/// <summary>
/// Rotates the specified tensor.
/// </summary>
/// <param name="tensor">The tensor.</param>
/// <param name="angle">The angle, in radian.</param>
/// <returns></returns>
public static MembraneStressTensor Rotate(MembraneStressTensor tensor, double angle)
{
var rads = angle;
//formulation based on this: http://www.creatis.insa-lyon.fr/~dsarrut/bib/Archive/others/phys/www.jwave.vt.edu/crcd/batra/lectures/esmmse5984/node38.html
// TODO: MAT - set values directly
var sigma = new Matrix(2, 2);
sigma.SetRow(0, new double[] { tensor.Sx, tensor.Txy });
sigma.SetRow(1, new double[] { tensor.Txy, tensor.Sy });
var t = new Matrix(2, 2);
t.SetRow(0, new double[] { Math.Cos(rads), Math.Sin(rads) });
t.SetRow(1, new double[] { -Math.Sin(rads), Math.Cos(rads) });
// TODO: MAT - the product could be directly computed in a helper method (CalcUtil).
var rotated = t * sigma * t.Transpose();
var buf = new MembraneStressTensor()
{
Sx = rotated[0, 0],
Sy = rotated[1, 1],
Txy = rotated[0, 1]
};
return(buf);
}
/// <summary>
/// Rotates the specified tensor.
/// </summary>
/// <param name="tensor">The tensor.</param>
/// <param name="angle">The angle, in radian.</param>
/// <returns></returns>
public static MembraneStressTensor Rotate(MembraneStressTensor tensor, double angle)
{
var rads = angle;
//formulation based on this: http://www.creatis.insa-lyon.fr/~dsarrut/bib/Archive/others/phys/www.jwave.vt.edu/crcd/batra/lectures/esmmse5984/node38.html
var sigma = new Matrix(2, 2);
sigma.SetRow(0, tensor.Sx, tensor.Txy);
sigma.SetRow(1, tensor.Txy, tensor.Sy);
var t = new Matrix(2, 2);
t.SetRow(0, Math.Cos(rads), Math.Sin(rads));
t.SetRow(1, -Math.Sin(rads), Math.Cos(rads));
var rotated = t * sigma * t.Transpose();
var buf = new MembraneStressTensor()
{
Sx = rotated[0, 0],
Sy = rotated[1, 1],
Txy = rotated[0, 1]
};
return(buf);
}
public double Sx, Sy, Txy; //σx, σy, τxy
public static MembraneStressTensor operator +(MembraneStressTensor left, MembraneStressTensor right)
{
var buf = new MembraneStressTensor();
buf.Sx = left.Sx + right.Sx;
buf.Sy = left.Sy + right.Sy;
buf.Txy = left.Txy + right.Txy;
return(buf);
}
public static MembraneStressTensor Transform(MembraneStressTensor tensor, Matrix transformationMatrix)
{
var tensorMatrix = ToMatrix(tensor);
var rtd = transformationMatrix.Transpose() * tensorMatrix * transformationMatrix;
var buf = FromMatrix(rtd);
return(buf);
}
public static MembraneStressTensor Transform(MembraneStressTensor tensor, Matrix transformationMatrix)
{
var tensorMatrix = ToMatrix(tensor);
// TODO: MAT - the product could be directly computed in a helper method (CalcUtil).
var rtd = transformationMatrix.Transpose() * tensorMatrix * transformationMatrix;
var buf = FromMatrix(rtd);
return(buf);
}
public static MembraneStressTensor GetPrincipalStresses(MembraneStressTensor tens)
{
var c1 = (tens.Sx + tens.Sy) / 2;
var c2 = Math.Sqrt(Math.Pow((tens.Sx - tens.Sy) / 2, 2) + Math.Pow(tens.Txy, 2));
var buf = new MembraneStressTensor();
buf.Sx = c1 + c2;
buf.Sy = c1 - c2;
return(buf);
}
public static MembraneStressTensor Multiply(MembraneStressTensor t1, double coef)
{
var buf = new MembraneStressTensor();
buf.Sx = t1.Sx * coef;
buf.Sy = t1.Sy * coef;
buf.Sz = t1.Sz * coef;
buf.Txy = t1.Txy * coef;
buf.Tyz = t1.Tyz * coef;
buf.Tzx = t1.Tzx * coef;
return(buf);
}
public static MembraneStressTensor operator -(MembraneStressTensor left, MembraneStressTensor right)
{
var buf = new MembraneStressTensor();
buf.Sx = left.Sx - right.Sx;
buf.Sy = left.Sy - right.Sy;
buf.Sz = left.Sz - right.Sz;
buf.Txy = left.Txy - right.Txy;
buf.Tyz = left.Tyz - right.Tyz;
buf.Tzx = left.Tzx - right.Tzx;
return(buf);
}
public static MembraneStressTensor FromMatrix(Matrix mtx)
{
var buf = new MembraneStressTensor();
buf.Sx = mtx[0, 0];
buf.Sy = mtx[1, 1];
buf.Sz = mtx[2, 2];
buf.Txy = mtx[0, 1];
buf.Tyz = mtx[1, 2];
buf.Tzx = mtx[2, 0];
return(buf);
}
public static Matrix ToMatrix(MembraneStressTensor tensor)
{
var tens = new Matrix(3, 3);
tens[0, 0] = tensor.Sx;
tens[1, 1] = tensor.Sy;
tens[2, 2] = tensor.Sz;
tens[0, 1] = tens[1, 0] = tensor.Txy;
tens[0, 2] = tens[2, 0] = tensor.Tzx;
tens[1, 2] = tens[2, 1] = tensor.Tyz;
return(tens);
}
