具有区间参数的不确定结构静力区间分析的一种算法

A Method for Static Interval Analysis of Uncertain Structures with Interval Parameters

将结构系统中的不确定性参数用区间数来表示,用有限元法建立静力区间线性方程组。对该方程组的求解提出了一种区间逐步离散的方法。此方法通过令独立的不确定性参数取区间内的离散值,将区间线性方程组的求解转化为相应的确定性问题,再搜索各方程解中的最大最小值得到每个区间分量的边界。先用数学算例对该算法的正确性和有效性进行了验证,然后应用于静力区间分析的工程算例,并与其它算法进行了比较。计算结果表明该算法的计算效率和准确性较高。

By representing the uncertain parameters as interval numbers, the static governed equations of the structural system are obtained in this paper by means of the finite element method. These equations are linear interval equations, for which some solution methods are discussed and an interval-step-dividing method is presented. In this method, the independent uncertain parameters are given the discrete values of the interval, and the linear interval equations are changed to the corresponding certain ones. Then the bounds of every interval solution components are determined by searching for the maximums and the minimums. Some mathematical examples are used to examine the correctness and efficiency of the approach which is applied to some engineering problems of static interval analysis. Compared with other methods, the calculated results show that the method of this paper has a high calculating efficiency.