/// <summary>
/// Integrates the shear force along intersection of element with defined plane.
/// </summary>
/// <param name="element">The element.</param>
/// <param name="plane">The plane.</param>
/// <returns>Integrated force</returns>
public static Force IntegrateNormalForce(this TriangleFlatShell element, Plane plane, LoadCombination cmb)
{
//step 1: does intersect?
//step 2: get a tensor (no matter where, this is constant stress)
//step 3: find rotation amount for tensors
//step 4: rotate tensors
//step 5: integrate forces
if (!DoesIntersects(element, plane))
return Force.Zero;
var intersection = GetIntersection(element, plane);
//step 2
var tensor = element.GetInternalForce(0, 0, cmb);
//step 3
var t = element.GetTransformationMatrix().Transpose(); //transpose of t
var nLocal = (Vector)(t * plane.Normal.ToMatrix()).ToPoint();//project of N to local element coord system
var theta = Math.Atan2(nLocal.Y, nLocal.X) - Math.PI / 2;
//step 4
var rotatedTensor = MembraneStressTensor.Rotate(tensor.MembraneTensor, theta);
// shear direction
var shearLocalDirection = new Vector(Math.Cos(theta), Math.Sin(theta), 0);//direction of shear force in local element coord system, which is vector I rotated by amount theta
var shearGlobalDirection = (Vector)(t.Transpose() * shearLocalDirection.ToMatrix()).ToPoint();
var fShearAmount = rotatedTensor.Txy * element.Thickness * intersection.Length;//shear force
var shearForce = fShearAmount * shearGlobalDirection.GetUnit();
return new Force(shearForce, Vector.Zero);
}
private static double GetError(MembraneStressTensor test, MembraneStressTensor accurate)
{
var v1 = new Vector(test.Sx, test.Sy, test.Txy);
var v2 = new Vector(accurate.Sx, accurate.Sy, accurate.Txy);
return(GetError(v1, v2));
}
/// <summary>
/// Rotates the define local stress tensor into direction of plane.
/// </summary>
/// <param name="shell">The shell.</param>
/// <param name="localStressTensor">The local stress tensor.</param>
/// <param name="targetPlane">The target plane.</param>
/// <returns>
/// Rotated tensor
/// </returns>
/// <exception cref="System.NotImplementedException"></exception>
public static MembraneStressTensor RotateTensor(this TriangleFlatShell shell, MembraneStressTensor localStressTensor, Plane targetPlane)
{
var t = shell.GetTransformationMatrix().Transpose();
var plane = targetPlane;
var nLocal = (Vector)(t * plane.Normal.ToMatrix()).ToPoint();//project of N to local element coord system
var theta = Math.Atan2(nLocal.Y, nLocal.X) - Math.PI / 2;
var buf = MembraneStressTensor.Rotate(localStressTensor, theta);
return buf;
}
public GeneralStressTensor GetLocalStressAt(Element targetElement, Displacement[] localDisplacements, params double[] isoCoords)
{
//Note: membrane internal force is constant
//step 1 : get transformation matrix
//step 2 : convert globals points to locals
//step 3 : convert global displacements to locals
//step 4 : calculate B matrix and D matrix
//step 5 : M=D*B*U
//Note : Steps changed...
//var trans = this.GetTransformationMatrix();
//var lp = GetLocalPoints();
//var g2l = new Func<Vector, Vector>(glob => (trans.Transpose() * glob.ToMatrix()).ToVector());
//var l2g = new Func<Vector, Vector>(local => (trans*local.ToMatrix()).ToPoint());
//var d1g = this.nodes[0].GetNodalDisplacement(combination);
//var d2g = this.nodes[1].GetNodalDisplacement(combination);
//var d3g = this.nodes[2].GetNodalDisplacement(combination);
//step 3
var d1l = localDisplacements[0]; // new Displacement(g2l(d1g.Displacements), g2l(d1g.Rotations));
var d2l = localDisplacements[1]; //new Displacement(g2l(d2g.Displacements), g2l(d2g.Rotations));
var d3l = localDisplacements[2]; //new Displacement(g2l(d3g.Displacements), g2l(d3g.Rotations));
var u =
new Matrix(new[]
{ d1l.DX, d1l.DY, d2l.DX, d2l.DY, /**/ d3l.DX, d3l.DY });
var d = this.GetDMatrixAt(targetElement, isoCoords);
var b = this.GetBMatrixAt(targetElement, isoCoords);
var sCst = d * b * u;
var buf = new MembraneStressTensor();
buf.Sx = sCst[0, 0];
buf.Sy = sCst[1, 0];
buf.Txy = sCst[2, 0];
return(new GeneralStressTensor(buf));
}
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 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 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));
}
}
/// <summary>
/// Gets the stress due to the membrane action. Needs to be combined with bending stress!!!
/// </summary>
/// <param name="targetElement">Element under consideration</param>
/// <param name="combination">A load combination</param>
/// <returns>The stress in the element due to the membrane action. Needs to be combined with the stress due to bending!</returns>
public MembraneStressTensor GetMembraneInternalStress(Element targetElement, LoadCombination combination)
{
//code moved to GetLocalInternalStressAt()
//Note: membrane internal force is constant
//step 1 : get transformation matrix
//step 2 : convert globals points to locals
//step 3 : convert global displacements to locals
//step 4 : calculate B matrix and D matrix
//step 5 : M=D*B*U
var lds = new Displacement[targetElement.Nodes.Length];
var tr = targetElement.GetTransformationManager();
for (var i = 0; i < targetElement.Nodes.Length; i++)
{
var globalD = targetElement.Nodes[i].GetNodalDisplacement(combination);
var local = tr.TransformGlobalToLocal(globalD);
lds[i] = local;
}
//step 3
var d1l = lds[0];
var d2l = lds[1];
var d3l = lds[2];
var uCst = targetElement.MatrixPool.Allocate(6, 1);
uCst.FillColumn(1, d1l.DX, d1l.DY, d2l.DX, d2l.DY, /**/ d3l.DX, d3l.DY);
//cst -> constant over entire element -> provide random values for local
var dbCst = this.GetDMatrixAt(targetElement, new double[] { 0, 0 });
var bCst = this.GetBMatrixAt(targetElement, new double[] { 0, 0 });
var sCst = dbCst * bCst * uCst;
var buf = new MembraneStressTensor();
buf.Sx = sCst[0, 0];
buf.Sy = sCst[1, 0];
buf.Txy = sCst[2, 0];
return(buf);
}
#endregion
public GeneralStressTensor GetLoadStressAt(Element targetElement, ElementalLoad load, double[] isoLocation)
{
throw new NotImplementedException();
}
#region strain
/// <summary>
/// Determine the strain in the element for a given load case
/// </summary>
/// <param name="targetElement">Element under consideration</param>
/// <param name="loadCase">Loadcase for strain determination</param>
/// <param name="isoCoords">The location - doesn't matter since it is constant in the CST element</param>
/// <returns></returns>
public StrainTensor GetMembraneInternalStrain(Element targetElement, LoadCase loadCase, params double[] isoCoords)
{
//Note: membrane internal force is constant
//step 1 : get transformation matrix
//step 2 : convert globals points to locals
//step 3 : convert global displacements to locals
//step 4 : calculate B matrix
//step 5 : e=B*U
//Note : Steps changed...
var lds = new Displacement[targetElement.Nodes.Length];
var tr = targetElement.GetTransformationManager();
for (var i = 0; i < targetElement.Nodes.Length; i++)
{
var globalD = targetElement.Nodes[i].GetNodalDisplacement(loadCase);
var local = tr.TransformGlobalToLocal(globalD);
lds[i] = local;
}
// var locals = tr.TransformGlobalToLocal(globalDisplacements);
var b = GetBMatrixAt(targetElement, isoCoords);
var u1l = lds[0];
var u2l = lds[1];
var u3l = lds[2];
var uCst =
targetElement.MatrixPool.Allocate(new[]
{ u1l.DX, u1l.DY, /**/ u2l.DX, u2l.DY, /**/ u3l.DX, u3l.DY });
var ECst = b * uCst;
var buf = new StrainTensor();
buf.S11 = ECst[0, 0];
buf.S22 = ECst[1, 0];
buf.S12 = ECst[2, 0];
return(buf);
}
public GeneralStressTensor GetLocalInternalStressAt(Element targetElement, Displacement[] localDisplacements, params double[] isoCoords)
{
//Note: membrane internal force is constant
//step 1 : get transformation matrix
//step 2 : convert globals points to locals
//step 3 : convert global displacements to locals
//step 4 : calculate B matrix and D matrix
//step 5 : M=D*B*U
var lds = localDisplacements;
//step 3
var d1l = lds[0];
var d2l = lds[1];
var d3l = lds[2];
var uCst =
targetElement.MatrixPool.Allocate(new[]
{ d1l.DX, d1l.DY, d2l.DX, d2l.DY, /**/ d3l.DX, d3l.DY });
//cst -> constant over entire element -> provide random values for local
var dbCst = this.GetDMatrixAt(targetElement, new double[] { 0, 0 });
var bCst = this.GetBMatrixAt(targetElement, new double[] { 0, 0 });
var sCst = dbCst * bCst * uCst;
var buf = new MembraneStressTensor();
buf.Sx = sCst[0, 0];
buf.Sy = sCst[1, 0];
buf.Txy = sCst[2, 0];
return(new GeneralStressTensor(buf));
}
public static Tuple<Force,Point> GetTotalForce(this TriangleFlatShell element, Plane plane, int n)
{
//step 1: find intersection points
//step 2: find tensors at intersection points
//step 3: find rotation amount for tensors
//step 4: rotate tensors
//step 5: integrate forces
//step 1
var globalPoints = GetIntersectionPoints(element, plane, n);
if (!globalPoints.Any())
return new Tuple<Force, Point>();
var t = element.GetTransformationMatrix().Transpose(); //transpose of t
var locals = globalPoints.Select(i => (t * i.ToMatrix()).ToPoint()).ToArray();
//step 2
var tensors = GeTensorsAtIntersection(element, plane, n);
var memTensors = tensors.Select(i => i.MembraneTensor).ToList();
var bendTensors = tensors.Select(i => i.BendingTensor).ToList();
//step 3
var nLocal = (Vector)(t * plane.Normal.ToMatrix()).ToPoint();//project of N to local element coord system
var theta = Math.Atan2(nLocal.Y, nLocal.X) - Math.PI/2;
//step 4
var rTensors = tensors.Select(i => MembraneStressTensor.Rotate(i.MembraneTensor, theta)).ToList();
var avg = rTensors.Aggregate((i, j) => i + j);
avg = MembraneStressTensor.Multiply(avg, 1.0 / tensors.Length);
var length = (globalPoints.First() - globalPoints.Last()).Length;
var fShearAmount = avg.Txy * element.Thickness * length;//shear force
var fCompAmount = avg.Sy * element.Thickness * length;//compressive force
// shear dirction
var shearLocalDirection = new Vector(Math.Cos(theta), Math.Sin(theta), 0);//direction of shear force in local element coord system, which is vector I rotated by amount theta
var shearGlobalDirection = (Vector) (t.Transpose()*shearLocalDirection.ToMatrix()).ToPoint();
//compressive direction
var compLocalDirection = new Vector(-Math.Sin(theta), Math.Cos(theta), 0);//direction of shear force in local element coord system, which is vector I rotated by amount theta
var compGlobalDirection = (Vector)(t.Transpose() * compLocalDirection.ToMatrix()).ToPoint();
var shearForce = fShearAmount*shearGlobalDirection.GetUnit();
var compForce = fCompAmount*compGlobalDirection.GetUnit();
var totForce = shearForce + compForce;
var bufFrc = new Force(totForce, Vector.Zero);
var loc = globalPoints.Aggregate((i, j) => (Point)((Vector)i + (Vector)j));
loc.X /= globalPoints.Length;
loc.Y /= globalPoints.Length;
loc.Z /= globalPoints.Length;
return new Tuple<Force, Point>(bufFrc, loc);
//return bufFrc;
}
