Topology optimization of acoustic and vibroacoustic problems using the hybrid finite element-wave based method

Abstract

To find an optimal solution in acoustic and vibroacoustic problems by topology optimization often requires a high computational cost. A common analysis in acoustic and vibroacoustic involves tens or hundreds of frequency components. Moreover, a fine resolution of the design domain leads to extremely heavy computational cost. The approximation technique such as reduced order modeling and Padé approximation can be applied to reduce computational cost. However, they still show unsatisfactory performances and also have unsolved issues regarding the accuracy of the solutions and sensitivities. To resolve these issues, a novel efficient topology optimization method that uses the hybrid finite element-wave based method is proposed in this dissertation. In the proposed method, the entire problem domain is divided into design and non-design domains. The finite element method is applied to the design domain for the material interpolation in topology optimization. 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 used to construct the hybrid models for both acoustic and vibroacoustic problems. To use an efficient gradient-based optimizer, design sensitivities are computed by using the adjoint variable method that is presented in this dissertation. The performance evaluation of the proposed design method is conducted in 2D / 3D acoustic and vibroacoustic problems. The comparative studies for optimization results and computation cost are conducted for conventional topology optimization and the proposed method. In all numerical tests, the proposed design method significantly reduces the computational cost while maintaining identical results as those obtained from the conventional topology optimization method. Moreover, the efficiency of the proposed method further increases in 3D problems. The optimization results confirm that the proposed method can effectively handle largescale acoustic and vibroacoustic problems that conventional approach is infeasible due to huge computational burdens.