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
