基于非概率可靠性的结构优化设计研究

基于不确定参量的凸集合描述,研究了考虑非概率可靠性约束时,结构优化设计模型的求解问题。由于非概率可靠性指标是用一个极小极大模型来定义的,故以该指标作为设计约束,将得到一个嵌套的二级优化模型。为了求解该模型,提出了一种序列线性化的计算方法。利用非概率可靠性分析的拉格朗日乘子,逐步构造可靠性指标的一阶近似,通过序列线性规划法求解二级优化问题。该算法可用于区间变量和超椭球凸集模型并存的情形,具有较好的适用性。论文给出了主要的敏度计算公式,并通过简单算例对所提算法进行了验证。

Approach to Optimization of Uncertain Structures Based on Non-probabilistic Reliability

The optimization problem of uncertain structures based on non-probabilistic reliability is investigated.The uncertain parameters are bounded by convex models.The non-probabilistic reliability index is adopted to evaluate safety of structures and taken as a design constraint so that the optimum design can resist a given level of uncertainty.Since the non-probabilistic reliability index is defined by a min-max model,the reliability-based design is a two-level optimization problem that involves a nested loop procedure for the overall optimization and iterative reliability evaluation.To solve this problem efficiently,a sequential linearization method is developed.The method is easily integrated into sequential linear programming(SLP) algorithm and can be used in cases of the mixture of ellipsoidal convex models and interval variables.A simple example is given to demonstrate the proposed approach.