不确定性结构区间分析的改进Monte Carlo方法

将结构系统中的不确定性参数用区间数来表示，建立了系统的区间有限元控制方程。利用Monte Carlo数值仿真方法对区间有限元控制方程进行求解，得到了结构的位移和应力响应区间。并针对—殷Monte Carlo方法在区间仿真中存在的缺陷，对其进行了改进，使其计算效率大为提高．数值仿真算例表明：经改进的Monte Carlo方法仿真求解计算量大为减少，且能给出较高精度的响应区间，并克服了区间运算中的扩张问题。

Improved Monte Carlo Method for Interval Analysis of Uncertain Structures

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. By representing the uncertain parameters as interval numbers, the governed equations of the structural system were obtained by means of the interval finite element method. The interval finite element governed equations were solved by the Monte Carlo numerical simulation method. And the displace responses and stress responses were obtained. An improved Monte Carlo numerical simulation method was proposed for improving the performance of common Monte Carlo method. Numerical examples are presented to illustrate the feasibility and validity of the method. Improved Monte Carlo method for solving the interval equations is easy to implement. High accuracy solutions can be gotten by this method. And the overestimation which is the major drawback of interval analysis is overcome.