/// <summary>
/// Gets the stress of a shell element (combination of a membrane + bending element) as the combination of both stresses
/// </summary>
/// <param name="shellThickness">The location where you want to calculate the bending stress (max at shellthickness)</param>
/// <param name="probeLocation">The location of the stress probe. Top of thickness/shell, bottom or envelope (max abs of both). </param>
public void UpdateTotalStress(double shellThickness, SectionPoints probeLocation)
{
switch (probeLocation)
{
case SectionPoints.Envelope:
{
CauchyStressTensor top = MembraneTensor + BendingStressTensor.ConvertBendingStressToCauchyTensor(BendingTensor, shellThickness, 1);
CauchyStressTensor bottom = MembraneTensor + BendingStressTensor.ConvertBendingStressToCauchyTensor(BendingTensor, shellThickness, -1);
if (Math.Abs(CauchyStressTensor.GetVonMisesStress(top)) > Math.Abs(CauchyStressTensor.GetVonMisesStress(bottom)))
{
this.TotalStressTensor = top;
}
else
{
this.TotalStressTensor = bottom;
}
break;
}
case SectionPoints.Top:
{
this.TotalStressTensor = MembraneTensor + BendingStressTensor.ConvertBendingStressToCauchyTensor(BendingTensor, shellThickness, 1);
break;
}
case SectionPoints.Bottom:
{
this.TotalStressTensor = MembraneTensor + BendingStressTensor.ConvertBendingStressToCauchyTensor(BendingTensor, shellThickness, -1);
break;
}
default:
break;
}
}
/// <summary>
/// Reverse Transforms the specified tensor using transformation matrix.
/// </summary>
/// <param name="tensor">The tensor.</param>
/// <param name="transformationMatrix">The transformation matrix.</param>
/// <returns>reversely transformed tensor</returns>
public static BendingStressTensor TransformBack(BendingStressTensor tensor, Matrix transformationMatrix)
{
var tensorMatrix = ToMatrix(tensor);
var rtd = transformationMatrix * tensorMatrix * transformationMatrix.Transpose();
var buf = FromMatrix(rtd);
return(buf);
}
public static FlatShellStressTensor Transform(FlatShellStressTensor tensor, Matrix transformationMatrix)
{
var buf = new FlatShellStressTensor
{
MembraneTensor = CauchyStressTensor.Transform(tensor.MembraneTensor, transformationMatrix),
BendingTensor = BendingStressTensor.Transform(tensor.BendingTensor, transformationMatrix)
};
return(buf);
}
/// <summary>
/// Reverse Transforms the specified tensor using transformation matrix.
/// </summary>
/// <param name="tensor">The tensor.</param>
/// <param name="transformationMatrix">The transformation matrix.</param>
/// <returns>reversely transformed tensor</returns>
public static BendingStressTensor TransformBack(BendingStressTensor tensor, Matrix transformationMatrix)
{
var tensorMatrix = ToMatrix(tensor);
// TODO: MAT - the product could be directly computed in a helper method (CalcUtil).
var rtd = transformationMatrix * tensorMatrix * transformationMatrix.Transpose();
var buf = FromMatrix(rtd);
return(buf);
}
/// <summary>
/// Mutiplies the specified tensor with specified coefficient.
/// </summary>
/// <param name="tensor">The left.</param>
/// <param name="coefficient">The coefficient.</param>
/// <returns><see cref="tensor"/> * <see cref="coefficient"/></returns>
public static BendingStressTensor Multiply(BendingStressTensor tensor, double coefficient)
{
var buf = new BendingStressTensor();
buf.M11 = coefficient * tensor.M11;
buf.M22 = coefficient * tensor.M22;
buf.M33 = coefficient * tensor.M33;
buf.M12 = coefficient * tensor.M12;
buf.M23 = coefficient * tensor.M23;
buf.M31 = coefficient * tensor.M31;
buf.M21 = coefficient * tensor.M21;
buf.M32 = coefficient * tensor.M32;
buf.M13 = coefficient * tensor.M13;
return(buf);
}
/// <summary>
/// Subtract the specified tensors and return the result.
/// </summary>
/// <param name="left">The left.</param>
/// <param name="right">The right.</param>
/// <returns><see cref="left"/> - <see cref="right"/></returns>
public static BendingStressTensor Subtract(BendingStressTensor left, BendingStressTensor right)
{
var buf = new BendingStressTensor();
buf.M11 = left.M11 - right.M11;
buf.M22 = left.M22 - right.M22;
buf.M33 = left.M33 - right.M33;
buf.M12 = left.M12 - right.M12;
buf.M23 = left.M23 - right.M23;
buf.M31 = left.M31 - right.M31;
buf.M21 = left.M21 - right.M21;
buf.M32 = left.M32 - right.M32;
buf.M13 = left.M13 - right.M13;
return(buf);
}
/// <summary>
/// Adds the specified tensors and return the result.
/// </summary>
/// <param name="left">The left.</param>
/// <param name="right">The right.</param>
/// <returns><see cref="left"/> + <see cref="right"/></returns>
public static BendingStressTensor Add(BendingStressTensor left, BendingStressTensor right)
{
var buf = new BendingStressTensor();
buf.M11 = left.M11 + right.M11;
buf.M22 = left.M22 + right.M22;
buf.M33 = left.M33 + right.M33;
buf.M12 = left.M12 + right.M12;
buf.M23 = left.M23 + right.M23;
buf.M31 = left.M31 + right.M31;
buf.M21 = left.M21 + right.M21;
buf.M32 = left.M32 + right.M32;
buf.M13 = left.M13 + right.M13;
return(buf);
}
/// <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 BendingStressTensor TransformGlobalToLocal(BendingStressTensor tensor)
{
var matrix = BendingStressTensor.ToMatrix(tensor);
Matrix buf = null;
if (VeryMagicNumber == 1)
{
buf = At_B_A(LambdaMatrix, matrix);
}
if (VeryMagicNumber == 2)
{
buf = A_B_At(TransformMatrix, matrix);
}
return(BendingStressTensor.FromMatrix(buf));
}
/// <summary>
/// Generates a tensor from defined matrix
/// </summary>
/// <param name="matrix">The matrix.</param>
/// <returns>generated tensor</returns>
public static BendingStressTensor FromMatrix(Matrix mtx)
{
var buf = new BendingStressTensor();
buf.M11 = mtx[0, 0];
buf.M22 = mtx[1, 1];
buf.M33 = mtx[2, 2];
buf.M12 = mtx[0, 1];
buf.M21 = mtx[1, 0];
buf.M23 = mtx[1, 2];
buf.M32 = mtx[2, 1];
buf.M31 = mtx[2, 0];
buf.M13 = mtx[0, 2];
return(buf);
}
/// <summary>
/// Converts the defined tensor into a 3x3 matrix.
/// </summary>
/// <param name="tensor">The tensor.</param>
/// <returns>generated matrix</returns>
public static Matrix ToMatrix(BendingStressTensor tensor)
{
var tens = new Matrix(3, 3);
tens[0, 0] = tensor.M11;
tens[1, 1] = tensor.M22;
tens[2, 2] = tensor.M33;
tens[0, 1] = tensor.M12;
tens[1, 0] = tensor.M21;
tens[0, 2] = tensor.M13;
tens[2, 0] = tensor.M31;
tens[1, 2] = tensor.M23;
tens[2, 1] = tensor.M32;
return(tens);
}
/// <summary>
/// The bending stress tensor needs to be converted into a cauchy stress tensor. Best to get the bending stresses at the integration points
/// </summary>
/// <param name="shellThickness">The thickness of the shell (for maximum bending stress)</param>
/// <param name="lambda">Thickness coordinate. Must be between -1 (bottom) and 1 (top). A value of 0 results in 0 stress (bendings stress is equal to zero for all components on the mid-fibre) </param>
/// <returns>The stress due to the bending of the plate. Add/subtract this stress with the membrame stress to get the total stress</returns>
public static CauchyStressTensor ConvertBendingStressToCauchyTensor(BendingStressTensor tensor, double shellThickness, double lambda)
{
//follows same logic as bending of the beams
//sigma = M . z / I
CauchyStressTensor cauchyStressTensor = new CauchyStressTensor();
var z = shellThickness / 2.0 * lambda;
var I = Math.Pow(shellThickness, 3) / 12;
cauchyStressTensor.S11 = tensor.M11 * z / I;
cauchyStressTensor.S22 = tensor.M22 * z / I;
//cauchyStressTensor.S11 = tensor.M13 * z / I;//due to naming on bending stress components defined here: https://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252014000900010#fig1
//cauchyStressTensor.S22 = tensor.M31 * z / I;//due to naming on bending stress components defined here: https://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252014000900010#fig1
cauchyStressTensor.S12 = tensor.M12 * z / I; //are you sure?
cauchyStressTensor.S21 = tensor.M21 * z / I; //are you sure?
return(cauchyStressTensor);
}
public FlatShellStressTensor(CauchyStressTensor membraneTensor, BendingStressTensor bendingTensor)
{
MembraneTensor = membraneTensor;
BendingTensor = bendingTensor;
}
public FlatShellStressTensor(CauchyStressTensor membraneTensor)
{
MembraneTensor = membraneTensor;
BendingTensor = new BendingStressTensor();
}
public FlatShellStressTensor(BendingStressTensor bendingTensor)
{
MembraneTensor = new CauchyStressTensor();
BendingTensor = bendingTensor;
}
