Combined shape and topology optimization for sound barrier by using the isogeometric boundary element method

Abstract This study presents a combined shape and topology optimization method for designing sound barriers by using the isogeometric boundary element method. The objective function of combined optimization is defined as the sound pressure in reference plane. The sensitivity analysis for the combined optimization is conducted by using either the direct differentiation method or the adjoint variable method. For a shape design, the design variables are the positions of control points in isogeometric analysis, which can control the barrier shape flexibly. In the topology update, the artificial density of an integral element is selected as the design variable to find the optimal distribution of sound absorbing material (SAM) on the barrier surface. In the combined optimization process, the shape and SAM distribution of the sound barrier can be changed in each iteration process to improve the noise reduction. Four different iteration schemes for combined optimization are compared to find an effective one. Numerical tests are provided to demonstrate the validity and efficiency of the proposed methods.