Stress Contour Plots and Nodal Averaging

[trainguy]

Can anyone tell me the standard (FEA) industry approach regarding (stress)contour plots? I am hoping to use nodal contours WITH averaging as this gives smaller looking hot spots. Is this standard practice? The analyses are mostly linear static, but I also have a non-linear static run to document.

My plots with nodal contours of Maximum values are simply too "red".

When should we use elemental contours?

 

[EdR]

Trainguy:

You may get multiple different responses to this question but here is mine......First a couple of background items....

FEM does NOT produce continuous stresses and/or strains between elements...only displacements (for static analysis). Also stresses/strains may be computed at different points within the element depending on the code and options selected..(yes these points don't necessarily have to be at Gauss points). As a result most results are averaged in some manner to get "nodal" stresses. How this averaging is done lies at the heart of your question..

Generally it is done simply by taking the stresses/strains from the points nearest a node and averaging them directly with values from other elements (which are in the same direction) connected to that node....This is fundamentally the equivalent to assuming a linear variation of stresses/strains between points at which the code computes them...Yes there may be some difference when the elements connected to a node are of different size, etc...but generally this difference will be small, particularly if the meshing is adequate to represent the response...Also if you think about it any assumption about the variation being a higher order than linear is very hard to justify....There are those who try and project nodal values from the shape functions and then average the values as described above but their results are little different than from the simple method and the added computational effort is significant. So my final recommendation is to check how the specific cods computes the "nodal" stresses...recognise what effect this will have on plotted results (like not being exactly zero on a free boundary) and accept those results...

Also note that the "hot" spots produced by the elemental stresses can be less accurate representations of the actual stress/strain at a point than the averaged values, depending on what caused the "hot"spot (and that is something you should probably be able to explain in determining the overall validity of the results)

Finally I can think of no useful purpose for raw elemental contours except for debugging or locating the "hot" spots discussed above, which if present should be explained...

Hope this helps

Ed.R.

 

[trainguy]

Thank you EdR, for your informative post. Here I was hoping to get a quick "this is how it's usually done" answer, and sure enough, I end up learning something!

Any other opinions out there?

tg

 

[corus]

"Raw" elemental contours will indicate how good your mesh is. If the elemental nodal values are within 75% of each other at coincident nodes (say) then your mesh is ok. Most codes include an option for viewing these elemental "block" contours as well as the smoothed averaged nodal contours.

 

[McLeod]

Depending on the specifics of your software, elemental contours may also be useful for controlling how and when output values are averaged. Results from elements of different thickness, material properties, etc. are typically NOT averaged.

I use MSC.Nastran for Windows (FEMAP + NASTRAN), which can use corner stresses instead of centroid stresses for elemental contours, giving essentially the same results as a nodal stress contour. Elemental contours have the added bonus of being able to control averaging. Typically, I allow averaging between elements, but not between elements with different properties, or between elements that intersect at angles greater than the default criterion (20 deg). This is especially useful when modeling with planar elements.

Whichever method you choose, the choices should be documented along with the results, because as you've already seen the results can vary widely due to the visualization method.

There are other considerations if you're concerned about the "redness" of your plot. Have you established that your results are converged by crunching at least 3 meshes of increasing density? How are your color levels being selected - automatically or by some material criterion?

NAFEMS (

http://www.nafems.org/publications/)

has several excellent publications which address these issues.