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Why Larger Nodal than Element Values of Stress?

Question asked by John Willett on Dec 3, 2015
Latest reply on Dec 9, 2015 by Jim Riddell

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In some studies I'm getting maximum von Mises stress values that are much larger in the nodal presentation than in the element presentation For example, the following images are from a linear, static analysis of a rod in a cylindrical hole, modeled in half symmetry. The stress due to a (hidden) rod is being concentrated on an outside (non-reentrant) edge of the part with the hole, looking from below:

Nodal Stress:

Element Stress:

I thought I understood from SW Help and elsewhere that, although element stresses are computed from an average of the 4 Gauss within the (second-order, tetrahedral) element, they are not considered "smoothed." Nodal stresses, on the other hand, are supposed to be smoothed by averaging the element values in all contiguous elements. But an average cannot be larger than any of the terms that go into it!

I started looking at element values because I read that it was a good way to assess the adequacy of the mesh: Too much variability among contiguous elements (as illustrated above) means that the mesh is too coarse. But the comparison above suggests that I'm misunderstanding how nodal stresses are computed and also maybe underestimating the maximum stresses by using element values. Any clarification would be appreciated. -- John Willett

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Mike Pogue Dec 3, 2015 11:46 AM
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I think you have the definition a little off. This video makes it clearer than I could SolidWorks Simulation - Element Stresses and Nodal Stresses - YouTube . Another thing to look at is that the element stress is close to the nodal stress--a good sign of convergence. I'm not sure what the conditions or goal of your study are, but it's very unlikely that reporting yielding in that small of a volume is going to have any real-world effect (no warranty stated or implied ).
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- John Willett @ Mike Pogue on Dec 3, 2015 12:50 PM
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  >>I think you have the definition a little off. This video makes it clearer than I could SolidWorks Simulation - Element Stresses and Nodal Stresses - YouTube .<<
  
  Great resource, Mike. Thanks!
  
  I can bring Anthony's explanation into agreement with SW Help ["...you can report a single element stress value as the arithmetic average (mean) from all Gauss points within each element."], if I assume that "extrapolation" means simply that the element value at each node is that of the nearest Gauss point. Then the element stress from averaging the nodes becomes simply the average of its Gauss points.
  
  Then everything makes sense except the observation that the nodal results appear to be consistently larger than the element results, both in Anthony's convergence example and in mine. Is there some reason for this, or is it just dumb luck?
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  - Mike Pogue @ John Willett on Dec 3, 2015 1:29 PM
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    I believe the nodal stress is higher by definition, because the software reports the node in the element with the highest stress.
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    - John Willett @ Mike Pogue on Dec 3, 2015 1:42 PM
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      >>I believe the nodal stress is higher by definition, because the software reports the node in the element with the highest stress.<<
      
      Mike -- While that would certainly explain it, it does not agree with either Anthony's or SW Help's explanation. For example, SW Help says, "When you plot nodal stresses, the program averages the stress values from all adjacent elements contributing at that node."
      
      Can anyone else weight in here with an explanation (or counterexample)? -- John Willett
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      - Mike Pogue @ John Willett on Dec 3, 2015 1:47 PM
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        Each node is shared by multiple elements. In my understanding, SW will extrapolate to each node from the Gaussian points of each element that node is touching. Each extrapolation will produce a different answer for the same node. The average of the answers is the stress at that node.
        
        But in the nodal stress plot, each element takes the highest stress of any node it contains, each node having been calculated as above.
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        John Willett @ Mike Pogue on Dec 9, 2015 12:14 PM
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        Dear Mike -- In case anybody is interested, I asked tech support at my VAR about why nodal stress tends to be larger than element stress. After several iterations here's what I pieced together. It basically agrees with Anthony's video but with a little additional information and an important additional inferrence:
        
        >>Each node is shared by multiple elements. In my understanding, SW will extrapolate to each node from the Gaussian points of each element that node is touching. Each extrapolation will produce a different answer for the same node. The average of the answers is the stress at that node.<<
        
             This is correct as far as it goes. The missing piece of information is that, as I had guessed above, the "extrapolation" is simply taking the value at the Gaussian point spatially closest to the node. Given that the element value is an average of the Gaussian points it contains and that the nodal value is the average of the closest Gaussian points in each element sharing that node, one would not immediately expect either nodal or element values to have generally larger magnitudes, but...
        
        >>But in the nodal stress plot, each element takes the highest stress of any node it contains, each node having been calculated as above.<<
        
             The above is apparently not the correct explanation (or else I don't understand what you mean). The averaging in the two cases is as you explained above with no special selection of maximum values. The reason that nodal values tend to be higher than element values near singularities (like the edge of the hole in my images above) is a bit more subtle and requires inference:
        
             Imagine a quasi-linear singularity like an edge with tetrahedral elements scattered over it. The Gaussian points nearest the singularity will have the highest stress values. For elements along the singularity there will usually be some Gaussian points in each that have smaller stress because they are further from the singularity. Averaging all of these together will typically give a result smaller than the maximum in the element. For nodes that are close to the singularity, however, the story is different. These nodes are shared by several elements, each of which generally contributes its largest Gaussian point to the nodal average. This is not by definition but rather because of the "extrapolation" method, which associates the nearest Gaussian point with the node and these nearest Gaussian points also tend to be closest to the singularity, hence largest. Thus the nodal value often becomes the average of the largest Gaussian points in the contiguous elements.
        
             Thus my VAR tells me that best practice uses nodal stress values (which better pick out the maxima), but that element stresses are often used as a good way to test convergence of the simulation.
        
             Does this make sense? -- John Willett
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Seckin Uslu Dec 4, 2015 4:00 AM
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There can be a possible sharpness that area. Make a finer mesher and re run analysis.

If the stress getting higher, add a radyus that area and re run analysis.

SOLIDWORKS Simulation - Stress on Sharp Edges / Tensioni sugli Angoli Vivi - YouTube
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- John Willett @ Seckin Uslu on Dec 4, 2015 1:41 PM
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  >>
  There can be a possible sharpness that area. Make a finer mesher and re run analysis.
  If the stress getting higher, add a radyus that area and re run analysis.<<
  
  Thanks, Seckin, but I think you're missing the point. I want to understand why the element and node versions of stress are so different in this and other simulations, not to get a better solution to any particular simulation. -- John Willett
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Jim Riddell Dec 9, 2015 12:38 PM
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This should help clear things up (haha):
http://www.eng-tips.com/viewthread.cfm?qid=232206
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- John Willett @ Jim Riddell on Dec 9, 2015 1:45 PM
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  >>This should help clear things up (haha)<<
  
  James -- "haha" indeed! Do you think I've got the gist of it above? -- John Willett
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  - Jim Riddell @ John Willett on Dec 9, 2015 2:16 PM
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    I'm not positive that I agree with your VAR since other solvers report only elemental stress and it is difficult to get nodal but overall you seem to have the main points as commonly accepted.
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Why Larger Nodal than Element Values of Stress?

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