Design of absorbing material distribution for noise barrier via accelerated BEM and optimality criteria method

A BEM-based topology optimization framework, incorporating the optimality criteria (OC) algorithm, is developed for the design of sound-barrier systems with optimally distributed sound-absorbing materials. Within this framework, the acoustic effect of the absorbing medium is incorporated by means of an impedance boundary condition. Inspired by the solid isotropic material with penalization (SIMP) concept, the optimization model employs the elemental material density as the design variable, enforces a prescribed volume constraint on the total amount of absorbing material, and formulates the objective function as the minimization of the acoustic pressure evaluated on a designated reference surface. To assist the SIMP interpolation in producing a distinct binary (0-1) material pattern, a regularized Heaviside-type mapping function is introduced. The BEM is then employed to carry out the acoustic field analysis required throughout the optimization process. Furthermore, a Taylor-expansion-based accelerated BEM is incorporated to efficiently evaluate the sound pressure amplitudes over a prescribed frequency range, significantly reducing the computational cost while maintaining high accuracy.