Selective Cell-Based Smoothed Finite Element Method Using 10-Node Tetrahedral Element with Radial Element Subdivision

Abstract

A new optimal formulation of the selective cell-based smoothed finite element method using 10-node tetrahedral elements (SelectiveCS-FEM-T10) is proposed for nearly incompressible large deformation problems. SelectiveCS-FEM-T10 is a generic name for S-FEM formulations that apply the selective reduced integration (SRI) and the cell-based S-FEM (CS-FEM) simultaneously to the 10-node tetrahedral (T10) elements, and thus it has various formulation variations. The conventional SelectiveCS-FEM-T10 naturally subdivides a T10 element into twelve 4-node tetrahedral (T4) subelements with a dummy node at the element center. Meanwhile, the new SelectiveCS-FEM-T10 radially subdivides it into sixteen T4 subelements around the dummy node. Owing to this radial element subdivision, all the edges of the subelements, including the frame edges, are subjected to strain smoothing only via the edge-based S-FEM (ES-FEM) within an element. Besides, SelectiveCS-FEM-T10 can be implemented into general finite element codes as a T10 element because it is a CS-FEM, which only applies intra-element strain smoothing. Our demonstrative analyses reveal that the new SelectiveCS-FEM-T10 is more robust than the best available T10 element against severe large deformation. They also show that the accuracy of the new SelectiveCS-FEM-T10 is almost equal to the conventional T10 elements as it does not cause shear/volumetric locking and pressure checkerboarding.