An edge-based smoothed finite element method (ES-FEM) for analyzing three-dimensional acoustic problems

Coupled analysis of 3D structural–acoustic problems using the edge-based smoothed finite element method/finite element method

“…Compared with the methods using node-based strain smoothing, such as the NS-PIM and NS-FEM, there are no spurious non-zeros energy modes found in free vibration analyses and hence the ES-FEM is temporally stable. The primary variable and its gradient solutions of ES-FEM are also found much more accurate than those of the FEM model using the same constant strain triangular meshes and even more accurate than those of the FEM using quadrilateral elements with the same set of nodes for 2D mechanics problems [15]. In addition, no additional degree of freedom at nodes and underdetermined parameters are introduced, and it has been found that the linear ES-FEM is much more efficient than the linear FEM for 2D solid mechanics problem with the same triangular mesh [16].…”

“…To overcome the temporal instability problems, an edge-based smoothed FEM (ES-FEM) [13] has therefore been proposed for static, vibration problems of solid mechanics, plate and shells [14], and acoustic problems [15]. Compared with the methods using node-based strain smoothing, such as the NS-PIM and NS-FEM, there are no spurious non-zeros energy modes found in free vibration analyses and hence the ES-FEM is temporally stable.…”

A coupled smoothed finite element method (S-FEM) for structural-acoustic analysis of shells

“…One is the loss of accuracy and reliability due to the pollution error caused by numerical dispersion. He et al [35][36][37] proved that the "compounded" effects of differences in "stiffness" between the exact continuous system and the discretized model are the main cause for dispersion error. As is known to all, the traditional FEM model based on the standard Galerkin weakform exhibits "overly-stiff" property, which makes the numerical speed of sound propagates faster than its real value.…”

Dispersion free analysis of acoustic problems using the alpha finite element method

“…(ii) higher order methods, such as generalized high order approximations ( p-version) [6,7], the partition of unity method (PUM) [8,9] and the discontinuous enrichment method (DEM) [10,11] (iii) meshless method, such as element-free Galerkin method (EFGM) [12,13]. They all can give improved solutions compared to the standard FEM, however, properly "softened" stiffness for the discrete model is much more effective and direct to the root of the numerical pollution error [14].…”