Stochastic Analysis in Structural Optimization

Structural optimization typically aims at high performance levels for a clearly specified set of conditions. Unfortunately, this goal can usually be achieved only by sacrificing robustness of the design. This implies a high sensitivity with respect to unforeseen stochastic situations or unavoidable random manufacturing tolerances. In order to prevent structural failure due to loss of robustness it is therefore desirable to incorporate a suitable measure of robustness into the optimization process. This can be achieved by introducing additional constraint conditions or appropriate modifications of the objective function. An example for such a design concept is reliability-based optimization based on the notion of the failure probability. This is most appropriate for high-risk structures such as e.g. power-generating facilites. Alternatively, simpler stochastic measures such as variances or standard deviations might be more appropriate for the design of low-risk structural elements which are frequently found e.g. in the automotive industry. The paper discusses the basic requirement for robust optimization and attempts to outline pros and cons of different approaches to the solution of this problem.