Topology optimization of exterior acoustic-structure interaction systems using the coupled FEM-BEM method

This paper presents an efficient topology optimization procedure for exterior acoustic-structure interaction problems, in which the coupled systems are formulated by the boundary element method (BEM) and the finite element method (FEM). So far, the topology optimization based on the coupled FEM-BEM still faces several issues needed to be addressed, especially the efficient design sensitivity analysis for the coupled systems. In this work, we contribute to these issues in two main aspects. Firstly, the adjoint variable method (AVM) formulations are derived for sensitivity analysis of arbitrary objective function, and the feedback coupling between the structural and acoustic domains are taken into consideration in the sensitivity analysis. Secondly, in addition to the application of fast multipole method (FMM) in the acoustic BEM response analysis, the FMM is now updated to adapt to the arising different multiplications in the AVM equations. These accelerations save considerable computing time and memory. Numerical tests show that the developed approach permits its application to large-scale problems. Finally, some basic observations for the optimized designs are drawn from the numerical investigations.