Multi-criteria optimizations and robustness estimations for problems of crashworthiness, structural dynamics, and acoustics of car bodies.

Recent work on optimization for crashworthiness have shown that evolutionary algorithms, e.g. [

1

] perform superior compared to other optimization strategies when meta-modelling fail in representing the physics of the problems [

2

]. This is valid especially for simultaneous optimization of several disciplines, i.e. for multi-disciplinary optimization (MDO). These problems are normally driven by the most non-linear problem (e.g. a frontal impact).

The high non-linearity of the optimization problems may lead to optimal designs which are loosing their optimality when the design variables are altered only slightly. Unfortunately, this will happen in all real industrial applications - either by additional constraints, by manufacturing irregularities, or by uncertainties inherent to the system. Thus, a robustness analysis should be integrated in the overall optimization scheme.

For many of the industrial-sized problems, computing time is not a negligible criterion for the successful implementation of the optimization into the product development process [

3

]. Evolutionary algorithms require a high amount of CPU time; an additional robustness analysis is thus problematic. Nevertheless, multi-criteria optimization problems have recently been solved successfully for acoustics, structural dynamics and even for crashworthiness.

Because a real robustness analysis is often too time demanding, a first estimate of the robustness of the chosen design on the Pareto front can be obtained by regarding the neighbouring points on the front. The variance of the design variables of these points along the Pareto front indicates sensitivities and therefore robustness. This will be demonstrated in first examples taken from industrial studies on acoustics, structural dynamics, and crashworthiness.