基于粗糙集理论下的结构随机分析中的有限元法

根据粗糙集理论中的上、下近似集概念和随机参数的定义，可以把结构分析中的随机参数转化为一定置信度意义下的区间数。当置信度从0取到1，将得到相应的上、下近似集所定义的一系列区间。利用区间算法的概念，可以运用普通的有限元程序对含有随机因素的工程结构进行强度分析。文中在讨论一般算法的前提下，提出三种算法即枚举法、区间方程组算法和区间算法结合力学知识算法。其中最后一种算法可以大大简化计算量。最后算例表明所提方法是有效的。

ANALYSIS OF THE RANDOM-STRUCTURE WITH THE ROUGH SET THEORY

Using concepts of the upper (lower) approximation in the rough set theory and the definition of confidence degree, random parameters in an engineering structure could be transferred into the interval numbers. When the confidence degree took from 0 to 1, a series of intervals in the upper (lower) approximation was determined respectively. With the algorithm of the interval operation, an engineering random structural problem was be studied by using a general finite element method program. Based on the algorithm of the interval equations, three new methods were presented, that is, enumerating, algorithm of the interval equations and combining with the concepts of the mechanics. Especially, with the last method, the calculating amount of the random finite element method could be as nearly as that of the general finite element method. Finally the examples show the methods currently and efficiently.