计算不确定结构系统静态响应的一种可靠方法

不确定性广泛存在于工程结构分析和设计过程之中，不能简单地予以忽略。目前，概率方法、模糊方法和区间方法是不确定性建模的三种主要方法。本文把具有不确定性的结构材料参数、几何参数和所受外力用区间数描述，通过求解线性区间方程组准确地计算了结构静态响应。计算结果易于扩张是区间计算的一个主要缺陷，本文提出了一种有效避免这一问题的方法。该方法把区间函数的计算和区间线性方程组的求解转化为相应的全局优化问题，来确定解中的每个区间元素的边界值，并采用一种智能性算法(实数编码遗传算法)来求解这些全局优化问题。本文首先采用数学和结构分析算例对该方法的正确性和有效性进行了验证，然后把该方法与有限元方法相结合计算不确定结构系统的响应范围，并和求解同类问题的方法进行了比较。

A reliable approach to compute the static response of uncertain structural system

Uncertainties widely exist in engineering structural analysis and design problems and cannot be just neglected. The probabilistic method, the fuzzy method and the interval method are the three major approaches to model uncertainties at present. Representing the uncertain structural material parameters, uncertain structural geometric parameters and the uncertain loading conditions as the interval numbers, the structural static response accurately by solving linear interval equations. Overestimation is a major drawback in interval computation. Thus, a reliable computation approach was proposed to overcome it in the paper. The presented approach is based on the inclusion monotone property of interval mathematics and the physical/real meaning expressed by the interval function. The interval function and the linear interval equations were solved by solving the corresponding optimization problems to determine the endpoints/bounds of every interval element of the solutions of the problem. Moreover, an intellective algorithm named as real-code genetic algorithm was used to locate the global optima of these optimization problems. Some mathematical and structural examples were used to examine the efficiency of the approach first. Then, this approach was combined with finite element method to determine the response interval of uncertain structural system. A very sharp enclosure for the solution set, due to material, geometric and loading uncertainty in structural analysis problems, was obtained.