摘要
本文提出了一种有效的两工况作用下的杆系结构拓扑优化设计方法。它在以下三个方面克服了当前拓扑优化领域内线性规划类方法所面临的主要困难,首先,从结构力学的基本方程出发,引入内力设计变量,既克服了已有方法要求预定位移场这一主要困难,又为在拓扑优化过程中考虑应力、位移等性态约束创造了有利条件;其次,现有方法均无法解决多工况问题,本方法虽未推广到多工况,但可解决两工况问题;再者,现有方法在拓扑优化过程中无法计及应力、位移等性态约束,本方法巧妙地解决了这一问题。最后给出的几个工程优化算例,表明该方法具有理论基础牢固,计算工作量小,程序易于实现等明显优点。
This paper presents a new efficient algorithm of topology optimization for truss structures under two loading cases. In the method, three main defections of the optimization method in the past two decades are surmounted. Firstly, the main difficulty of pregiven displacement field is warded off with the introduction of force design variables; Secondly, the problem with two loading conditions could be dealt with; Thirdly, the behavior constraints such as displacement and stress ones are formulated mathematically as a linear function of the force design variables; Finally, several examples show that the method has firm theory basis, small computation and is easy to be programed.
