Smoothed finite element method for two-dimensional acoustic numerical computation

In the acoustic finite element method (FEM), typical problems of four-node isoparametric element are low accuracy and even wrong solution for irregular meshes in numerical implementation. This paper proposes to use the smoothed finite element method (SFEM) for the acoustic analysis of irregular quadrilateral mesh, and the formulation of SFEM is presented for the two-dimensional acoustic problem. The acoustic SFEM incorporates cell-wise smoothing operations into standard finite element method and the smoothed acoustic pressure gradient is obtained by using cell-wise smoothing operation. The acoustic stiffness matrix can be calculated by using the smoothed acoustic pressure gradient matrix and the domain integrals involving shape function gradients can be recast into boundary integrals involving only shape functions. More importantly, as no coordinate transformation is involved, it is more efficient than isoparametric element. Numerical example of a two-dimensional tube and car cavity are presented to show that the acoustic SFEM achieves higher accuracy as compared with FEM when quadrilateral meshes are seriously distorted especially in the high frequency calculation. Hence the SFEM can be well applied in solving the two-dimensional acoustic problems with very irregular meshes, and has application foreground. © 2010 Journal of Mechanical Engineering.