This conference paper was submitted for presentation at the NAFEMS World Congress 2025, held in Salzburg, Austria from May 19–22, 2025.

Abstract

If an industrial design buckles during operation, which is in most cases an undesirable behavior, there is for sure a good advice needed on how to avoid the buckling phenomenon, if possible. Of course, the CAE guys should provide this advice, which indeed can be provided in linear buckling cases by appropriate optimization techniques. The situation becomes much worse in case of nonlinear buckling, where contact forces and geometrically nonlinear displacements and even plasticity have to be taken into account. No optimization method is currently available, which works for the objective function '˜no buckling'™. It is the purpose of this paper to describe how one can get a modified design which does not buckle under the given loading. This can be understood as a first step to optimization. Whether buckling happens or not during a nonlinear static analysis cannot be known in advance. If buckling happens, one could even get a final result after buckling, but this does not give any hint on how to modify the design to avoid buckling. Classical optimization methods start from a result and ask, how the design has to be changed to modify one or several results of the analysis. Even, if one finds a way to overcome the nonlinear buckling by optimization, one has to be aware of the fact, that this modified design could show another buckling case at another load level. This could cause another optimization of this buckling case. The number of necessary optimizations to get a non-buckling design under the given loading could not be predicted. One important reason for this situation is contact, because any design change may directly change the contact forces, which trigger the possible occurrence of buckling. So, if nonlinear static analysis under contact leads to buckling, we have to find a useful strategy to get a non-buckling design under the given loading. Here, the basic idea is to use the occurring buckling mode shapes to derive a design modification. The buckling modes are not only easy to compute, but they will also give the chance to repeat the modification of the design with any number of sequent buckling cases. This would open a way to find a modified non-buckling design by one single process and one single job. This paper will demonstrate the process using an industrial use case. In addition, this process will be performed for both elastic and plastic material properties to show the difference between both cases. All computations and result evaluations are performed using the industrial CAE code PERMAS.