Issues that FEA salesfolk may forget to mention.

Re-Entrant Corners

The focus on drawings can lead to rushing the drawings where the fillets are not drawn for every re-entrant corner. St. Venant's theorem indicates that these errors can be small if there are no major load paths through that area. If the mesh is held at the drawing level, this can be a decision made for future designs where this assumption may not apply.

Yet re-entrant corners are still found in major and local magazines as a showcase for a "good" FE model. And the error can be infinite for even a modest re-entrant corner: Like in this collage summary of the following paper's results.

Facets, facets, everywhere

Coming soon, how h-level (element segmentation) can introduce an effect similar to the above stress concentrations -- and they are still concentrations until the angle is 180 degrees. Facets are faces that surround pipe interiors and exteriors. Facets are on the edge of a hole in a plate. Facets are everywhere.
    Coming later are quotes from the introductory presentations about push-button FEA from the 1998, 1999, ... MSC User’s Conferences. The push from manufacturers to use non-degreed designers to do structural analysis was frightening but backed up with millions of dollars, warping the ordinary evolution of technology. In spite of some automation improvements, the parallels between ‘the future’ seen then, the projections of FEA use expected then, compared to now (2025), are frightening.

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Where is the maximum stress?

maxStressOnThinShellFacetJoint2.png For thin-shell theory, where is the maximum stress on this folded card only loaded under its own weight while it stands on a flat table?

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Example problems

These problems of ignoring the singularities and non-singular geometric false high stress locations used to be endemic in the cover of magazines, Mechanical Engineering and the like. Maybe the sales organizations are starting to learn their lesson, but it keeps happening so much that most of us do not even point it out anymore. The problem with a near-singularity is that the combination of h-level and p-level (mesh density and polynomial order) will change the stress at the outside of the structure, which should be the location of highest stress (except for cases like Hertz contact stresses) and can often make the interpolation smaller or even of the wrong sign when using solid elements with high p-level near loading locations. The industry has “exclusion elements” to use Saint Venant’s method to ignore the stress in singular areas. And for non-singular geometric concentrations, internal angles more than 108 degrees but less than 180 degrees, what automated methods are there, training?
    Did you check to make sure that your exclusion, wait, your FE model incorrectness, did not affect the load path in a way that affects some future use of your model? Saint Venant had particular academic models in mind, models that were never “re-purposed” to use for something different. We know that loads converge before stress values do. However, large passenger aircraft often have load errors in the model that show up because in order to get the entire assembly to run they have to use thousands of pounds of force to twist and shove a location of the aircraft far from ‘critical areas’ of expected study in order to maintain the aircraft still – the aircraft model would literally be under load that would in a transient analysis have it accelerating in translation and rotation, on the order of a small plane motor vehicle meant to move the plane by the nose gear. The model we are familiar with was a bit larger than a 737 and smaller than a 757 with the stabilizing (fake) loads required ending up between 2,000 and 3,000 lbf (pound-force). As of 2000 this was common, but not something that makes it into the FEA sales literature. Using Saint Venant’s principle is not something that has no negative effect on the vehicle no matter how confident the chief engineer is. He is not the one who will lose his professional engineer license (which most of them do not have), it will be the stress engineer that made the model that goes up before the boards and courts.
    So sad that the software salesmen that push these methods of 5-minute analysis for the speed you get by skipping the double cost of modeling the fillets The model is such a small part of setting up an FE model that it is sheer madness to skip steps that seem to not matter in the initial check on the model, because when the model has a new task, and it will, you cannot afford to go back and correct your false savings because you will not remember where the shortcuts are. Such a shame.
    The folded card high stress would only be along the corner for thick-shell theory, something a solid model would tend to imply. For the specified question (Where is the highest strain on the [thin-shell theory] card?), think about the stress-strain relation where stress is Young's modulus times the strain. Where is the highest strain on the card? If you are unsure, press it down a bit. Where is it moving the most?
    For the published incorrect analyses like this public advertisement, the maximum stress on the left concentration is orders of magnitude higher than reported - for that model, but not infinity, which is the value on the right. It would be true that the actual part has lower stress than this model should show, but the model is not correct, which is one reason it is far from converging to the solution. Therefore, it cannot be of use in an A-B comparison.

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