ON TOPOLOGY OPTIMIZATION OF TRUSSES WITH MULTIPLE LOADING CONDITIONS AND BE-HAVIOUR CONSTRAINTS
考虑性态约束时多工况桁架结构拓扑优化设计

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.