Development of a 4-node hybrid stress tetrahedral element using a node-based smoothed finite element method

In this paper, a new 4-node hybrid stress element is proposed using a node-based smoothing technique of tetrahedral mesh. The conditions for hybrid stress field required are summarized, and the field should be continuous for better performance of a constant-strain tetrahedral element. Nodal stress is approximated by the node-based smoothing technique, and the stress field is interpolated with standard shape functions. This stress field is linear within each element and continuous across elements. The stress field is expressed by nodal displacements and no additional variables. The element stiffness matrix is calculated using the Hellinger-Reissner functional, which guarantees the strain field from displacement field to be equal to that from the stress field in a weak sense. The performance of the proposed element is verified by through several numerical examples.