中文摘要：

基于不确定性的凸模型描述，研究考虑非概率可靠性指标约束的结构优化问题．该优化模型是一个内层优化为极小极大问题的嵌套优化模型．为了有效地求解该模型，提出了一种基于目标性能的优化方法，通过寻找目标性能点来判断约束的满足情况，从而避免直接计算以极小极大（min-max）问题定义的非概率可靠性指标．提出的数值方法可处理材料、几何及载荷等不确定性参数，并且目标性能值的灵敏度计算公式简便，算法稳定．数值算例验证了所提出方法的正确性，也表明算法比文献中已有方法更为有效．

英文摘要：

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.