[v1.0.1] Wrong stress projection to points

[adtzlr]

Quadrature points are indexed differently compared to the cell connectivity (due to the usage of quadpy). Thus, stress projection delivers wrong results.

A collection of tasks:

• For linear quadratures the point ordering should be permuted in order to match cell ordering.
• add a tools.project function for the stress projection to mesh-points (basically the code-snippet above)
• argument to average results
• add tools.project() to Getting Started Example (see tests)
• check axisymmetric stress result
• add permute for Gauss-Legendre order=2 dim=3

[adtzlr]

Gauss-Legendre points and weights are now calculated by numpy (#96). Two improvements should be made:

• check if cell_type is Quad or Hexahedron, else raise NotImplementError
• for linear quadratures the point ordering should be permuted in order to match cell ordering.

The first point is probably not a good idea because this also works for higher order elements if a permuted quadrature is applied,

[adtzlr]

permutations are

• Quad permute = [0, 1, 3, 2]
• Hexahedron permute = [0, 1, 3, 2, 4, 5, 7, 6]

set them as default for order=1 and dim=2 or 3

[adtzlr]

Fixed for line, quad and hexahedron by #97 . For all other types, projection is still wrong. Probably add a warning or something else.

[adtzlr]

Another method is to use discontinous stress fields. This involves a disconnected mesh (see #101 and #102 ) as well as an inverse quadrature rule (see #103 and #104). Further work has to be done on modified regions, fields.

[adtzlr]

There was a typo in tovoigt which affected all versions <= 1.0.1. fixed; see #105 and #106

[adtzlr]

Another method is to use discontinous stress fields. This involves a disconnected mesh (see #101 and #102 ) as well as an inverse quadrature rule (see #103 and #104). Further work has to be done on modified regions, fields.

this code does the job (getting started example):

# ...
from felupe.math import dot, det, transpose, tovoigt

s = dot(P(F), transpose(F)) / det(F)

s2 = tovoigt(s).T.reshape(-1, 6)
m2 = mesh.as_discontinous()
q2 = quadrature.inv()
r2 = felupe.Region(m2, element, q2, grad=False)
f2 = felupe.Field(r2, dim=6, values=s2)

cauchy2 = f2.interpolate().T.reshape(-1, 6)

v2 = displacement.values[mesh.cells].reshape(-1, 3)
u2 = felupe.Field(r2, dim=3, values=v2)

felupe.tools.save(
    r2,
    u2,
    filename="result_with_cauchy_dg.vtk",
    point_data={"CauchyStress": cauchy2},
)

[adtzlr]

and this is the result from tools.topoints() (stress values translated from quadrature to mesh points; averaged), same colormap as above.

[adtzlr]

What is missing:

• add a tools.project function for the stress projection to mesh-points (basically the code-snippet above)
• argument to average results
• check how to handle mixed field problems

[adtzlr]

• add tools.project() to Getting Started Example (see tests)

[adtzlr]

What about axisymmetric analyses?