桁架结构拓扑优化设计的线性规划方法

Linear Programming Algorithm of Topological Optimization for Truss Structures

本文提出了一种新的桁架结构拓扑优化设计方法,在该方法中,以杆件内力为设计变量,以由结构力学的基本方程构成的位移、应力等物理量为约束,构成了拓扑优化的线性规划模型。它克服了目前桁架结构拓扑优化的两大困难——预定设计位移场与在拓扑优化过程中无法考虑位移、应力等性态约束。文章最后给出了两个考题,说明了本方法的可行性与有效性。

This paper presents a new efficient method of topology optimization for truss structures. In the method, firstly, behavior constraints such as displacement and stress are formulated mathematically as the linear function of the force design variables. Secondly, the main difficulty of pregiven displacement field is warded off because of the introduction of force design variables. Finally, two examples are given to demonstrate the feasibility and efficaciousness of the method.