A Subdivision-Based Combined Shape and Topology Optimization in Acoustics

We propose a combined shape and topology optimization approach in this research for 3D acoustics by using the isogeometric boundary element method with subdivision surfaces. The existing structural optimization methods mainly contain shape and topology schemes, with the former changing the surface geometric profile of the structure and the latter changing the material distribution topology or hole topology of the structure. In the present acoustic performance optimization, the coordinates of the control points in the subdivision surfaces fine mesh are selected as the shape design parameters of the structure, the artificial density of the sound absorbing material covered on the structure surface is set as the topology design parameter, and the combined topology and shape optimization approach is established through the sound field analysis of the subdivision surfaces boundary element method as a bridge. The topology and shape sensitivities of the approach are calculated using the adjoint variable method, which ensures the efficiency of the optimization. The geometric jaggedness and material distribution discontinuities that appear in the optimization process are overcome to a certain degree by the multiresolution method and solid isotropic material with penalization. Numerical examples are given to validate the effectiveness of the presented optimization approach.