考虑性态约束时多工况桁架结构拓扑优化设计

本文提出了一种适用于桁架结构的拓扑优化设计方法。它以杆内力为设计变量,以结构重量为目标函数。该方法的主要特点是:第一,通过引入杆内力为设计变量,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条件;第二,将多工况的拓扑优化问题描述为一个非光滑的数学规划问题,再通过一个变量代换将其转化为一般的规划为题,进而将原问题的求解又转化为几个线性规划问题的求解;第三,基于结构力学的三个基本方程,将位移与应力约束提成为线性不等式约束,这些约束同重量的目标函数一起构成了拓扑优化设计的线性规划模型。最后,将本方法应用于几个工程算例,得到了满意的数值计算结果。

ON TOPOLOGY OPTIMIZATION OF TRUSSES WITH MULTIPLE LOADING CONDITIONS AND BE-HAVIOUR CONSTRAINTS

A topology optimization method for truss structures is described in this paper. In this method, the member forces are considered as design variables and the structural weight as objective function. Three main advantages, compared with the prevailing methods, existed in the method. Firstly, the introduction of new design variables makes that not only the main difficulty of pregiven displacement field is warded off but it is more easily for the constraints such as stress and displacement to be dealt with during the topology optimization. Secondly, the topology optimization problem under multiple loading conditions is mathematically stated as a nonsmooth programming problem and the latter is then transformed into a smooth one by means of variable transformation, so that the solution of primary problem is finally changed into the solution of several linear programming problems. Thirdly, the constraints such as displacement and stress, based on three basic equations of structural mechanics, are expressed as linear nonequal constraints. Finally, the method is applied to several practical examples and the excellent results are gotten.