About applying directly the alpha finite element method ($\alpha $FEM) for solid mechanics using triangular and tetrahedral elements

Abstract

An alpha finite element method ($\alpha $FEM) has been recently proposed to compute nearly exact solution in strain energy for solid mechanics problems using three-node triangular ($\alpha$FEM-T3) and four-node tetrahedral ($\alpha $FEM-T4) elements. In the $\alpha$FEM, a scale factor $\alpha \in [0, 1]$ is used to combine the standard fully compatible model of the FEM with a quasi-equilibrium model of the node-based smoothed FEM (NS-FEM). This novel combination of the FEM and NS-FEM makes the best use of the upper bound property of the NS-FEM and the lower bound property of the standard FEM. This paper concentrates on applying directly the $\alpha $FEM for solid mechanics to obtain the very accurate solutions with a suitable computational cost by using $\alpha = 0.6$ for 2D problems and $\alpha = 0.7$ for 3D problems.