对偶法求解应力与位移约束不同显式的优化模型

基于响应面法,通过内力将应力约束显式化为正变量的一阶近似,位移约束采用倒变量一阶近似,建立以桁架结构重量最小为目标的截面优化模型,采用对偶规划理论转化为拟无约束模型,采用序列二次规划算法求解。此方法同应力约束零阶近似和一阶近似(使用响应面方法显式化)等方法进行了算例比较,表明本文的优化模型有较好的求解效率。

Duality solution to optimization model with stress and displacement constraints in different approximate forms

Based on Response Surface Methodology,stress constraints are linearized in terms of direct variables through the handling of internal force,and displacement constraints are approximated in first-order form dependent on reciprocal variables.The cross-sectional optimization model of truss with minimal weight is transformed into quasi-unbownded model using the dual programming theory,which can be solved by sequential quadratic programming algorithm.Its computational efficiency is compared to the approaches of zero-order and first-order approximation of stress constraints(also expressed explicitly by RSM) through several numerical examples,which show the proposed method has advantages in some aspects.