基于模糊随机损伤力学的模糊自适应有限元分析

Fuzzy self-adapting finite element method based on Fuzzy stochastic damage mechanics

为延拓非确定损伤理论研究以揭示损伤力学本质,基于损伤、概率、模糊隶属度在[0,1]区间上协调一致性提出模糊随机损伤力学观念。构造解释了3类损伤变量模糊性态及对应模糊映射分布,即降半分布、"秋千"分布和组合"秋千"分布,实现了随机损伤变量模糊化自适应生成与构建。依据扩张原理及随机损伤变量满足β概率分布,对模糊集上随机损伤变量的CDF、PDF积分修正,结合当量正态理论,将3类模糊随机损伤泛函引入本构方程,完成模糊随机有限元可靠度与模糊随机损伤同步分析。用自主研制分析软件对龙滩碾压混凝土坝做三维模糊随机损伤场力学性态研究,由复杂随机场与模糊随机损伤分析的成功融合证明分析方法是适用的、可行的、必要的。

Fuzzy stochastic damage mechanics development original model was introduced to discover the essential of damage mechanics with damage uncertainty＇ s proper expansion based on the harmony of damage conception, probability, fuzzy degree of membership on [0,1] scale. Three damage variables＇ fuzzy definition status and the corresponding fuzzy mapping distributions were formulated, namely, half depressed distribution, swing distribution and combined swing distribution, by which the stochastic damage variables＇ fuzzy process was realized during adaptive generation. According to the expansion theory and the β probabilistic distribution,CDF and PDF of fuzzy stochastic damage variables were adjusted. Based on the equivalent normalization theory, the model was clarified by the introduction of the three fuzzy stochastic damage functionals into the constitutional model and then the reliability and the fuzzy stochastic damage were analyzed on the basis of the fuzzy stochastic finite element method. 3-dimension fuzzy stochastic damage mechanical status of the numerical model of Longtan rolled-concrete dam was researched by the self-developed fuzzy stochastic damage finite element method. Compatible application of the comprehensive random field study and the fuzzy stochastic damage model research proves that all of the work are applicable, viable and essential.