Topology Optimization for Frequencies Using an Evolutionary Method

Abstract

This paper presents an evolutionary method for structural topology optimization subject to frequency constraints. The evolutionary structural optimization (ESO) method is based on the idea that by gradually removing inefficient material, the residual shape of structure evolves toward an optimum. The method is further developed by allowing the material to be added as well as removed, and this new approach is called the bidirectional ESO method (BESO). BESO has been successfully used for problems of stress and stiffness/displacement constraints. Its application to frequency optimization is addressed in this paper. Three kinds of optimization objectives, namely, maximizing a single frequency, maximizing multiple frequencies, and designing structures with prescribed frequencies are considered. Four examples are tested by BESO and ESO. The objective functions yielded by the two methods are close, and BESO is computationally more efficient in most cases.