具有多随机因素结构系统的优化设计

Optimum Design for Structural Systems with Many Random Factors

提出了具有多随机因素的系统 ,即考虑结构元件面积 ,长度 ,弹性模量 ,结构强度和外载荷均为随机变量情况下 ,进行优化设计的方法 .在这种结构中 ,极限状态方程是一个含有多随机变量的非线性函数 ,而且有些随机变量很难用显式表达 ,故采用随机有限元法进行可靠性分析 ,给出了系统可靠性指标的敏度表达式 ;用最佳矢量法求解系统可靠度约束下的最小重量设计问题 .迭代过程中 ,采用梯度步和最佳矢量步进行计算 .最后给出一个算例 ,表明该方法的有效性 .该法计算效率高 ,收敛稳定 。

The optimum design method is presented to the structural systems with many random factors, consider that the sectional area, length, module and loads are random variables. The limited condition equation is a nonlinear function including many random variables, and some of these variables can not be easily expressed using explicit formula.The reliability analysis is therefore conducted using the stochastic finite element method. So the sensitivity expression of minimum weight design under the restriction of structural systems reliability degree. In the iterative procedure, adopt the gradient step method and the optimum vector method to calculate. At the last, a numerial example is provided to demostrate the validity of above analysis. the method is efficient in the calculation, stably converges and fits the need of engineering.