基于非概率集合理论的结构可靠性分析

摘要

基于非概率集合理论，给出了非概率可靠性指标的定义，阐述了不确定结构的区间分析和凸集合模型两种非概率可靠性的计算方法，并分析了两种方法获得非概率可靠性指标之间的关系。将不确定参数用区间和凸集合两种方式进行定量化描述，利用非概率可靠性指标的计算方法，对结构可靠性进行预测，通过比较两种方法对结构状态函数的响应范围，判断两种方法的合理性。通过两个算例进行分析，并与Monte Carlo方法比较，验证了凸集合方法用于结构可靠性分析的可行性与优越性。%Based on the non-probabilistic set theory, the non-probabilistic reliability index was defined, and computational process of interval analysis and convex set analysis was introduced and the relationship between the two non-probabilistic reliability indexes was analyzed. The uncertainty parameters were described by the interval and convex set methods. The non-probabilistic reliability index was calculated to predict the structural reliability. The reasonableness of these two methods wass judged by comparison with their response ranges of structural state function. By comparison with the Monte Carlo method, example results demonstrated the feasibility and superiority of convex set analvsis in structural reliability analysis.