Accurate calculation of a stress gradient

[vpub]

Hello,

I am trying to calculate a stress gradient within a 2-D structure as accurately as possible. I have compared results in a simple example where the analytical solution is known (infinite plate with a hole).

I thought that the finer the mesh, the more accurate the result. But in fact I encountered some problems because of the extrem refinement (stress results are not good around the hole). I used a scaled model but the same problem occured. Thus it seems that a too fine model is not a good solution.

Does somebody have a good method or good advices in order to calculate this stress gradient.

Please feel free to ask if you want some detail about my case.

Thank you.

 

[corus]

Most likely you will have an error in your model as an FE solution will converge to the exact solution with increasing mesh refinement. You would need to post pictures of your model before any comment could be made.

corus

 

[vpub]

Well, how can I post pictures on this forum ?

vpub.

 

[corus]

You'll have to create a web-site using one of the many free services available such as geocities or netomat.net.

corus

 

[vpub]

That can be found now at

http://www.geocities.com/vlebaube/gradient.html

vpub.

 

[Drej]

The stress contours look fine to me. What exactly is the problem? If anything your mesh maybe just too fine (the elements are very small). Have you picked a particular node - at the re-entrant corner for example - and looked at the stress and displacement convergence?

 

[corus]

I agree with Drej, it looks fine to me. The only problem I see is that you are looking for the solution for an infinite plate and your plate isn't quite infinite so your answer isn't quite right. An error of 1% (assuming 3.000 is the exact answer) for your approximate infinte plate looks good enough to me. Perhaps there comes a point when you are refining the mesh so much that rounding errors in the computation come into play. This might be a reason for the slight discrepancy between your results and the 'exact' solution, given the other point I made.

corus

 

[vpub]

What you both are saying is right. But the problem I have is not to get the exact stress values but to get the value of the stress gradient as good as possible. And here when the mesh is too fine it does not allow to have a good precision (probably due to numerical problems). So I was asking if somebody knows another method or a solution from a "normal" mesh in order to calculate this gradient.