A Stabilization Method of F-barES-FEM-T4 for Dynamic Explicit Analysis of Nearly Incompressible Materials

Abstract

A stabilization method of the F-bar aided edge-based smoothed finite element method with four-node tetrahedral elements (F-barES-FEM-T4), which is named SymF-barES-FEM-T4, is proposed. The proposed formulation aims to remove the instability associated with energy divergence of F-barES-FEM-T4 in dynamic analysis. The stiffness matrix of F-barES-FEM-T4 is asymmetric due to the adoption of F-bar method, meanwhile that of SymF-barES-FEM-T4 is symmetrized so that the dynamics system of the formulation is stabilized. The differences between F-barES-FEM-T4 and SymF-barES-FEM-T4 in their formulations are only the definition of the [Formula: see text]-matrix and the corresponding volume in the internal force calculation. Therefore, SymF-barES-FEM-T4 is applicable in dynamic explicit schemes as is the case with F-barES-FEM-T4. A few demonstrations of dynamic explicit analysis for nearly incompressible materials reveal that SymF-barES-FEM-T4 conserves the total energy and does not cause energy divergence in the free vibration problems. They also reveal that SymF-barES-FEM-T4 has a moderate capability in the suppression of pressure checkerboarding: worse than F-barES-FEM-T4 but better than Selective ES/NS-FEM-T4.