Topology optimization considering uncertainties and failure consequences

Abstract

Results of structural optimization should be robust with respect to the uncertainties inherently present in resistance of materials and structural loads. This notion has lead to the development of different approaches to structural optimization: stochastic or robust optimization, fuzzy optimization and reliability-based structural optimization. The robust formulation yields multi-objective optimization problems, where the mean performance of the system should be maximized whereas performance variance should be minimized. The balance between these objectives is a subjective choice of the analyst. In reliability-based design optimization, a probabilistic measure of system performance, also subjectively chosen by the analyst, is used as design constraint. Consequences of failure are not explicitly taken into account by these formulations. However, the main effect of uncertainties is the possibility of reaching a state of undesirable system performance. This possibility can be measured in terms of probability, and then multiplied by the cost (monetary measure) of failure. The resulting term, also known as expected failure cost, can be incorporated in the objective function, leading to an unconstrained optimization problem (minimization of total expected costs). This formulation, also known as risk optimization, allows one to find the optimum point of compromise between competing failure modes, as well as the optimum safety margin with respect to each failure mode. This formulation has not been applied to the topology optimization of plane structures. The objective of the present research project is to investigate the effects of uncertainty and of failure consequences in the optimal topology of plane structures. The study is relevant because, besides materials, the form or topology of the structure also defines which failure modes are more likely. (AU)