非确定结构系统区间分析的泛灰求解方法

工程中的不确定性问题可以用区间分析、概率理论或模糊理论来求解。采用泛灰区间分析法来处理结构静力分析和设计中的不确定性问题。将结构系统中的不确定性参数用区间数来表示，用有限元法建立系统的控制方程。该控制方程是线性区间方程组。然后，在概述泛灰数的概念及其运算规则的基础上，介绍了泛灰数与区间数的转化，利用泛灰数的可扩展性对区间进行分析，研究了泛灰线性方程求解，然后将它应用于结构静力分析和设计中的不确定性问题，泛灰数不仅具有区间分析的功能，而且能解决区间分析所不能解决的问题。文中给出了两个算例，列出了本文算法与其他算法的结果比较。

Interval analysis method of uncertain structural systems using universal grey number

The uncertain problems in engineering can be solved by using the interval, probabilistic or fuzzy theories. The interval analysis is used to model the uncertainty in the static structural analysis and design. By representing the uncertain parameters as interval numbers, the governing equations of the structural system are obtained by means of the finite element method. These equations are interval linear equations. Based on the concept and the rules of four algebraic operation of the universal Grey number, the universal Grey number is changed into the interval Grey number, and the interval analysis with extensible characteristic of the universal Grey number and the solution to universal Grey linear equations are given. The universal Grey function can be dealt with some problems that the Grey number or interval analysis can't be solved. The present method used in the uncertain structural system and design in engineering is more useful than the interval analysis. Some solution methods are discussed and two examples are presented to illustrate the computational aspects of universal Grey solution method and other methods.