荆南长江干堤模糊自适应随机损伤机理研究

Fuzzy self-adapting stochastic damage mechanism for Jingnan main dike of Yangtse Rive

基于损伤、概率、模糊隶属度在[0,1]区间内度量的协调一致性,得出了发展模糊随机损伤力学的观念.提出了模糊随机损伤的基本概念模型、推导了基于损伤的模糊随机变分列式.在分析损伤变量广义不确定性实质的基础上,构造并解释了3类损伤变量的模糊性态,提出了模糊损伤的降半分布、"秋千"分布和组合"秋千"分布,它们可以分别探讨不同形式下随机损伤的模糊演变过程,实现了随机损伤变量的模糊化和去模糊化过程的自适应生成与构建.根据扩张原理及随机损伤变量满足β概率分布的理论和定义,对模糊集上随机损伤变量的累积分布函数(CDF)、概率密度函数(PDF)积分进行修正,实现了模糊随机有限元可靠度与模糊随机损伤的同步分析.自主研制了模糊随机损伤有限元程序,并对荆南干堤的典型堤段进行了三维模糊随机损伤场力学性态的分析与研究.

Fuzzy stochastic damage mechanics development original model was introduced based on the harmony of damage conception, probability, fuzzy degree of membership on [0, 1] scale. Then a fuzzy stochastic damage conceptional model was proposed and a fuzzy stochastic variational formulation was deduced. Three damage variables＇ fuzzy definition status were formulated and translated by analyzing damage variable generalized uncertain essentiality. Furthermore, setup was three fuzzy damage variables＇ distribution, namely, half depressed distribution, swing distribution and combined swing distribution. The three distribution simulated various fuzzy evolution under diverse stochastic damage situation, and stochastic damage variables＇ fuzzy and de-fuzzy process were realized during adaptive generation and formation. Fuzzy stochastic finite element method and fuzzy stochastic damage were implemented concurrently under expansion theory with the adjustment on cumulative distribution function （CDF） and probabilistic density function （PDF） of fuzzy stochastic damage variables submitting to β probabilistic distribution. Three-dimensional fuzzy stochastic damage mechanical status of Jingnan main dike typical numerical model was analyzed by fuzzy stochastic damage finite element method program under property authority.