龙滩碾压混凝土坝随机损伤力学分析的模糊自适应有限元研究

RESEARCH ON FUZZY SELF-ADAPTING FINITE ELEMENT IN STOCHASTIC DAMAGE MECHANICS ANALYSIS FOR LONGTAN ROLLED-CONCRETE DAM

在分析了损伤、概率、模糊隶属度在[0,1]区间内度量协调一致性基础上,为了更深刻理解和更本质地描述与研究损伤力学提出发展模糊随机损伤力学的观念。探讨损伤变量广义不确定性实质,进而构造并解释三类损伤变量的模糊性态,提出对应的模糊映射分布形式,即降半分布、"秋千"分布和组合"秋千"分布,三者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自适应生成与构建。分析并论证损伤广义概率特性,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概率分布函数和概率密度函数积分进行修正,结合当量正态理论,将三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的同步分析,实现了损伤模型的清晰化过程。借助自主研制的模糊随机损伤有限元程序,对龙滩碾压混凝土坝进行三维模糊随机损伤场力学性态的分析与研究,从而把随机场参数的统计相关性、非正态分布性全面融入模糊随机损伤分析的模型中,把损伤变量的不确定性做了完善的延拓、将模糊和随机两种不确定因素合理有效地引入连续损伤力学的分析与建模中。该研究工作对非确定损伤力学研究及结构可靠度分析都提供了一定的参考价值。

The origin and development of fuzzy stochastic damage mechanics are introduced in order to interpret and describe damage mechanics more essentially with the analysis of harmony of damage conception, probability, fuzzy degree of membership in interval[0, 1]. Three kinds of fuzzy conditions of damage variables are formulated and translated by analyzing damage variable generalized uncertain essentiality; the corresponding fuzzy mapping distributions, namely, half depressed distribution, swing distribution, combined swing distribution, by which the fuzzy evolving processes of stochastic damage with different forms can be discussed, were put forward; and the fuzzy process of the stochastic damage variables is realized during adaptive generation and formation. Furthermore, by the demonstration of damage variable＇s generalized probabilistic characteristics, according to the expansion theory and the theory and definition that damage variable accords with β probability distribution, the integrations of CDF, PDF for stochastic damage variable in fuzzy sets are modified. At the same time, combining with the equivalent normalization theory, three kinds of fuzzy stochastic damage functional are introduced into constitutive model to realize the sync analysis of reliability of fuzzy stochastic finite element method and fuzzy stochastic damage in fuzzy sets; and the damage model is clarified. 3D fuzzy stochastic damage mechanical characters of Longtan rolled-concrete dam are researched by self-developed fuzzy stochastic damage finite element method. The statistical dependence and abnormality of the random field parameters are considered comprehensively in fuzzy stochastic damage model. The uncertainty of the damage variable is extended perfectly; and the uncertainties of fuzzy and randomness are introduced into analysis and modeling of continuous damage mechanics rationally and efficiently. The research can provide references for innovation and extension of nondeterministic damage mechanics research and structure reliability analysis.