@article{Trung_Hung_2010, place={Hanoi, Vietnam}, title={About applying directly the alpha finite element method (\(\alpha\)FEM) for solid mechanics using triangular and tetrahedral elements}, volume={32}, url={https://vjs.ac.vn/index.php/vjmech/article/view/292}, DOI={10.15625/0866-7136/32/4/292}, abstractNote={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.}, number={4}, journal={Vietnam Journal of Mechanics}, author={Trung, Nguyen Thoi and Hung, Nguyen Xuan}, year={2010}, month={Dec.}, pages={235–246} }