基于Lingo和Matlab的空间桁架结构联合优化设计

摘要

本文研究了位移和应力约束下桁架结构的尺寸优化设计问题.首先,基于Matlab的有限元分析和符号计算功能,采用近似方法得到位移约束的显式函数,再结合桁架结构应力约束的计算公式,构造优化设计的数学模型,最后,采用Lingo和Matlab软件分别进行优化求解.数值算例的结果表明,两种方法得到的优化结果完全一致,都能明显的减轻设计结构的重量,且方法简单,易实施.%This paper investigates the size optimization of truss structure under displacement and stress constraints. Firstly, based on finite element analysis and symbolic computation, explicit function of displacement constraints is obtained by approximate method. Secondly, combined with calculation formula of stress constraints of truss structure, mathematical model of optimization problem is established. Finally, optimization solution is carried out by lingo and Matlab. The results show that solutions of the two methods are close to each other, and they both can reduce effectively the weight of design structure. Also the method is simple, and is easy to implement.