An eighteen-node hybrid-stress solid-shell element for homogenous and laminated structures

Abstract

Solid-shell elements are often equipped with two layers of nodes. Thus, the thickness (normal) strain along the thickness direction is essentially constant. When these elements are subjected to pure bending, the shrinkage/expansion induced by the in-plane strain and the Poisson's ratio coupling in the upper and lower halves of the elements cancel each other. With a constant thickness strain, the plane strain state is resulted that leads to thickness locking. In this paper, a modified generalized laminate stiffness matrix is devised to resolve not only the thickness locking but also some abnormalities of solid-shell elements in laminate analyses. Associated with the modified matrix, a set of generalized stresses can be defined and a modified Hellinger–Reissner functional can be derived by treating the generalized stresses as the independent variables. Based on the functional, an eigenteen-node hybrid-stress solid-shell element suitable for laminate analyses is proposed via a stabilization approach. All the benchmark tests indicate that the present stabilized element is close to the reduced integration element in accuracy.