/// <summary>
/// Gets the internal stress at defined <see cref="isoLocation"/>.
/// tensor is in local coordinate system.
/// </summary>
/// <param name="loadCase">the load case </param>
/// <param name="isoLocation"></param>
/// <returns>Stress tensor of flat shell, in local coordination system</returns>
/// <remarks>
/// for more info about local coordinate of flat shell see page [72 of 166] (page 81 of pdf) of "Development of Membrane, Plate and Flat Shell Elements in Java" thesis by Kaushalkumar Kansara freely available on the web
/// </remarks>
public CauchyStressTensor GetLocalInternalStress(LoadCase loadCase, double[] isoLocation)
{
var helpers = GetHelpers();
var gst = new GeneralStressTensor();
var tr = this.GetTransformationManager();
var ld = this.Nodes.Select(i => tr.TransformGlobalToLocal(i.GetNodalDisplacement(loadCase))).ToArray();
for (var i = 0; i < helpers.Count(); i++)
{
var st = helpers[i].GetLocalInternalStressAt(this, ld, isoLocation);
gst += st;
}
var buf = new CauchyStressTensor();
buf += gst.MembraneTensor;
{
//step2: update Cauchy based on bending,
//bending tensor also affects the Cauchy tensor regarding how much distance between desired location and center of plate.
//old code: buf.UpdateTotalStress(_section.GetThicknessAt(new double[] { localX, localY }) * localZ, probeLocation);
var lambda = 0.0;
if (isoLocation.Length == 3)
{
lambda = isoLocation[2];
}
if (lambda > 1.0 || lambda < -1.0)
{
throw new Exception("lambda must be between -1 and +1")
{
}
}
;
var thickness = Section.GetThicknessAt(isoLocation);
//var z = thickness * lambda;//distance from plate center, measure in [m]
buf += BendingStressTensor.ConvertBendingStressToCauchyTensor(gst.BendingTensor, thickness, lambda);
/*epsi1on: no need to subtract, only need to add because negativeness of lambda taken into account in ConvertBendingStressToCauchyTensor
* if (lambda > 0)
* {
* //top -> add bending stress
* buf += gst.BendingTensor.ConvertBendingStressToCauchyTensor(gst.BendingTensor, thickness, lambda);
* }
* else
* {
* //bottom -> subtract bending stress
* buf -= gst.BendingTensor.ConvertBendingStressToCauchyTensor(gst.BendingTensor,thickness, lambda);
* }
*/
}
return(buf);
}
#endregion
}
/// <summary>
/// Gets the internal stress at defined location.
/// tensor is in local coordinate system.
/// </summary>
/// <param name="isoLocation">The location for the stress probe in iso coordinates. Order: x,y,z. Maximum bending stress at the shell thickness (z=1.0). Must be withing 0 and 1.</param>
/// <param name="combination">The load combination.</param>
/// <param name="probeLocation">The probe location for the stress.</param>
/// <returns>Stress tensor of flat shell, in local coordination system</returns>
/// <remarks>
/// for more info about local coordinate of flat shell see page [72 of 166] (page 81 of pdf) of "Development of Membrane, Plate and Flat Shell Elements in Java" thesis by Kaushalkumar Kansara freely available on the web
/// </remarks>
public CauchyStressTensor GetInternalStress(double[] isoLocation, LoadCombination combination, SectionPoints probeLocation)
{
var helpers = GetHelpers();
var gst = new GeneralStressTensor();
var tr = this.GetTransformationManager();
var ld = this.Nodes.Select(i => tr.TransformGlobalToLocal(i.GetNodalDisplacement(combination))).ToArray();
for (var i = 0; i < helpers.Count(); i++)
{
var st = helpers[i].GetLocalInternalStressAt(this, ld, isoLocation);
gst += st;
}
var buf = new CauchyStressTensor();
buf += gst.MembraneTensor;
{
var lambda = 0.0;
switch (probeLocation)
{
case SectionPoints.Envelope:
{
var thickness = Section.GetThicknessAt(isoLocation);
//top
var bufTop = new CauchyStressTensor();
bufTop += gst.MembraneTensor;
bufTop += BendingStressTensor.ConvertBendingStressToCauchyTensor(gst.BendingTensor, thickness, 1.0);
//bottom
var bufBottom = new CauchyStressTensor();
bufBottom += gst.MembraneTensor;
bufBottom += BendingStressTensor.ConvertBendingStressToCauchyTensor(gst.BendingTensor, thickness, -1.0);
if (Math.Abs(CauchyStressTensor.GetVonMisesStress(bufTop)) > Math.Abs(CauchyStressTensor.GetVonMisesStress(bufBottom)))
{
buf = bufTop;
}
else
{
buf = bufBottom;
}
break;
}
case SectionPoints.Top:
{
lambda = 1.0;
var thickness = Section.GetThicknessAt(isoLocation);
buf += BendingStressTensor.ConvertBendingStressToCauchyTensor(gst.BendingTensor, thickness, lambda);
break;
}
case SectionPoints.Bottom:
{
lambda = -1.0;
var thickness = Section.GetThicknessAt(isoLocation);
buf += BendingStressTensor.ConvertBendingStressToCauchyTensor(gst.BendingTensor, thickness, lambda);
break;
}
default:
break;
}
}
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("ABAQUS from Abaqus inc. available from www.simulia.com");
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 GeneralStressTensor(CauchyStressTensor membraneTensor)
{
MembraneTensor = membraneTensor;
BendingTensor = new BendingStressTensor();
}
public GeneralStressTensor(BendingStressTensor bendingTensor)
{
MembraneTensor = new CauchyStressTensor();
BendingTensor = bendingTensor;
}
public GeneralStressTensor(CauchyStressTensor membraneTensor, BendingStressTensor bendingTensor)
{
MembraneTensor = membraneTensor;
BendingTensor = bendingTensor;
}
