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I hope this is the correct forum to post this question because I did not find one that really suits this question.

Basically I was reading this paper: 2D Triangular Elements

I like to implement things myself in Java and I did implement the formulas described in the paper. The result looks good (almost).

The first thing was creating a grid which looks like this (ignore the red dot):

enter image description here

And after solving it using the conjugate gradient method with $\text{res}=10^{-14}$ and after about $5500$ iterations, I get this result:

enter image description here

This looks alright and from an engineering point of view reasonable but if I zoom in, you can see this result:

enter image description here

There seems to be some kind of checkerboard pattern. The overall solution seems reasonable but the local solution seems wrong. Especially because elements with a different orientation seem to have a slightly different result.

You might argue that my implementation is wrong but I verified this many many times. Also at the end of the paper is an example with actual numbers which are also returned from my program when I input the grid from the paper.

My question now is:

Is this checkerboard pattern something that occures in FEA or should the result look "smooth"? The paper uses linear elements. Could this be the cause?

I am very happy for any help and/or advice!

Greetings Finn

Finn Eggers
  • 932
  • Do you have an analytical solution available? – copper.hat Jan 14 '20 at 19:49
  • I once verified it using a different example where there is nothing but a rod with a load at its end. the displacement at the end was correct to a millimeter – Finn Eggers Jan 14 '20 at 19:50
  • What are you solving? – copper.hat Jan 14 '20 at 19:57
  • stress/strain in 2d elements – Finn Eggers Jan 14 '20 at 19:57
  • Can you try solving a much simpler system to see if there are any bugs? Did you write the plotting side of things as well? – copper.hat Jan 14 '20 at 20:01
  • Yes I implememented the plotting myself aswell.

    Yeah sure. 1 second

     – Finn Eggers Jan 14 '20 at 20:01
  • I guess I would have expected more 'monotonicity' and the regularity suggests a minor bug. – copper.hat Jan 14 '20 at 20:02
  • http://prntscr.com/qnpnbk

    The problem also occurs here

     – Finn Eggers Jan 14 '20 at 20:03
  • Sorry, first, I am no expert. However, the artifacts in the latter also have that sort of rotation thing going on. Is there anything in the plotting that skips over pairs or anything like that? (A bit vague, I know.) – copper.hat Jan 14 '20 at 20:04
  • No. It's going through all the triangles and the color is calculated for each triangle. This also happens for irregular grids which I used aswell – Finn Eggers Jan 14 '20 at 20:05
  • @FinnEggers did you try to solve the problem with different meshes? Or different Solvers? I would suggest solving the same problem with FreeFem++, since you can very easily define the model and access all the FE matrices for comparison. – PierreCarre Jan 15 '20 at 10:02
  • No I haven’t done that. I know that their solution looks smoother but they use higher polynomials for interpolation – Finn Eggers Jan 15 '20 at 10:03
  • @FinnEggers In FreeFem++ you explicitly choose the FE spaces, so you can reproduce your results exactly. Moreover, you can import the FreeFem++ solution to your own visualization module. – PierreCarre Jan 15 '20 at 13:57

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