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。
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.