A structural topological optimization method with variable displacement constraint limits

In each sub-loop solving of the ICM (Independent,Continuous and Mapping) method, whether in what quantities do topologydesign variables change, structural displacements etc. characteristicquantities and their derivatives are approximately obtained by using theirvalues at the beginning of the sub-loop iterations. This measurement maylead to large errors of the mentioned quantity estimations. If there is onlya type of constraints (such as displacement constraints) in an optimizationmodel, the errors may be larger. In order to deal with this problem, for thestructural topological optimization problem with the objective functionbeing the structural weight and only displacement constraints, this paperproposes a new structural topological optimization method, being based onthe ideas of the ICM method (Independent, Continuous and Mapping) and theevolutionary structural optimization method. New displacement constraintlimits are formed and introduced to the optimization model at the beginningstep of each sub-loop iterations to control variations of topological designvariables. Moreover, the element deletion and adding criterion and a set ofstructural optimization strategy are given. Some elements with artificialmaterial property are inserted around the cavities and boundaries of thestructure optimized so that the structure optimized is a non singularstructure and the proposed method is of an element restorable function. Anda structural characteristics mapping transformation relation between theeffective structure and the structural maximum design domain is built.Incorporating the dual programming method, a new continuum structuraltopological optimization method is proposed. The several examples show thatthere is not any objective oscillation phenomenon in optimizationiterations, and the proposed method is of validity and effectiveness.