An edge-based smoothed tetrahedron finite element method (ES-T-FEM) for thermomechanical problems

This paper presents an edge-based smoothed tetrahedron finite element method (ES-T-FEM) to improve the accuracy of the finite element method for three-dimensional thermomechanical problems. In this approach, the smoothed Galerkin weak form is then used to construct discretized system equations using smoothing domains constructed based on edges. The model created by ES-T-FEM is softer than the standard finite element method (FEM) and face-based smoothed finite element method (FS-FEM). In addition, a novel mixed formulation of FS-FEM and FEM is proposed in solid mechanical model for thermoelastic problem. Numerical results demonstrate that the proposed method possesses a close-to-exact stiffness of the continuous system and gives better results than both FEM and FS-FEM using tetrahedron mesh. The proposed method is an innovative and unique numerical method with its distinct features, which possesses strong potentials in the successful applications thermomechanical problems.