Solid-shell approach based on first-order or higher-order plate and shell theories for the finite element analysis of thin to very thick structures

Abstract

A new solid-shell approach dedicated to thin to very thick structures is presented. Plate or shell displacement fields are directly applied on a solid finite element model which contains several elements through the thickness. Any plate or shell theory based on kinematic assumptions can be used, in this study three theories have been considered. The classical first-order theory, the modified first-order theory and a higher-order theory lead to the FOSS, the MFOSS and the HOSS models respectively. Kinematic relations are imposed at nodes to meet through-the-thickness plate or shell displacement fields. From a numerical point of view, linear equations are applied on the assembled finite element model. The methodology relies on the slave and master nodes technique. Slave nodes are eliminated, leading to a reduction of the model size. Two examples are presented: a clamped square plate under distributed loading and a quarter of cylinder under pressure. For the thin and thick cases, displacements and stresses are observed. The FOSS model leads to unsatisfactory results. The HOSS model gives excellent results in the thin as well as the thick cases, by comparison with the solid approach. The MFOSS model is satisfactory for thin structures and leads to moderate errors in the thick case. This approach is also efficient from a computational cost point of view.