谐和激励下的连续体结构拓扑优化

在ESO方法的基础上研究了谐和激励下连续体结构的拓扑优化问题。利用模态截断的方法和一些近似手段建立了结构的动响应表达式，并依此提出了结构优化设计评价的性能指标。采用一定的优化准则和进化优化步骤完成优化过程。算例结果表明了所提方法的有效性和合理性。

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. First, 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. Then, 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. Finally, 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.