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An alpha finite element method (αFEM) has been recently proposed to compute nearly exact solution in strain energy for solid mechanics problems using three-node triangular (αFEM-T3) and four-node tetrahedral (αFEM-T4) elements. In the αFEM, a scale factor α ∈ [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 αFEM for solid mechanics to obtain the very accurate solutions with a suitable computational cost by using α = 0.6 for 2D problems and α = 0.7 for 3D problems.

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