Topology optimization of vibroacoustic problems using the hybrid finite element–wave based method

Abstract

Determining an optimized solution by means of topology optimization in vibroacoustic problems often requires a high computational cost. Conventional density-based topology optimization using the finite element method is a time-consuming approach, owing to the large model size and repeated function evaluations involved in the frequency response. To address this issue, an efficient topology optimization method that uses the hybrid finite element–wave based method is proposed in this paper. In this method, the entire problem domain is divided into design and non-design domains. The mixed displacement–pressure finite element method is applied to the design domain for material interpolation in the topology optimization. Moreover, the wave based method, which is an efficient numerical scheme for acoustic problems, is applied to the non-design domain to reduce the computational cost. A direct coupling approach is proposed to construct hybrid models for vibroacoustic problems. The adjoint variable method is also presented to compute the design sensitivities efficiently. The effectiveness of the proposed method is demonstrated by benchmark problems. The optimization results indicate that the proposed method can significantly reduce the computational cost, while maintaining almost identical optimized layouts to those obtained using the conventional approach.