• Brief Report •

### A structural topological optimization method with variable displacement constraint limits

Jianhua Rong Xiaojuan Xing Guo Deng

• Received:2007-08-30 Revised:2008-04-23 Online:2009-05-25 Published:2009-05-25

Abstract: In each sub-loop solving of the ICM (Independent, Continuous and Mapping) method, whether in what quantities do topology design variables change, structural displacements etc. characteristic quantities and their derivatives are approximately obtained by using their values at the beginning of the sub-loop iterations. This measurement may lead to large errors of the mentioned quantity estimations. If there is only a type of constraints (such as displacement constraints) in an optimization model, the errors may be larger. In order to deal with this problem, for the structural topological optimization problem with the objective function being the structural weight and only displacement constraints, this paper proposes a new structural topological optimization method, being based on the ideas of the ICM method (Independent, Continuous and Mapping) and the evolutionary structural optimization method. New displacement constraint limits are formed and introduced to the optimization model at the beginning step of each sub-loop iterations to control variations of topological design variables. Moreover, the element deletion and adding criterion and a set of structural optimization strategy are given. Some elements with artificial material property are inserted around the cavities and boundaries of the structure optimized so that the structure optimized is a non singular structure and the proposed method is of an element restorable function. And a structural characteristics mapping transformation relation between the effective structure and the structural maximum design domain is built. Incorporating the dual programming method, a new continuum structural topological optimization method is proposed. The several examples show that there is not any objective oscillation phenomenon in optimization iterations, and the proposed method is of validity and effectiveness.