private MembraneStressTensor GetMembraneInternalForce(LoadCombination combination)
{
//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 = new Displacement(g2l(d1g.Displacements), g2l(d1g.Rotations));
var d2l = new Displacement(g2l(d2g.Displacements), g2l(d2g.Rotations));
var d3l = new Displacement(g2l(d3g.Displacements), g2l(d3g.Rotations));
var uCst =
new Matrix(new[]
{ d1l.DX, d1l.DY, d2l.DX, d2l.DY, /**/ d3l.DX, d3l.DY });
var dbCst = CstElement.GetDMatrix(_elasticModulus, _poissonRatio, _formulationType);
var bCst = CstElement.GetBMatrix(lp.Select(i => i.X).ToArray(),
lp.Select(i => i.Y).ToArray());
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);
}
private PlateBendingStressTensor GetBendingInternalForce(double localX, double localY, LoadCombination cmb)
{
//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(cmb);
var d2g = this.nodes[1].GetNodalDisplacement(cmb);
var d3g = this.nodes[2].GetNodalDisplacement(cmb);
//step 3
var d1l = new Displacement(g2l(d1g.Displacements), g2l(d1g.Rotations));
var d2l = new Displacement(g2l(d2g.Displacements), g2l(d2g.Rotations));
var d3l = new Displacement(g2l(d3g.Displacements), g2l(d3g.Rotations));
var uDkt =
new Matrix(new[]
{ d1l.DZ, d1l.RX, d1l.RY, /**/ d2l.DZ, d2l.RX, d2l.RY, /**/ d3l.DZ, d3l.RX, d3l.RY });
var dbDkt = DktElement.GetDMatrix(this._thickness, this._elasticModulus, this._poissonRatio);
var b = DktElement.GetBMatrix(localX, localY,
lp.Select(i => i.X).ToArray(),
lp.Select(i => i.Y).ToArray());
var mDkt = dbDkt * b * uDkt; //eq. 32, batoz article
var buf = new PlateBendingStressTensor();
buf.Mx = mDkt[0, 0];
buf.My = mDkt[1, 0];
buf.Mxy = mDkt[2, 0];
return(buf);
}
public static DataTable[] OpenseesValidate(Model model, LoadCase loadcase, bool validateStiffness = false)
{
var gen = new TclGenerator();
gen.ElementTranslators.Add(new BarElement2Tcl()
{
TargetGenerator = gen
});
gen.ElementTranslators.Add(new TetrahedronToTcl()
{
TargetGenerator = gen
});
gen.ElementLoadTranslators.Add(new UniformLoad2Tcl()
{
TargetGenerator = gen
});
gen.ExportElementForces = false;
gen.ExportNodalDisplacements = true;
gen.ExportTotalStiffness = validateStiffness;
gen.ExportNodalReactions = true;
var tcl = gen.Create(model, LoadCase.DefaultLoadCase);
var nodesFile = gen.nodesOut;
var elementsFile = gen.elementsOut;
var stiffnessFile = gen.stiffnessOut;
var tclFile = System.IO.Path.GetTempFileName() + ".tcl";
Debug.WriteLine("{0}", tclFile);
System.IO.File.WriteAllText(tclFile, tcl);
if (!System.IO.File.Exists(openSeeslocation))
{
throw new Exception("Opensees.exe not found, please put opensees.exe into 'C:\\Opensees\\Opensees.exe'");
}
var stInf = new ProcessStartInfo(openSeeslocation);
stInf.Arguments = tclFile;
stInf.RedirectStandardOutput = true;
stInf.UseShellExecute = false;
var prc = Process.Start(stInf);
prc.WaitForExit();
var code = prc.ExitCode;
var stiffness = stiffnessFile == null ? null : System.IO.File.ReadAllText(stiffnessFile);
var ndisp = new XmlDocument();
ndisp.Load(nodesFile);
var nreact = new XmlDocument();
nreact.Load(gen.reactionsOut);
if (gen.ExportElementForces)
{
var elOut = new XmlDocument();
elOut.Load(elementsFile);
var elmParts = elOut.DocumentElement.LastChild.InnerText.Trim().Split('\n').Select(i => i.Trim()).Where(i => !string.IsNullOrEmpty(i)).ToArray();
}
var nodalDispParts = ndisp.DocumentElement.LastChild.InnerText.Trim().Split('\n').Select(i => i.Trim()).Where(i => !string.IsNullOrEmpty(i)).ToArray();
var nodalReactParts = nreact.DocumentElement.LastChild.InnerText.Trim().Split('\n').Select(i => i.Trim()).Where(i => !string.IsNullOrEmpty(i)).ToArray();
var openseesDs = nodalDispParts[0].Split(' ').Select(double.Parse).ToArray();
var openseesReacts = nodalReactParts[0].Split(' ').Select(double.Parse).ToArray();
var myDs = model.Nodes.SelectMany(i => Displacement.ToVector(i.GetNodalDisplacement(loadcase))).ToArray();
var myReacts = model.Nodes.SelectMany(i => Force.ToVector(i.GetSupportReaction(loadcase))).ToArray();
var absNodalDisp = new double[myDs.Length];
var relNodalDisp = new double[myDs.Length];
var absNodalReac = new double[myDs.Length];
var relNodalReac = new double[myDs.Length];
var nums = Enumerable.Range(0, myDs.Length).ToArray();
FindError(openseesDs, myDs, relNodalDisp, absNodalDisp);
FindError(openseesReacts, myReacts, relNodalReac, absNodalReac);
//var k = absNodalDisp;
//var key = new Func<double[]>(() => (double[])absNodalDisp.Clone());
var nodalDispTbl = new DataTable();
var nodalReactTbl = new DataTable();
var elmFrcTbl = new DataTable();
{
nodalDispTbl.Columns.Add("Node #", typeof(int));
nodalDispTbl.Columns.Add("DoF", typeof(string));
nodalDispTbl.Columns.Add("DoF #", typeof(int));
nodalDispTbl.Columns.Add("OpenSees Delta", typeof(double));
nodalDispTbl.Columns.Add("BFE Delta", typeof(double));
nodalDispTbl.Columns.Add("Relative Error", typeof(double));
nodalDispTbl.Columns.Add("Absolute Error", typeof(double));
}
{
nodalReactTbl.Columns.Add("Node #", typeof(int));
nodalReactTbl.Columns.Add("DoF", typeof(string));
nodalReactTbl.Columns.Add("DoF #", typeof(int));
nodalReactTbl.Columns.Add("OpenSees Support Reaction", typeof(double));
nodalReactTbl.Columns.Add("BFE Support Reaction", typeof(double));
nodalReactTbl.Columns.Add("Relative Error", typeof(double));
nodalReactTbl.Columns.Add("Absolute Error", typeof(double));
}
{
elmFrcTbl.Columns.Add("Elm #", typeof(int));
elmFrcTbl.Columns.Add("Relative Error", typeof(double));
elmFrcTbl.Columns.Add("Absolute Error", typeof(double));
}
for (int i = 0; i < myDs.Length; i++)
{
nodalDispTbl.Rows.Add(
i / 6,
((DoF)(i % 6)).ToString(),
nums[i],
openseesDs[i],
myDs[i],
relNodalDisp[i],
absNodalDisp[i]
);
nodalReactTbl.Rows.Add(
i / 6,
((DoF)(i % 6)).ToString().Replace("D", "F").Replace("R", "M"),
nums[i],
openseesReacts[i],
myReacts[i],
relNodalReac[i],
absNodalReac[i]
);
}
/*
* for (int i = 0; i < model.Elements.Count; i++)
* {
* var bar = model.Elements[i] as BarElement;
*
* var myFrc = bar.GetInternalForceAt(0, LoadCase.DefaultLoadCase);
*
* nodalDispTbl.Rows.Add(
* i ,
* ((DoF)(i % 6)).ToString(),
* nums[i],
* openseesDs[i],
* myDs[i],
* relNodalDisp[i],
* absNodalDisp[i]
* );
*
* }
*/
return(new[] { nodalDispTbl, nodalReactTbl });
}
private MembraneStressTensor GetMembraneInternalForce(LoadCombination combination)
{
//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 = new Displacement(g2l(d1g.Displacements), g2l(d1g.Rotations));
var d2l = new Displacement(g2l(d2g.Displacements), g2l(d2g.Rotations));
var d3l = new Displacement(g2l(d3g.Displacements), g2l(d3g.Rotations));
var uCst =
new Matrix(new[]
{ d1l.DX, d1l.DY, d2l.DX, d2l.DY, /**/ d3l.DX, d3l.DY });
var dbCst = CstElement.GetDMatrix(_elasticModulus, _poissonRatio, _formulationType);
var bCst = CstElement.GetBMatrix(lp.Select(i => i.X).ToArray(),
lp.Select(i => i.Y).ToArray());
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);
}
private PlateBendingStressTensor GetBendingInternalForce(double localX, double localY, LoadCombination cmb)
{
//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(cmb);
var d2g = this.nodes[1].GetNodalDisplacement(cmb);
var d3g = this.nodes[2].GetNodalDisplacement(cmb);
//step 3
var d1l = new Displacement(g2l(d1g.Displacements), g2l(d1g.Rotations));
var d2l = new Displacement(g2l(d2g.Displacements), g2l(d2g.Rotations));
var d3l = new Displacement(g2l(d3g.Displacements), g2l(d3g.Rotations));
var uDkt =
new Matrix(new[]
{ d1l.DZ, d1l.RX, d1l.RY, /**/ d2l.DZ, d2l.RX, d2l.RY, /**/ d3l.DZ, d3l.RX, d3l.RY });
var dbDkt = DktElement.GetDMatrix(this._thickness, this._elasticModulus, this._poissonRatio);
var b = DktElement.GetBMatrix(localX, localY,
lp.Select(i => i.X).ToArray(),
lp.Select(i => i.Y).ToArray());
var mDkt = dbDkt * b * uDkt; //eq. 32, batoz article
var buf = new PlateBendingStressTensor();
buf.Mx = mDkt[0, 0];
buf.My = mDkt[1, 0];
buf.Mxy = mDkt[2, 0];
return(buf);
}
#endregion
#region stresses
/// <summary>
/// Gets the internal stress at defined location.
/// tensor is in local coordinate system.
/// </summary>
/// <param name="localX">The X in local coordinate system (see remarks).</param>
/// <param name="localY">The Y in local coordinate system (see remarks).</param>
/// <param name="combination">The load combination.</param>
/// <param name="probeLocation">The probe location for the stress.</param>
/// <param name="thickness">The location for the bending stress. Maximum at the shell thickness</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 FlatShellStressTensor GetInternalStress(double localX, double localY, LoadCombination combination, double thickness, SectionPoints probeLocation)
{
var buf = new FlatShellStressTensor();
if ((this._behaviour & PlaneElementBehaviour.ThinPlate) != 0)
{
buf.MembraneTensor = GetMembraneInternalForce(combination);
}
if ((this._behaviour & PlaneElementBehaviour.Membrane) != 0)
{
buf.BendingTensor = GetBendingInternalForce(localX, localY, combination);
}
buf.UpdateTotalStress(thickness, probeLocation);
return(buf);
}
#endregion
#region strains
public StrainTensor GetMembraneInternalStrain(LoadCombination combination)
{
//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 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 = new Displacement(g2l(d1g.Displacements), g2l(d1g.Rotations));
var d2l = new Displacement(g2l(d2g.Displacements), g2l(d2g.Rotations));
var d3l = new Displacement(g2l(d3g.Displacements), g2l(d3g.Rotations));
var uCst =
new Matrix(new[]
{ d1l.DX, d1l.DY, d2l.DX, d2l.DY, /**/ d3l.DX, d3l.DY });
var bCst = CstElement.GetBMatrix(lp.Select(i => i.X).ToArray(),
lp.Select(i => i.Y).ToArray());
var ECst = bCst * uCst;
var buf = new StrainTensor();
buf.S11 = ECst[0, 0];
buf.S22 = ECst[1, 0];
buf.S12 = ECst[2, 0];
return(buf);
}
public override string ToString()
{
StringBuilder sb = new StringBuilder();
sb.AppendFormat("{0}{1}:\n", offset, Model);
sb.AppendFormat("{0}{0}Power: {1}\n", offset, Power);
sb.AppendFormat("{0}{0}Displacement: {1}\n", offset, Displacement == -1 ? "n/a" : Displacement.ToString());
sb.AppendFormat("{0}{0}Efficiency: {1}\n", offset, Efficiency);
return(sb.ToString());
}
protected VirtualConstraint(SerializationInfo info, StreamingContext context) : base(info, context)
{
_settlement = (Displacement)info.GetValue("_settlement", typeof(Displacement));
_constraint = (Constraint)info.GetValue("_constraint", typeof(Constraint));
}
public override string ToString()
{
if (IsRegister)
{
return(Register.Name);
}
if (IsImmediate)
{
return(Immediate.ToString());
}
if (IsLabel)
{
if (IsMemory)
{
return("[" + Label + "]");
}
else
{
return(Label);
}
}
if (IsMemory)
{
// Register + (Index * Scale) + Displacement
string s = "[";
if (Register != null)
{
s = s + Register.Name;
}
else
{
s = s + Immediate.ToString();
}
if (Index != null)
{
s = s + "+" + Index.Name;
}
if (Scale != 0)
{
s = s + "*" + Scale.ToString();
}
if (Displacement != 0)
{
if (Displacement >= 0)
{
s = s + "+" + Displacement.ToString();
}
else
{
s = s + Displacement.ToString();
}
}
s = s + "]";
return(s);
}
return(string.Empty);
}
private static GenericStructure WriteDisplacement(Displacement disp)
{
throw new NotImplementedException();
}
