3D-shell models and finite elements

Abstract: We consider shell models obtained by assuming a quadratic expansion of the 3D displacements across the thickness, without any assumption on the stress tensor. We can show that these models are asymptotically consistent with classical shell models, hence shell models can be generated with ease for general constitutive laws. Furthermore, these models lead to natural discretizations in the form of 3D isoparametric elements. These elements can be made as reliable as other existing shell elements, in particular as regards numerical locking. In addition, they make the analysis of coupled problems involving shells very easy, e.g. in sandwich shells or in fluid-structure interaction. Overall, these "3D-shell elements" appear to combine the advantages of 3D and shells.