A coupled ES-BEM and FM-BEM for structural acoustic problems

In this paper, a coupled numerical method of the edge-based smoothed finite element (ES-FEM) with the fast multipole BEM (FM-BEM) is proposed to analyze structural acoustic problems. The vibrating structure is modeled using the so-called ES-FEM-DSG3 method, where the 3-node linear triangle plate elements based on the Reissner-Mindlin plate theory with the discrete shear gap (DSG) technique for overcoming the shear locking are applied. The edge-based gradient smoothing operations are applied to “soften” the “overly-stiff” behavior in the standard FEM, which significantly reduces the inherent numerical dispersion error. The normal velocities on the surface of the structure are imposed as boundary conditions for the acoustic domain which is modeled using the FM-BEM for both the interior and exterior acoustic domains. Comparing with the conventional BEM, the matrix vector multiplication and the memory requirement in the FM-BEM are reduced dramatically. The coupled ES-FEM/ FM-BEM method takes the advantages of both ES-FEM and FM-BEM, which can avoid drawbacks of the “overly-stiff” behavior in FEM and computational inefficiency in the conventional BEM. Two numerical examples are presented to verify and demonstrate the effectiveness of the combined method: one academic problem for studying in detail the accuracy and efficiency of the present method, and one application to a practical vehicle noise simulation.