Generalized Mass-Redistributed Smoothed Finite Element Method (MR-SFEM) for Acoustic and Acoustic-Structural Interaction Problems

Abstract

The standard finite element method (FEM) is known for its “over-stiff” behavior, which leads to the pollution error in acoustic and acoustic-structural problems. In this paper, a generalized mass-redistributed smoothed FEM (MR-SFEM) is proposed to analyze the acoustic and acoustic-structure interaction problems. In the new MR-SFEM, the generalized mass matrix reconstitution technology is used for both the structural and acoustic discretized system based on the SFEM, which can provide a perfect balance of the discretized system matrix both in the structure and acoustic domain. The global equations of acoustic-structural interaction problems are established by coupling the MR-SFEM for the structure and for the acoustic domain. Some numerical examples of acoustic and acoustic-structure interaction problems have been used to assess the present formulation, and the results show that the present method has much better performance in terms of accuracy, convergence, and efficiency than those obtained using the standard FEM, edge-based FEM (ES-FEM), and face-based FEM (FS-FEM).