非确定结构系统区间分析的直接优化法

工程中的非确定性问题可以用区间分析、随机理论或模糊集理论进行求解。本文采用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。本文讨论了一些求解区间线性方程组的方法并提出了一种直接优化法。将方程组中的所有区间数都作为设计变量，区间量的变化区间作为相应的设计变量的边界约束，运用约束优化法求出方程组解的各元素的最大值和最小值。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

Direct Optimization Method of Uncertain Structural Systems Using Interval Analysis

The uncertain problems in engineering can be solved by using interval, probabilistic or fuzzy theories. Interval analysis is used to model the uncertainty in the static structural analysis and design. By representing the uncertain parameters as interval numbers, the governed equations of the structural system are obtained by means of the finite element method. These equations are interval linear equations. Some solution methods are discussed and a direct optimization method is presented. Taking all the interval numbers in the equations as optimal design variables and representing the lower and the upper bounds of each interval number as the boundary constrain of the variable respectively, the maximum and the minimum of various components of the solution are achieved by using the constrained optimization method. Two examples are presented to illustrate the computational aspects of the direct optimization method and other methods.