A hybrid hexahedral solid-shell element with self-equilibrated stresses for the geometrically nonlinear static analysis of composite laminated structures

Hybrid finite elements with self-equilibrated assumed stresses have proven to provide several advantages for analysing shell structures. They guarantee high performance when using coarse meshes and accurately represent the stress field. Additionally, they do not require assumptions about the displacement field within the element domain, and the integration is efficiently performed only along their contours. This work exploits those advantages to develop a solid-shell finite element for the geometrically nonlinear static analysis of composite laminated structures. In particular, an eight-node finite element, which has 24 displacement variables and 18 stress parameters, is developed. The displacement field is described only by translations, eliminating the need for complex finite rotation treatments in large displacement problems. A Total Lagrangian formulation is used with the Green-Lagrange strain tensor and the second Piola-Kirchhoff stress tensor. Thickness locking is cured using an assumed natural strain formulation for the transversal normal stress, and the assumed stress field eliminates shear locking. Then, for the analysis of linear-elastic problems, no domain integration is needed, and all the element operators are obtained by line integrals. The resulting formulation is efficient and allows for easy implementation. Computed numerical results show the accuracy and robustness of the presented element when used for both the linear elastic static and geometrically nonlinear elastic static analysis of composite laminated shell structures.