On topology optimization of continuous structures under harmonic excitation

In recent years, the evolutionary structural optimization (ESO) method has been developed into an effective tool for engineering design. However, no attempt has been made to incorporate dynamic response constraints of structures subjected to harmonic excitations. We extend and modify the ESO method to control the dynamic responses of structures under harmonic excitations. Based on the structural modal truncation method and some approximate process, an expression of dynamic response of a structure under harmonic excitations considering engineering requirements is formed. A performance index is proposed for the optimal process where structural elements are removed so as to minimize the change of the response amplitude of the corresponding degree of freedom. Thus the optimization model with dynamic response constraints and an optimal criterion are formulated. The optimal steps of topology optimization of continuous structures under dynamic response constraints are introduced. The algorithm has been implemented in an optimization software by evolutionary optimization procedure. A numerical example is provided to demonstrate the validity and effectiveness of the proposed method.