Open Access

ARTICLE

Acoustic Design Shape and Topology Sensitivity Formulations Based on Adjoint Method and BEM

T. Matsumoto¹, T. Yamada¹, T. Takahashi¹, C.J. Zheng², S. Harada¹

1 Nagoya University, Nagoya, Japan.
2 USTC, Hefei, China.

Computer Modeling in Engineering & Sciences 2011, 78(2), 77-94. https://doi.org/10.3970/cmes.2011.078.077

Abstract

Shape design and topology sensitivity formulations for acoustic problems based on adjoint method and the boundary element method are presented and are applied to shape sensitivity analysis and topology optimization of acoustic field. The objective function is assumed to consist only of boundary integrals and quantities defined at certain number of discrete points. The adjoint field is defined so that the sensitivity of the objective function does not include the unknown sensitivity coefficients of the sound pressures and particle velocities on the boundary and in the domain. Since the final sensitivity expression does not have the sensitivity coefficients of the sound pressure and particle velocity on the boundary, BEM analyses only for the primary acoustic field and the adjoint field are needed to calculate the sensitivities of the objective function. The derived formulations are applied to shape sensitivity analyses and a topology optimization of a sound scatterer placed in an infinite space. The level-set method is utilized to control the shape of the domain in the iterative process of obtaining the optimum shape of the scatterer.

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Keywords

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