public AuxiliaryStatesTensors ComputeTensorsAt(CartesianPoint globalIntegrationPoint,
TipCoordinateSystem tipCoordinateSystem)
{
// Common calculations
PolarPoint2D polarCoordinates =
tipCoordinateSystem.TransformPointGlobalCartesianToLocalPolar(globalIntegrationPoint);
var commonValues = new CommonValues(polarCoordinates.R, polarCoordinates.Theta);
// Displacement field derivatives
Matrix2by2 displacementGradientMode1, displacementGradientMode2;
TipJacobians polarJacobians = tipCoordinateSystem.CalculateJacobiansAt(polarCoordinates);
ComputeDisplacementDerivatives(polarJacobians, commonValues,
out displacementGradientMode1, out displacementGradientMode2);
// Strains
Tensor2D strainTensorMode1 = ComputeStrainTensor(displacementGradientMode1);
Tensor2D strainTensorMode2 = ComputeStrainTensor(displacementGradientMode2);
// Stresses
Tensor2D stressTensorMode1, stressTensorMode2;
ComputeStressTensors(commonValues, out stressTensorMode1, out stressTensorMode2);
return(new AuxiliaryStatesTensors(displacementGradientMode1, displacementGradientMode2,
strainTensorMode1, strainTensorMode2, stressTensorMode1, stressTensorMode2));
}
public double[] EvaluateFunctionsAt(XNode node)
{
PolarPoint2D polarPoint = TipSystem.TransformPointGlobalCartesianToLocalPolar(node);
var enrichments = new double[enrichmentFunctions.Count];
for (int i = 0; i < enrichments.Length; ++i)
{
enrichments[i] = enrichmentFunctions[i].EvaluateAt(polarPoint);
}
return(enrichments);
}
public EvaluatedFunction2D EvaluateAllAt(PolarPoint2D point, TipJacobians jacobian)
{
double sqrtR = Math.Sqrt(point.R);
double cosThetaHalf = Math.Cos(point.Theta / 2.0);
double sinThetaHalf = Math.Sin(point.Theta / 2.0);
double value = sqrtR * cosThetaHalf;
var gradientPolar = Vector2.Create(0.5 / sqrtR * cosThetaHalf, -0.5 * sqrtR * sinThetaHalf);
Vector2 gradientGlobal = jacobian.TransformScalarFieldDerivativesLocalPolarToGlobalCartesian(gradientPolar);
return(new EvaluatedFunction2D(value, gradientGlobal));
}
public TipJacobians(TipCoordinateSystem tipSystem, PolarPoint2D polarCoordinates)
{
this.tipSystem = tipSystem;
double r = polarCoordinates.R;
double cosTheta = Math.Cos(polarCoordinates.Theta);
double sinTheta = Math.Sin(polarCoordinates.Theta);
inverseJacobianPolarToLocal = Matrix2by2.CreateFromArray(new double[, ]
{
{ cosTheta, sinTheta }, { -sinTheta / r, cosTheta / r }
});
inverseJacobianPolarToGlobal = inverseJacobianPolarToLocal * tipSystem.RotationMatrixGlobalToLocal;
}
public EvaluatedFunction2D[] EvaluateAllAt(NaturalPoint point, XContinuumElement2D element,
EvalInterpolation2D interpolation)
{
PolarPoint2D polarPoint = TipSystem.TransformPointGlobalCartesianToLocalPolar(
interpolation.TransformPointNaturalToGlobalCartesian());
TipJacobians tipJacobians = TipSystem.CalculateJacobiansAt(polarPoint);
var enrichments = new EvaluatedFunction2D[enrichmentFunctions.Count];
for (int i = 0; i < enrichments.Length; ++i)
{
enrichments[i] = enrichmentFunctions[i].EvaluateAllAt(polarPoint, tipJacobians);
}
return(enrichments);
}
/// <summary>
/// Gives a displacement a(s) value between a(v1) and a(v2).
/// Increments/decrements a(s) with 2 * PI until between a(v1) and a(v2).
/// </summary>
/// <param name="s"></param>
/// <param name="v1"></param>
/// <param name="v2"></param>
/// <returns> The generated vertex-displacement pair. </returns>
public static VertDispl DisplacementInBetween(PolarPoint2D s, VertDispl v1, VertDispl v2)
{
var bot = Math.Min(v1.alpha, v2.alpha);
var top = Math.Max(v1.alpha, v2.alpha);
if (MathUtil.EqualsEps(bot, top))
{
return(new VertDispl(s, bot));
}
var temp = s.Theta;
while (MathUtil.GreaterEps(temp, top))
{
temp -= MathUtil.PI2;
}
while (MathUtil.LessEps(temp, bot))
{
temp += MathUtil.PI2;
}
return(new VertDispl(s, temp));
}
public double EvaluateAt(PolarPoint2D point)
{
return(Math.Sqrt(point.R) * Math.Cos(point.Theta / 2.0) * Math.Sin(point.Theta));
}
internal double alpha; // angular displacement
public VertDispl(PolarPoint2D p, double alpha)
{
this.p = p;
this.alpha = alpha;
}
public TipJacobians CalculateJacobiansAt(PolarPoint2D polarCoordinates)
{
return(new TipJacobians(this, polarCoordinates));
}
