/// <summary>
/// Transforms the defined stress tensor from global system to local system.
/// </summary>
/// <param name="tensor">The tensor.</param>
/// <returns>tensor in local coordination system</returns>
public GeneralStressTensor TransformGlobalToLocal(GeneralStressTensor tensor)
{
var buf = new GeneralStressTensor(
TransformGlobalToLocal(tensor.MembraneTensor),
TransformGlobalToLocal(tensor.BendingTensor));
return(buf);
}
/// <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]
if (lambda > 0)
{
//top -> add bending stress
buf += gst.BendingTensor.ConvertBendingStressToCauchyTensor(z);
}
else
{
//bottom -> subtract bending stress
buf -= gst.BendingTensor.ConvertBendingStressToCauchyTensor(z);
}
}
return(buf);
}
public GeneralStressTensor GetLocalInternalForce(Element targetElement, LoadCase loadCase, params double[] isoCoords)
{
//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 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 b = GetBMatrixAt(targetElement, isoCoords);
var d = GetDMatrixAt(targetElement, isoCoords);
var u1l = lds[0];
var u2l = lds[1];
var u3l = lds[2];
var uDkt =
targetElement.MatrixPool.Allocate(new[]
{ u1l.DZ, u1l.RX, u1l.RY, /**/ u2l.DZ, u2l.RX, u2l.RY, /**/ u3l.DZ, u3l.RX, u3l.RY });
var mDkt = d * 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;
var bTensor = new BendingStressTensor();
//var buf = new List<Tuple<DoF, double>>();
bTensor.M11 = mDkt[0, 0];
bTensor.M22 = mDkt[1, 0];
bTensor.M21 = bTensor.M12 = mDkt[2, 0];
var buf = new GeneralStressTensor(bTensor);
return(buf);
}
/// <inheritdoc/>
public IEnumerable <Tuple <DoF, double> > GetLocalInternalForceAt(Element targetElement,
Displacement[] globalDisplacements, params double[] isoCoords)
{
//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 tr = targetElement.GetTransformationManager();
var locals = tr.TransformGlobalToLocal(globalDisplacements);
var b = GetBMatrixAt(targetElement, isoCoords);
var d = GetDMatrixAt(targetElement, isoCoords);
var u1l = locals[0];
var u2l = locals[1];
var u3l = locals[2];
var uDkt =
targetElement.MatrixPool.Allocate(new[]
{ u1l.DZ, u1l.RX, u1l.RY, /**/ u2l.DZ, u2l.RX, u2l.RY, /**/ u3l.DZ, u3l.RX, u3l.RY });
var mDkt = d * 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;
var bTensor = new BendingStressTensor();
//var buf = new List<Tuple<DoF, double>>();
bTensor.M11 = mDkt[0, 0];
bTensor.M22 = mDkt[1, 0];
bTensor.M21 = bTensor.M12 = mDkt[2, 0];
var buf = new GeneralStressTensor(bTensor);
throw new NotImplementedException();
}
/// <summary>
/// Gets the stresses for a single element
/// </summary>
/// <param name="targetElement"></param>
/// <param name="loadCase"></param>
/// <param name="isoCoords"></param>
/// <returns></returns>
public GeneralStressTensor GetLocalInternalForce(Element targetElement, LoadCase loadCase, params double[] isoCoords)
{
//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 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 d = GetDMatrixAt(targetElement, isoCoords);
var u1l = lds[0];
var u2l = lds[1];
var u3l = lds[2];
var uDkt = targetElement.MatrixPool.Allocate(6, 1);
// TODO: MAT - set values directly
uDkt.SetColumn(1, new double[] { u1l.DX, u1l.DY, /**/ u2l.DX, u2l.DY, /**/ u3l.DX, u3l.DY });
var mDkt = d * b * uDkt; //eq. 32, batoz article
var bTensor = new CauchyStressTensor();
bTensor.S11 = mDkt[0, 0];
bTensor.S22 = mDkt[1, 0];
bTensor.S12 = bTensor.S21 = mDkt[2, 0];
var buf = new GeneralStressTensor(bTensor);
return(buf);
throw new NotImplementedException();
}
public GeneralStressTensor GetLocalStressAt(Element targetElement, Displacement[] localDisplacements, params double[] isoCoords)
{
//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 pt = new IsoPoint(isoCoords);
var tr = targetElement.GetTransformationManager();
var locals = localDisplacements;// tr.TransformGlobalToLocal(globalDisplacements);
var b = GetBMatrixAt(targetElement, isoCoords);
var d = GetDMatrixAt(targetElement, isoCoords);
var u1l = locals[0];
var u2l = locals[1];
var u3l = locals[2];
var uDkt =
targetElement.MatrixPool.Allocate(new[]
{ u1l.DZ, u1l.RX, u1l.RY, /**/ u2l.DZ, u2l.RX, u2l.RY, /**/ u3l.DZ, u3l.RX, u3l.RY });
var mDkt = d * b * uDkt; //eq. 32, batoz article
var bTensor = new BendingStressTensor();
bTensor.M11 = mDkt[0, 0];
bTensor.M22 = mDkt[1, 0];
bTensor.M21 = bTensor.M12 = mDkt[2, 0];
var buf = new GeneralStressTensor(bTensor);
return(buf);
}
public GeneralStressTensor GetLocalInternalStressAt(Element targetElement, Displacement[] localDisplacements, params double[] isoCoords)
{
var lds = localDisplacements;// new Displacement[targetElement.Nodes.Length];
/*var tr = targetElement.GetTransformationManager();
*
* for (var i = 0; i < targetElement.Nodes.Length; i++)
* {
* var globalD = targetElement.Nodes[i].GetNodalDisplacement(cmb);
* var local = tr.TransformGlobalToLocal(globalD);
* lds[i] = local;
* }
*/
var b = GetBMatrixAt(targetElement, isoCoords);
var d = GetDMatrixAt(targetElement, isoCoords);
var u1l = lds[0];
var u2l = lds[1];
var u3l = lds[2];
var uDkt =
targetElement.MatrixPool.Allocate(new[]
{ u1l.DZ, u1l.RX, u1l.RY, /**/ u2l.DZ, u2l.RX, u2l.RY, /**/ u3l.DZ, u3l.RX, u3l.RY });
var mDkt = d * b * uDkt; //eq. 32, batoz article
var bTensor = new BendingStressTensor();
bTensor.M11 = mDkt[0, 0];
bTensor.M22 = mDkt[1, 0];
bTensor.M21 = bTensor.M12 = mDkt[2, 0];
var buf = new GeneralStressTensor(bTensor);
return(buf);
}
/// <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, params 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;
if (isoLocation.Length == 3)// local Z and bending tensor does affect on cauchy tensor, only on center of plate where lambda=0 bending tensor have no effect on cauchy
{
//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(thickness, lambda);
* }
* else
* {
* //bottom -> subtract bending stress
* buf -= gst.BendingTensor.ConvertBendingStressToCauchyTensor(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, LoadCase cse, SectionPoints probeLocation)
{
//added by rubsy92
if (isoLocation[2] < 0 || isoLocation[2] > 1.0)
{
throw new Exception("z must be between 0 and 1. 0 is the centre of the plate and 1 is on the plate surface. Use the section points to get the top/bottom.")
{
};
}
var helpers = GetHelpers();
var gst = new GeneralStressTensor();
var tr = this.GetTransformationManager();
var ld = this.Nodes.Select(i => tr.TransformGlobalToLocal(i.GetNodalDisplacement(cse))).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);
}
/// <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);
}
