Abstract:

Aimed at the volumetric locking problems that were produced by the calculation of the nearly incompressible material in numerical simulation, two schemes based on the smoothed finite element method (SFEM) were proposed. The first scheme was to decompose the material properties matrix into two parts, the volumetric part and nonvolumetric part, and the stiffness matrix was also correspondingly decomposed into two parts. Then, the cellbased smoothed finite element method (CS-FEM) using one subcell (SC=1) was used only on the volume-part and the CS-FEM using more than one subcell (SC>1) was used on the remaining part. The second scheme was to use the node-based smoothed finite element method (NS-FEM) that was free from volumetric locking to calculate the volumetric part and to use the edge-based finite element method (ES-FEM) that had accurate results to calculate the remaining part. Results of the numerical study showed that both schemes were correct and effective,and the second scheme was more accurate than NS-FEM.

Key words: smoothed finite element method (SFEM), volumetric locking, selective integration