Paul M. Kurowski
President
Design Generator Inc.
London, Ontario, Canada

Thanks to progress in CAD and a high-level integration with FEA, analysis models are now prepared in CAD and solved with add-in FEA programs. This combination of CAD with FEA is so good that it blurs the difference between reality and abstract simulation models. For example, inexperienced FEA users tend to attribute the behavior of real objects to FEA models which are based on restrictive and simplifying assumptions.

To illustrate the problem, consider a CAD model in Two aligned links. What is the stiffness of the corresponding FEA model under a vertical load? Or to pose the question a different way: What displacement will be calculated for a given load? Not all FEA users will correctly answer the first question by stating that the stiffness of the FEA model is zero. Instead of considering the assumptions that went into the FEA model, we naturally recall practical experiences with similar linkages. Real-world experience tells us that links in a horizontal position can not support a vertical load, instead they will rotate a bit to find equilibrium under the load. This reasoning is true for real linkage but not for its FEA model. Unfortunately, we attribute the behavior of a real object to the corresponding FEA model, ignoring simplifying assumptions which are always present in the FEA model. Doing so makes it an attribution error.

Now and next month This first of two FE Updates looks at attribution errors, those made by assuming FEA can do more than it can. In next month’s column, Kurowski shows more common attribution errors and how to correct them. Models for both columns are available at designgenerator.com/MD2008.

The FEA model that could come from Two aligned links would be based on the assumption that model geometry, including the angle between links, DOES NOT change. This is a fundamental assumption of linear analysis. And as long as the pin-supported links remain horizontal they can’t support any vertical load, hence the stiffness is zero. Stiffness does changes with the link angle, but the initial stiffness is zero. Even when an FEA model of this linkage is based on nonlinear assumptions, which do account for changes in geometry during loading, the initial stiffness is still zero.

In another example, Block and shaft shows the deformed shape of a rubber block when an inserted steel shaft rotates. Many FEA users are surprised to see that square hole enlarges and the handle also grows larger. Restraints, materialproperties, and even errors in FEA code are blamed for the seemingly inexplicable results. The real explanation is simpler. In linear analysis, points move from the undeformed to deformed position along a straight path. When rotation is involved, the path of a point is perpendicular to the radius.

The same applies to a beam in bending. If we understood the assumptions in FEA model we would not be surprised to observe how a beam grows longer while it bends. Yet, we attribute properties of a real beam to an FEA model and then wonder about “strange” results.

Attribution errors also let us expect the impossible from an FEA model. For instance, having calculated the stress-based factor of safety of a curved I-beam we may sign-off on the design because FEA results reported no problems. Yet the beam will fail in buckling long before it develops dangerously high stresses. The fault is not with the FEA model. It correctly predicted stresses but was not intended to model buckling and so a likely mode of failure goes unnoticed. To detect buckling, we need to run a buckling analysis, not a static analysis.

Why doesn’t it melt? illustrates an odd expectation from the thermal analysis of a part made of aluminum bronze. Its melting point is 600°C. A fringe plot for a particular simulation shows the maximum temperature as 2,000°C. One student questioned the validity of the model because it did not melt! He attributed properties of a real plumbing part to an FEA model which was intended to model conductive heat transfer — not melting.

Users make similar errors meshing a model by attributing properties of real “little pieces” to finite elements ignoring the fact that the elements are abstract mathematical entities based on restrictive assumptions.

Serious errors come when, for example, users model a beam in bending with only one layer of first-order elements thereby making it incapable of modeling a bending-stress distribution. A similar and unfortunately common error uses a coarse mesh where the element size is larger than the size of stress-concentration area.

FEA attribution errors lead to invalid FEA results, and those to poor design decisions. To avoid the errors, we must understand the process that generates FEA results. Knowing FEA’s limits and shortcomings lets users avoid them and gain useful results from models.

Two aligned links

Aligned between links

Block and shaft

Beams grows longer