Mean‐strain 10‐node tetrahedron with energy‐sampling stabilization

In this study, a new mean‐strain 10‐node tetrahedral element is developed using energy‐sampling stabilization. The proposed 10‐node tetrahedron is composed of several four‐node linear tetrahedral elements, four tetrahedra in the corners and four tetrahedra that tile the central octahedron in three possible sets of four‐node linear tetrahedra, corresponding to three different choices for the internal diagonal. The assumed strains are calculated from mean ‘basis function gradients.’ The energy‐sampling technique introduced previously for removing zero‐energy modes in the mean‐strain hexahedron is adapted for the present element: the stabilization energy is evaluated on the four‐corner tetrahedra. The proposed element naturally leads to a lumped‐mass matrix and does not have unphysical low‐energy vibration modes. For simplicity, we limit our developments to linear elasticity with compressible and nearly incompressible material. The numerical tests demonstrate that the present element performs well compared with the classical 10‐node tetrahedral elements for shell and plate structures, and nearly incompressible materials. Copyright © 2016 John Wiley & Sons, Ltd.