Formulated alpha finite element method with deviatoric / volumetric split for highly precise deformation calculation by using three dimensional tetrahedral element (In case of infinitesimal isotropic elasticity)

Abstract

This paper presents a novel Formulated Alpha FEM with deviatoric / volumetric split, which is combination of standard FEM and Node-based Smoothed FEM (NS-FEM), to compute highly accurate deformation in mechanical problems using tetrahedral elements. The essential idea of the method is the use of a deviatoric alpha formulated on basis of the results of cantilever problem, and the volumetric alpha introduced NS-FEM. The features of this proposed method are: 1) immune from volumetric locking, 2) less sensitive to element distortion, and 3) to be carried out with the same preprocessing as standard FEM from user’s viewpoint. Several numerical examples show that the present method achieves higher accuracy compared to the standard FEM and Edge-based/NS-FEM which is known to be one of the best S-FEM formulations.

Keywords

• finite element method
• node-based smoothed finite element method
• alpha finite element method
• tetrahedral element
• volumetic locking free