两类变量综合处理的结构形状优化设计方法

本文针对截面变量为离散变量为连续变量的结构优化问题提出了一种优化设计的方法，首先将单元内力作一阶近似，利用凝聚函数多约束问题转化了单约束问题。在解过程中，把定义在连续区间上的形状变量看成是在一些离散以值的离工用变量，然后将两类变量统一考虑并利用相对差商法求解。将该算法应用于几个经典的结构优化算例，运算结果显示了该方法是可行的，优化结果也比较满意。

A comprehensive algorithm for shape optimization of structures with discrete variables

In this paper, a method for shape optimization with discrete sectional variables and continuous shape variables is presented. In the procedure of shape optimization, first, an approximate model is given by utilizing structural analysis based on the first order Taylor series expansion with respect to the member forces. Then, the multiconstraint problem are converted to a single constraint problem. After the cotinuous design region of shape variables are convered to a discrete set, the shape variables and sectional area variables can be considered simultaniously and the relative difference quotient values with respect to two kins of variables can be used to determine which variable shoulded be optimized. The algorithm is applied to several classical structural optimization examples and the results indicate that the algorithm has higher computational efficiency and accracy.