含模糊参数结构有限元方程的一种新解法  

A New Approach of Finite Element Analysis with Fuzzy Parameters

作　　者：陈原[1] 钱江[1] 

机构地区：[1]同济大学结构工程与防灾研究所,上海200092

出　　处：《力学季刊》2002年第2期210-218,共9页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(59823002)

摘　　要：实际工程问题中,常常会包含一些难以准确描述的系统参数。本文根据模糊集理论,将结构中的不确定参数转化为模糊参数,从而建立起含模糊参数的有限元平衡方程,应用一般模糊线性方程解的基本原理,对模糊有限元平衡方程解的概念及方法进行了讨论,并在此基础上提出了一种改进解的概念以及以摄动法为基础的求解方法。该方法假定当不确定参数相对于其清晰值的分解度不很大时,可以将其在清晰值附近作摄动展开。文中也简要讨论了改进解与现有的模糊有限元方程组各种解之间的关系。相对于现有的其它解法,本文建议的方法更易于与常规的有限元软件结合,用于处理工程实际问题。对算例结果的分析表明,本文方法可较好地符合实际要求。For engineering problems, it is often the case that there are some parameters that may not be precisely defined. In this paper, by using fuzzy sets theory, the establishment of finite element equations with fuzzy parameters was pressnted and the solution concept of finite element equations with fuzzy parameters was also discussed. In view of the difficulty to solve fuzzy finite element equation by using the existing methods, a new solution approach based on th perturbation method was proposed. It is assumed that the uncertain parameter may deviate from its crisp value only slightly thus the perturbation expansion at the crisp value can be applied. Compared with the existing approaches, the present one is relatively easier to be put into code in conjunction with conventional finite element software for practicl engineering purpose. Numerical example was given to illustrate the advantages of the new approach for fuzzy finite element equations.

关 键 词：模糊集 隶属度 Λ-截集 模糊线性方程组 摄动法 

分 类 号：O159[理学—数学] O241[理学—基础数学]