ACCURACY OF STRESS CALCULATION - WHICH METHOD IS BEST?

[Bhat165]

Hi,

I am doing a few coding on FEA using isoparametric continuum elements. I have read several books about the method of calculation of stress after the solution for displacement is available. My approach is: I calculate stress at the gauss points and then interpolate to the nodes using the shape functions. The final stress is the average of the stresses obtained from each element contributing to the node. Is my approach correct?

I have seen other proposed methods of stress calculation, such as using least square approximation from gauss point to nodal points, averaging over other adjacent elements etc.

My question is, what is the best method of stress calculation using isoparametric elements? Each method gives different answers to some extent. How do we make sure a software is giving correct stress? What are the methods available? Is my way of calculation correct?

Any help on this is appreciated with regard. Thanks.

Sudip

 

[brad]

There is no absolute "best". They all have merit. One way to check that the stress is "correct" is to see whether the different methods converge to a similar answer (if they don't, this is very often a sign of too coarse of a mesh).

Brad

 

[EdR]

Brad's comments are correct....The only addition I would make is to be careful when extrapolating from gauss points to nodes....depending on how it is done it can give very bad results....

Ed.R.

 

[Bhat165]

Hi Ed. R,

Can you explain a little bit by what do you mean by "depending on how it is done"? Thanks.

Sudip

 

[EdR]

The classic example is where the 1/4 point is used with parabolic shape functions which gives a singularity....

Ed.R.

 

[corus]

The normal method is as you have stated, to average the stress at common nodes from the interpolated values. Some codes will plot the element stresses with no averaging so that you can guage the accuracy of your mesh. Element nodal stresses that give similar values at common nodes between adjacent elements will show a good mesh. If you're using linear elements then there may be a greater difference between element nodal values as the stress is constant within the element but the averaged value between elements will be more accurate. The best way to test is to compare results against known benchmark examples. NAFEMS used to compare codes and give examples.