模糊运算和模糊有限元静力控制方程的求解

根据模糊数的区间形式表达和区间运算的性质，给出了模糊数和模糊变量的运算规则，据此并依据区间有限元理论，提出了结构模糊有限元静力控制方程的几种求解方法。方法可根据输入模糊数的隶属函数，给出结构响应量的可能性分布，且计算量小，易于实施，算例分析说明了方法是实用和可行的。

Fuzzy Arithmetric and Solving of the Static Governing Equations of Fuzzy Finite Element Method

The key component of finite element analysis of structures with fuzzy parameters, which is associated with handling of some fuzzy information and arithmetic relation of fuzzy variables, was the solving of the governing equations of fuzzy finite element method. Based on a given interval representation of fuzzy numbers, some arithmetic rules of fuzzy numbers and fuzzy variables were developed in terms of the properties of interval arithmetic. According to the rules and by the theory of interval finite element method, procedures for solving the static governing equations of fuzzy finite element method of structures were presented. By the proposed procedure, the possibility distributions of responses of fuzzy structures can be generated in terms of the membership functions of the input fuzzy numbers. It is shown by a numerical example that the computational burden of the presented procedures in low and easy to implement. The effectiveness and usefulness of the presented procedures are also illustrated.