Evolutionary structural optimization for dynamic problems

This paper presents a simple method for structural optimization with frequency constraints. The structure is modelled by a fine mesh of finite elements. At the end of each eigenvalue analysis, part of the material is removed from the structure so that the frequencies of the resulting structure will be shifted towards a desired direction. A sensitivity number indicating the optimum locations for such material elimination is derived. This sensitivity number can be easily calculated for each element using the information of the eigenvalue solution. The significance of such an evolutionary structural optimization (ESO) method lies in its simplicity in achieving shape and topology optimization for both static and dynamic problems. In this paper, the ESO method is applied to a wide range of frequency optimization problems, which include maximizing or minimizing a chosen frequency of a structure, keeping a chosen frequency constant, maximizing the gap of arbitrarily given two frequencies, as well as considerations of multiple frequency constraints. The proposed ESO method is verified through several examples whose solutions may be obtained by other methods.