction</param>
/// <returns></returns>
public static Model Generate3DTriangleElementGrid(int m, int n, int l)
{
var buf = new Model();
var dx = 1.0;
var dy = 1.0;
var dz = 1.0;
var nodes = new Node[m, n, l];
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
for (int k = 0; k < l; k++)
{
var pos = new Point(j * dx, i * dy, k * dz);
var nde = new Node()
{
Location = pos
};
buf.Nodes.Add(nde);
nodes[i, j, k] = nde;
}
}
}
//elements parallel to XZ
for (int j = 0; j < n; j++)
{
for (int i = 0; i < m - 1; i++)
{
for (int k = 0; k < l - 1; k++)
{
{
var elm2 = new TriangleElement();
elm2.Nodes[0] = nodes[i, j, k];
elm2.Nodes[1] = nodes[i, j, k + 1];
elm2.Nodes[2] = nodes[i + 1, j, k];
buf.Elements.Add(elm2);
}
{
var elm2 = new TriangleElement();
elm2.Nodes[0] = nodes[i + 1, j, k + 1];
elm2.Nodes[1] = nodes[i, j, k + 1];
elm2.Nodes[2] = nodes[i + 1, j, k];
buf.Elements.Add(elm2);
}
}
}
}
//elements parallel to YZ
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n - 1; j++)
{
for (int k = 0; k < l - 1; k++)
{
{
var elm2 = new TriangleElement();
elm2.Nodes[0] = nodes[i, j, k];
elm2.Nodes[1] = nodes[i, j, k + 1];
elm2.Nodes[2] = nodes[i, j + 1, k];
buf.Elements.Add(elm2);
}
{
var elm2 = new TriangleElement();
elm2.Nodes[0] = nodes[i, j + 1, k + 1];
elm2.Nodes[1] = nodes[i, j, k + 1];
elm2.Nodes[2] = nodes[i, j + 1, k];
buf.Elements.Add(elm2);
}
}
}
}
//elements parallel to XY
for (int k = 0; k < l; k++)
{
for (int j = 0; j < n - 1; j++)
{
for (int i = 0; i < m - 1; i++)
{
{
var elm2 = new TriangleElement();
elm2.Nodes[0] = nodes[i, j, k];
elm2.Nodes[1] = nodes[i + 1, j, k];
elm2.Nodes[2] = nodes[i, j + 1, k];
buf.Elements.Add(elm2);
}
{
var elm2 = new TriangleElement();
elm2.Nodes[0] = nodes[i + 1, j + 1, k];
elm2.Nodes[1] = nodes[i + 1, j, k];
elm2.Nodes[2] = nodes[i, j + 1, k];
buf.Elements.Add(elm2);
}
}
}
}
foreach (var elm in buf.Elements)
{
var triElm = elm as TriangleElement;
if (triElm == null)
{
continue;
}
triElm.Behavior = PlateElementBehaviours.Shell;
var h = RandomHelper.GetRandomNumber(0.01, 0.1);
var w = RandomHelper.GetRandomNumber(0.01, 0.1);
var e = RandomHelper.GetRandomNumber(100e9, 200e9);
var nu = RandomHelper.GetRandomNumber(0.2, 0.3);
var sec = (Sections.UniformParametric2DSection)(triElm.Section = new Sections.UniformParametric2DSection());
var mat = triElm.Material = Materials.UniformIsotropicMaterial.CreateFromYoungPoisson(e, nu);
sec.T = 0.1;
}
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
nodes[i, j, 0].Constraints = Constraint.Fixed;
}
}
return(buf);
}
public ValidationResult Validate()
{
var val = new ValidationResult();
val.Title = "I Beam torsion with triangle element";
var span = val.Span = new HtmlTag("span");
{//report
span.Add("p").Text("Validate an I Beam nodal displacement and reactions and internal forces");
span.Add("h3").Text("Validate with");
span.Add("paragraph").Text("SAP2000");
span.Add("h3").Text("Validate objective");
span.Add("paragraph").Text("compare nodal displacement for a model consist of Triangle Elements");
span.Add("h3").Text("Model Definition");
span.Add("paragraph")
.Text("An I shaped beam, totally fixed on one side and under a couple force on other side")
.AddClosedTag("br");
span.Add("h3").Text("Validation Result");
}
//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 };
var mat = new Materials.UniformIsotropicMaterial(e, no);
var sec = new Sections.UniformParametric2DSection(t);
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 TriangleElement()
{
Material = mat, Section = sec
};
elm1.Nodes[0] = n11;
elm1.Nodes[1] = n12;
elm1.Nodes[2] = n21;
model.Elements.Add(elm1);
var elm2 = new TriangleElement()
{
Material = mat, Section = sec
};
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 = Constraints.Fixed);
#endregion
model.Trace.Listeners.Add(new BriefFiniteElementNet.Common.ConsoleTraceListener());
new ModelWarningChecker().CheckModel(model);
model.Solve_MPC();
//show the model
//ModelVisualizer.TestShowVisualizer(model);
//generate a list of all results
List <string> results = new List <string>();
results.Add("Index ; S11 ; S12 ; S13 ; S21 ; S22 ; S23 ; S31 ; S32 ; S33 ; SVM");
foreach (var element in model.Elements)
{
var el = (TriangleElement)element;
var index = el.GetIndex();
var cauchy = el.GetInternalStress(new double[] { 0.166666666, 0.1666666, 1.0 }, LoadCombination.DefaultLoadCombination, SectionPoints.Envelope);
results.Add(index + ";" + cauchy.S11 + ";" + cauchy.S12 + ";" + cauchy.S13 + ";" + cauchy.S21 + ";" + cauchy.S22 + ";" + cauchy.S23
+ ";" + cauchy.S31 + ";" + cauchy.S32 + ";" + cauchy.S33 + ";" + CauchyStressTensor.GetVonMisesStress(cauchy));
cauchy = el.GetInternalStress(new double[] { 0.6666666, 0.1666666, 1.0 }, LoadCombination.DefaultLoadCombination, SectionPoints.Envelope);
results.Add(index + ";" + cauchy.S11 + ";" + cauchy.S12 + ";" + cauchy.S13 + ";" + cauchy.S21 + ";" + cauchy.S22 + ";" + cauchy.S23
+ ";" + cauchy.S31 + ";" + cauchy.S32 + ";" + cauchy.S33 + ";" + CauchyStressTensor.GetVonMisesStress(cauchy));
cauchy = el.GetInternalStress(new double[] { 0.166666666, 0.6666666, 1.0 }, LoadCombination.DefaultLoadCombination, SectionPoints.Envelope);
results.Add(index + ";" + cauchy.S11 + ";" + cauchy.S12 + ";" + cauchy.S13 + ";" + cauchy.S21 + ";" + cauchy.S22 + ";" + cauchy.S23
+ ";" + cauchy.S31 + ";" + cauchy.S32 + ";" + cauchy.S33 + ";" + CauchyStressTensor.GetVonMisesStress(cauchy));
}
//Write data if needed
//File.WriteAllLines("Insert path here!!", results.ToArray());
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 n50 = model.Nodes[50];
var n56 = model.Nodes[56];
var n57 = model.Nodes[57];
{//nodal displacements
span.Add("h4").Text("Nodal Displacements");
span.Add("paragraph").Text(string.Format("Validation output for nodal displacements:"));
var da = 1 / 0.0254 * A.GetNodalDisplacement().Displacements; // [inch]
var db = 1 / 0.0254 * B.GetNodalDisplacement().Displacements; // [inch]
var d50 = 1 / 0.0254 * n50.GetNodalDisplacement().Displacements; // [inch]
var d56 = 1 / 0.0254 * n56.GetNodalDisplacement().Displacements; // [inch]
var d57 = 1 / 0.0254 * n57.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
var abaqusDa = new Vector(-15.4207E-03, 88.2587E-03, 150.910E-03); //node 9
var abaqusDb = new Vector(-15.3246E-03, -88.2629E-03, -148.940E-03); //node 5
var abaqus8 = new Vector(-120.875E-06, 88.3894E-03, -1.01662E-03); //node 8
var abaqus12 = new Vector(15.3931E-03, 89.1206E-03, -149.515E-03); //node 12
var abaqus41 = new Vector(-189.084E-06, 72.3778E-03, -734.918E-06); //node 41
span.Add("paragraph").Text(string.Format("Validation output for nodal displacements:"));
span.Add("paragraph").Text(string.Format("Err at node A (displacement): {0:0.00}%", Util.GetErrorPercent(da, abaqusDa))).AddClosedTag("br");;
span.Add("paragraph").Text(string.Format("Err at node B (displacement): {0:0.00}%", Util.GetErrorPercent(db, abaqusDb))).AddClosedTag("br");;
span.Add("paragraph").Text(string.Format("Err at node 41 (57) (displacement): {0:0.00}%", Util.GetErrorPercent(d50, abaqus41))).AddClosedTag("br");;
span.Add("paragraph").Text(string.Format("Err at node 12 (56) (displacement): {0:0.00}%", Util.GetErrorPercent(d56, abaqus12))).AddClosedTag("br");;
span.Add("paragraph").Text(string.Format("Err at node 08 (50) (displacement): {0:0.00}%", Util.GetErrorPercent(d57, abaqus8))).AddClosedTag("br");;
}
{//element stress
{
var e81 = model.Elements[85] as TriangleElement;
var tr = e81.GetTransformationManager();
//t = 1/t;
var am = tr.TransformLocalToGlobal(e81.GetLocalInternalStress(LoadCase.DefaultLoadCase, 1 / 6.0, 1 / 6.0, 0) * (1 / t));
var at = tr.TransformLocalToGlobal(e81.GetLocalInternalStress(LoadCase.DefaultLoadCase, 1 / 6.0, 1 / 6.0, +1) * (1 / t));
var ab = tr.TransformLocalToGlobal(e81.GetLocalInternalStress(LoadCase.DefaultLoadCase, 1 / 6.0, 1 / 6.0, -1) * (1 / t));
var bm = tr.TransformLocalToGlobal(e81.GetLocalInternalStress(LoadCase.DefaultLoadCase, 4 / 6.0, 1 / 6.0, 0) * (1 / t));
var bt = tr.TransformGlobalToLocal(e81.GetLocalInternalStress(LoadCase.DefaultLoadCase, 4 / 6.0, 1 / 6.0, +1) * (1 / t));
var bb = tr.TransformLocalToGlobal(e81.GetLocalInternalStress(LoadCase.DefaultLoadCase, 4 / 6.0, 1 / 6.0, -1) * (1 / t));
var cm = tr.TransformLocalToGlobal(e81.GetLocalInternalStress(LoadCase.DefaultLoadCase, 1 / 6.0, 4 / 6.0, 0) * (1 / t));
var ct = tr.TransformLocalToGlobal(e81.GetLocalInternalStress(LoadCase.DefaultLoadCase, 1 / 6.0, 4 / 6.0, +1) * (1 / t));
var cb = tr.TransformLocalToGlobal(e81.GetLocalInternalStress(LoadCase.DefaultLoadCase, 1 / 6.0, 4 / 6.0, -1) * (1 / t));
var abacus_at = new CauchyStressTensor()
{
S11 = 103.814E-03, S22 = 249.185E-03, S12 = 1.03438, S21 = 1.03438
} *-1e9;
var abacus_bt = new CauchyStressTensor()
{
S11 = -34.7168E-03, S22 = -538.942E-03, S12 = 1.03438, S21 = 1.08243
} *-1e9;
var abacus_ct = new CauchyStressTensor()
{
S11 = -201.062E-03, S22 = -1.18348, S12 = 747.243E-03, S21 = 747.243E-03
} *-1e9;
var e1 = Util.GetErrorPercent(at, abacus_ct);
var e2 = Util.GetErrorPercent(bt, abacus_at);
var e3 = Util.GetErrorPercent(ct, abacus_bt);
span.Add("paragraph").Text(string.Format("Validation output for element stress:"));
span.Add("paragraph").Text(string.Format("Err at p1 element 81 (stress): {0:0.00}%", e1)).AddClosedTag("br");
span.Add("paragraph").Text(string.Format("Err at p2 element 81 (stress): {0:0.00}%", e2)).AddClosedTag("br");
span.Add("paragraph").Text(string.Format("Err at p3 element 81 (stress): {0:0.00}%", e3)).AddClosedTag("br");
//in abaqus e81 connected to 8-12-41
//in bfe e85 connected to 57-56-50
}
}
return(val);
}
public override TriangleCoordinatedMechanicalProperties GetMaterialPropertiesAt(TriangleElement targetElement, params double[] isoCoords)
{
var buf = new TriangleCoordinatedMechanicalProperties();
var mat = new AnisotropicMaterialInfo();
mat.Ex = mat.Ey = mat.Ez = this.E;
mat.NuXy = mat.NuYx =
mat.NuYz = mat.NuZy =
mat.NuXz = mat.NuZx =
this.Nu;
buf.Matterial = mat;
return(buf);
}
/// <summary>
/// convert abaqus iso coords to bfe coords
/// </summary>
/// <param name="elm">target triangle element</param>
/// <param name="elementTransformation">target triangle element</param>
/// <param name="v">coordinations in <see cref="elm"/>'s local coordination system (abaqus)</param>
/// <returns></returns>
public static double[] AbaqusCoord2BfeCoord(TriangleElement elm, Vector v)
{
///abaqus local coordination def: comment from https://engineering.stackexchange.com/questions/48285/abaqus-stri3-element-local-coordination-system?noredirect=1#comment87622_48285
///bfe local coordination def: comment from
{
//abaqus
var v12 = elm.Nodes[1].Location - elm.Nodes[0].Location; //from node 2 to node 1
var v13 = elm.Nodes[2].Location - elm.Nodes[0].Location; //from node 3 to node 1
var n = Vector.Cross(v12, v13).GetUnit(); //unit of positive normal
var cosOneTenth = Math.Cos(0.1 * Math.PI / 180); //cos(0.1 deg)
var takeI = false; //take projection of I vector as local x dir
var cos_normal_i = Vector.Dot(n, Vector.I); //cos angle between I and positive normal unit
var angle_n_i = Math.Acos(cos_normal_i) * 180.0 / Math.PI;
//due to Math.Acos documentation, 0° ≤ angle_n_i ≤ 180°
if (angle_n_i < 179.9 && angle_n_i > 0.1)
{
takeI = true;
}
else
{
takeI = false;
}
var _1Axis = takeI ? Vector.I : Vector.J;//needs to be projected on the plane with normal of `n`
//vector to plane project https://www.maplesoft.com/support/help/maple/view.aspx?path=MathApps%2FProjectionOfVectorOntoPlane
var alpha = Vector.Dot(n, _1Axis) / n.Length;
var proj1 = _1Axis - alpha * n; //it is local x axis
var local1 = proj1; //local x axis in global 3d
var local3 = n; //local y axis in global 3d
var local2 = Vector.Cross(local3, local1); //local z axis in global 3d
var lamX = local1.GetUnit(); //Lambda_X
var lamY = local2.GetUnit(); //Lambda_Y
var lamZ = local3.GetUnit(); //Lambda_Z
var lambda = Matrix.OfJaggedArray(new[] //eq. 5.13
{
new[] { lamX.X, lamY.X, lamZ.X },
new[] { lamX.Y, lamY.Y, lamZ.Y },
new[] { lamX.Z, lamY.Z, lamZ.Z }
});
var tr = TransformManagerL2G.MakeFromLambdaMatrix(lambda.AsMatrix());
//lambda for transform between abaqus local coordination system <> global system
//first need to convert v from element coord system to
//TODO: these are right only if both abaqus and bfe local system origins are same
Vector local;
{//transform from abaus local to bfe local
var abaqusLocal = v;
var global = tr.TransformLocalToGlobal(abaqusLocal);
var bfeLocal = elm.GetTransformationManager().TransformGlobalToLocal(global);
local = bfeLocal;
}
return(new double[] { local.X, local.Y, local.Z });
}
}
public ValidationResult Validate()
{
var val = new ValidationResult();
//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 };
var mat = new Materials.UniformIsotropicMaterial(e, no);
var sec = new Sections.UniformParametric2DSection(t);
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 TriangleElement()
{
Material = mat, Section = sec
};
elm1.Nodes[0] = n11;
elm1.Nodes[1] = n12;
elm1.Nodes[2] = n21;
model.Elements.Add(elm1);
var elm2 = new TriangleElement()
{
Material = mat, Section = sec
};
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 = Constraints.Fixed);
#endregion
model.Trace.Listeners.Add(new BriefFiniteElementNet.Common.ConsoleTraceListener());
new ModelWarningChecker().CheckModel(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 n50 = model.Nodes[50];
var n56 = model.Nodes[56];
var n57 = model.Nodes[57];
val.Title = "I Beam torsion with triangle element";
var da = 1 / 0.0254 * A.GetNodalDisplacement().Displacements; // [inch]
var db = 1 / 0.0254 * B.GetNodalDisplacement().Displacements; // [inch]
var d50 = 1 / 0.0254 * n50.GetNodalDisplacement().Displacements; // [inch]
var d56 = 1 / 0.0254 * n56.GetNodalDisplacement().Displacements; // [inch]
var d57 = 1 / 0.0254 * n57.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
var abaqusDa = new Vector(-15.4207E-03, 88.2587E-03, 150.910E-03); //node 9
var abaqusDb = new Vector(-15.3246E-03, -88.2629E-03, -148.940E-03); //node 5
var abaqus8 = new Vector(-120.875E-06, 88.3894E-03, -1.01662E-03); //node 8
var abaqus12 = new Vector(15.3931E-03, 89.1206E-03, -149.515E-03); //node 12
var abaqus41 = new Vector(-189.084E-06, 72.3778E-03, -734.918E-06); //node 41
Console.WriteLine("Err at A against abaqus (displacement): {0:0.00}%", GetError(da, abaqusDa));
Console.WriteLine("Err at B against abaqus (displacement): {0:0.00}%", GetError(db, abaqusDb));
Console.WriteLine("Err at 41 (57) against abaqus (displacement): {0:0.00}%", GetError(d50, abaqus41));
Console.WriteLine("Err at 12 (56) against abaqus (displacement): {0:0.00}%", GetError(d56, abaqus12));
Console.WriteLine("Err at 08 (50) against abaqus (displacement): {0:0.00}%", GetError(d57, abaqus8));
model.ReIndexElements();
model.ReIndexNodes();
//ModelVisualizerControl.VisualizeInNewWindow(model);
{
var e81 = model.Elements[85] as TriangleElement;
var tr = e81.GetTransformationManager();
//t = 1/t;
var am = tr.TransformLocalToGlobal(e81.GetLocalInternalStress(LoadCase.DefaultLoadCase, 1 / 6.0, 1 / 6.0, 0) * (1 / t));
var at = tr.TransformLocalToGlobal(e81.GetLocalInternalStress(LoadCase.DefaultLoadCase, 1 / 6.0, 1 / 6.0, +1) * (1 / t));
var ab = tr.TransformLocalToGlobal(e81.GetLocalInternalStress(LoadCase.DefaultLoadCase, 1 / 6.0, 1 / 6.0, -1) * (1 / t));
var bm = tr.TransformLocalToGlobal(e81.GetLocalInternalStress(LoadCase.DefaultLoadCase, 4 / 6.0, 1 / 6.0, 0) * (1 / t));
var bt = tr.TransformLocalToGlobal(e81.GetLocalInternalStress(LoadCase.DefaultLoadCase, 4 / 6.0, 1 / 6.0, +1) * (1 / t));
var bb = tr.TransformLocalToGlobal(e81.GetLocalInternalStress(LoadCase.DefaultLoadCase, 4 / 6.0, 1 / 6.0, -1) * (1 / t));
var cm = tr.TransformLocalToGlobal(e81.GetLocalInternalStress(LoadCase.DefaultLoadCase, 1 / 6.0, 4 / 6.0, 0) * (1 / t));
var ct = tr.TransformLocalToGlobal(e81.GetLocalInternalStress(LoadCase.DefaultLoadCase, 1 / 6.0, 4 / 6.0, +1) * (1 / t));
var cb = tr.TransformLocalToGlobal(e81.GetLocalInternalStress(LoadCase.DefaultLoadCase, 1 / 6.0, 4 / 6.0, -1) * (1 / t));
var abacus_at = new CauchyStressTensor()
{
S11 = 103.814E-03, S22 = 249.185E-03, S12 = 1.03438, S21 = 1.03438
} *-1e9;
var abacus_bt = new CauchyStressTensor()
{
S11 = -34.7168E-03, S22 = -538.942E-03, S12 = 1.03438, S21 = 1.08243
} *-1e9;
var abacus_ct = new CauchyStressTensor()
{
S11 = -201.062E-03, S22 = -1.18348, S12 = 747.243E-03, S21 = 747.243E-03
} *-1e9;
var e1 = GetError(at, abacus_ct);
var e2 = GetError(bt, abacus_at);
var e3 = GetError(ct, abacus_bt);
Console.WriteLine("Err at p1 element 81 (stress): {0:0.00}%", e1);
Console.WriteLine("Err at p2 element 81 (stress): {0:0.00}%", e2);
Console.WriteLine("Err at p3 element 81 (stress): {0:0.00}%", e3);
//in abaqus e81 connected to 8-12-41
//in bfe e85 connected to 57-56-50
}
for (int i = 0; i < model.Elements.Count; i++)
{
model.Elements[i].Label = i.ToString();
}
throw new NotImplementedException();
}
static Model Generate3DTriangleElementGridTest(int m, int n, int l)
{
var buf = new Model();
var dx = 0.15;
var dy = 0.15;
var dz = 0.15;
var nodes = new Node[m, n, l];
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
for (int k = 0; k < l; k++)
{
var pos = new Point(j * dx, i * dy, k * dz);
var nde = new Node()
{
Location = pos
};
buf.Nodes.Add(nde);
nodes[i, j, k] = nde;
}
}
}
//elements parallel to XZ
for (int j = 0; j < n; j++)
{
for (int i = 0; i < m - 1; i++)
{
for (int k = 0; k < l - 1; k++)
{
{
var elm2 = new TriangleElement();
elm2.Nodes[0] = nodes[i, j, k];
elm2.Nodes[1] = nodes[i, j, k + 1];
elm2.Nodes[2] = nodes[i + 1, j, k];
buf.Elements.Add(elm2);
}
{
var elm2 = new TriangleElement();
elm2.Nodes[0] = nodes[i + 1, j, k + 1];
elm2.Nodes[1] = nodes[i, j, k + 1];
elm2.Nodes[2] = nodes[i + 1, j, k];
buf.Elements.Add(elm2);
}
}
}
}
//elements parallel to YZ
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n - 1; j++)
{
for (int k = 0; k < l - 1; k++)
{
{
var elm2 = new TriangleElement();
elm2.Nodes[0] = nodes[i, j, k];
elm2.Nodes[1] = nodes[i, j, k + 1];
elm2.Nodes[2] = nodes[i, j + 1, k];
buf.Elements.Add(elm2);
}
{
var elm2 = new TriangleElement();
elm2.Nodes[0] = nodes[i, j + 1, k + 1];
elm2.Nodes[1] = nodes[i, j, k + 1];
elm2.Nodes[2] = nodes[i, j + 1, k];
buf.Elements.Add(elm2);
}
}
}
}
//elements parallel to XY
for (int k = 0; k < l; k++)
{
for (int j = 0; j < n - 1; j++)
{
for (int i = 0; i < m - 1; i++)
{
{
var elm2 = new TriangleElement();
elm2.Nodes[0] = nodes[i, j, k];
elm2.Nodes[1] = nodes[i + 1, j, k];
elm2.Nodes[2] = nodes[i, j + 1, k];
buf.Elements.Add(elm2);
}
{
var elm2 = new TriangleElement();
elm2.Nodes[0] = nodes[i + 1, j + 1, k];
elm2.Nodes[1] = nodes[i + 1, j, k];
elm2.Nodes[2] = nodes[i, j + 1, k];
buf.Elements.Add(elm2);
}
}
}
}
double t = 0.003;
double E = 210e9;
double nu = 0.3;
foreach (var elm in buf.Elements)
{
var triElm = elm as TriangleElement;
if (triElm == null)
{
continue;
}
triElm.Material = new UniformIsotropicMaterial(E, nu);
triElm.Section = new UniformParametric2DSection(t);
triElm.Behavior = PlaneElementBehaviours.FullThinShell;
triElm.MembraneFormulation = MembraneFormulation.PlaneStress;
}
for (int i = 0; i < m; i++)
{
nodes[i, 0, 0].Constraints = Constraint.Fixed;
}
for (int i = 0; i < m; i++)
{
nodes[i, n - 1, 0].Loads.Add(new NodalLoad(new Force(0, 2500, 2500, 0, 0, 0), LoadCase.DefaultLoadCase));
}
return(buf);
}
public ValidationResult Validate()
{
var val = new ValidationResult();
//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 };
var mat = new Materials.UniformIsotropicMaterial(e, no);
var sec = new Sections.UniformParametric2DSection(t);
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 TriangleElement()
{
Material = mat, Section = sec
};
elm1.Nodes[0] = n11;
elm1.Nodes[1] = n12;
elm1.Nodes[2] = n21;
model.Elements.Add(elm1);
var elm2 = new TriangleElement()
{
Material = mat, Section = sec
};
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 = Constraints.Fixed);
#endregion
model.Trace.Listeners.Add(new BriefFiniteElementNet.Common.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";
/**/
val.Title = "I Beam torsion with triangle element";
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
var abaqusDa = new Vector(-15.4207E-03, 88.2587E-03, 150.910E-03); //node 9
var abaqusDb = new Vector(-15.3246E-03, -88.2629E-03, -148.940E-03); //node 5
Console.WriteLine("Err at A against abaqus (displacement): {0:0.00}%", GetError(da, abaqusDa));
Console.WriteLine("Err at B against abaqus (displacement): {0:0.00}%", GetError(db, abaqusDb));
{
var e81 = model.Elements[85] as TriangleElement;
var stress = e81.GetLocalInternalStress(LoadCase.DefaultLoadCase, 1 / 6.0, 1 / 6.0, 0);
}
for (int i = 0; i < model.Elements.Count; i++)
{
model.Elements[i].Label = i.ToString();
}
throw new NotImplementedException();
}
/// <summary>
/// Gets the material properties at defined length.
/// </summary>
/// <param name="isoCoords">The location, in isoparametric coordination</param>
/// <returns>the mechanical properties of element</returns>
public abstract TriangleCoordinatedMechanicalProperties GetMaterialPropertiesAt
(TriangleElement targetElement, params double[] isoCoords);
