Modal basis approaches in shape and topology optimization of frequency response problems

Abstract eng:
The optimal design of mechanical parts subject to periodic excitations within a large frequency interval is quite challenging. Mechanical intuition in such problems is very limited and although Shape and Topology (S&T) optimization techniques could provide an answer in the conceptual design phase, the necessary computational time using traditional techniques is prohibited, mainly due to the costly adjoint analysis. In this work, we present two non-adjoint approaches for treating frequency response problems in S&T optimization. In the first method, we propose to use an approximation of the objective function and its shape derivative via a modal decomposition of the direct and adjoint states. In the second, we use the modal decomposition both to formulate the problem and to approximate the shape derivative of eigenvectors, in order to evitate the solution of an adjoint equation for every eigenvector. We present numerical examples for the minimization of the dynamic compliance.

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