结构外形优化的一种有效方法

 本文基于约束函数及目标函数对节点坐标与元件截面两类变量不同的非线性性质,将目标函数对元件截面变量及节点坐标变量在正变量空间内进行不完全的二阶台劳展开,而约束函数则对元件截面变量之逆变量、节点坐标变量之正变量进行线性台劳展开,从而得到一对于原问题近似精度较高的严格凸的近似问题,用对偶规划求解这一变量可分离的显式的凸问题是简便的。对算例的计算表明该方法是相当有效的。

AN EFFICIENT METHOD FOR THE CONFIGURATIONAL OPTIMIZATION OF STRUCTURES

In this paper a method is present for the configuratinal optimization of structures subject to displacement, stress and buckling constraints u-nder multiple load conditions. To construct a new sequence of approximate problems, we expand the objective function into a incomplete second order Taylor series in which the cross terms are ignored, and expand the constraint functions into linear Taylor series in the mixed design variable space （the design variables of structural elements are reciprocal）. Then, a separable convex approximate problem is obtained, This approximate problem can be solved by a dual method of convex programing. Computational result for two trusses show that the method presented in this paper is very efficient.