北京航空航天大学学报 ›› 2014, Vol. 40 ›› Issue (2): 222-228.

• 论文 • 上一篇    下一篇

结构模糊非概率混合可靠性分析方法

许孟辉, 邱志平   

  1. 北京航空航天大学 固体力学研究所, 北京 100191
  • 收稿日期:2013-04-12 出版日期:2014-02-20 发布日期:2014-03-03
  • 基金资助:
    国防基础科研计划资助项目(A2120110001,B2120110011);国家自然科学基金资助项目(10872017,90816024,10876100);“111”计划资助项目(B07009)

Reliability analysis of structures with fuzzy and non-probabilistic hybrid variables

Xu Menghui, Qiu Zhiping   

  1. Institute of Solid Mechanics, Beijing University of Aeronautics and Astronautics,Beijing 100191, China
  • Received:2013-04-12 Online:2014-02-20 Published:2014-03-03

摘要: 针对模糊非概率混合不确定性下结构可靠性分析问题,基于模糊数学分解原理将混合可靠性分析模型转化为[0,1]内连续分布隶属度水平下的非概率可靠性分析模型;针对非概率可靠度计算复杂性,基于逐维策略将结构功能函数最值的计算转化为最值点向量的逐维计算,提出一种确定结构功能函数界限的算法;通过在[0,1]内遍历隶属度值确定结构可靠度的隶属度函数实现结构可靠度模糊性的定量化.算例表明该方法的合理性,计算精度高和计算量小的特点为复杂工程结构可靠度分析及优化设计提供了可行途径.

Abstract: For the reliability analysis of structures in the case of coexistence of fuzzy and non-probabilistic uncertainties, the hybrid analysis model was transformed into non-probabilistic analysis models at different membership values distributed in the interval [0,1] continuously based on the decomposition principle of fuzzy mathematics theories. An algorithm for determining the minimum/maximum of the structural performance function was presented to overcome the complexity in calculating the non-probabilistic reliability based on the optimization strategy dimension by dimension, by which the determination of the extreme values was converted to that of the extreme point vectors of the performance function. The quantification of the fuzziness in structural reliability was accomplished with the membership function of the structural reliability obtained by traversing the membership value in the interval[0,1]. The reasonability of the presented method was proved by two engineering applications and the merits of high accuracy and efficiency suggest a feasible way for the reliability analysis and optimization of complicated engineering structures.

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