Comparative Analysis: Ansys vs. FEniCSx [Displacement in Linear Elasticity]

[jaribeiro]

@dokken

VTX

Thank you, @dokken. I switched to using the VTU format, and now the stress values are accurately represented within the cells

[jaribeiro]

@dokken

The values are not well defined at nodes when using a first order serendipity (equivalent to Lagrange) element, as the derivatives are discontinuous at both facets and vertices between cells.

Thank you for the excellent explanation; it makes sense. So, if I use higher-order elements, like quadratic elements, the discontinuities will start to reduce. In this case, is it possible to have the stress and von Mises values accurately represented at the nodes?

@dokken

Note that projections introduces Gibbs phenomenon, as shown in

Commercial software typically displays von Mises stress and other stress values at the nodes. Do you know if these software packages employ specific methods to address the Gibbs phenomenon, or do they simply overlook this issue? Thanks, @dokken

[dokken]

@jaribeiro

Thank you for the excellent explanation; it makes sense. So, if I use higher-order elements, like quadratic elements, the discontinuities will start to reduce. In this case, is it possible to have the stress and von Mises values accurately represented at the nodes?

If you use quadratic elements, the discontinuities are in DG-1, so still not well defined, But the differences should start to decrease.

[dokken]

@jaribeiro

Commercial software typically displays von Mises stress and other stress values at the nodes. Do you know if these software packages employ specific methods to address the Gibbs phenomenon, or do they simply overlook this issue

I simply dont know, as ive never used commercial fem software. Hopefully someone Else can comment on this aspect

[jaribeiro]

Thanks @dokken, I was finally able to replicate the results:

Displacement x:

Displacement y:

For the von mises stress:

The differences are almost negligible in the displacements. However, in the von Mises stress, there are some variations, but they can be explained by the reason you initially mentioned: “the discontinuities are in DG-1, so still not well defined. But the differences should start to decrease.”

Thanks for the help, @dokken!