On structural optimization for non-probabilistic reliability based on convex models

This paper discusses the setting and numerical solution of the non-probabilistic reliability-based structural optimization problem. Based on the convex model description for parameter scatters, the optimal design of non-deterministic structures is formulated as a nested optimization problem, in which the inner loop concerns a Min-max problem for evaluation of the reliability index. A performance measure-based method is proposed, where the feasibility of a design is determined through minimization of the performance function value within the parameter domain. The expensive computation of the non-probabilistic reliability index, as needed in the conventional approach, is thus avoided. The proposed approach is applicable to structural optimization problems accounting for deviations of material properties, geometrical dimensions and loading conditions. Moreover, the design sensitivity of the minimum performance function value can be readily evaluated. Numerical examples show the validity and efficiency of the present method.