A mixed shell formulation accounting for thickness strains and finite strain 3d material models

A non-linear quadrilateral shell element for the analysis of thin structures is presented. The Reissner-Mindlin theory with inextensible director vector is used to develop a three-field variational formulation with independent displacements, stress resultants and shell strains. The interpolation of the independent shell strains consists of two parts. The first part corresponds to the interpolation of the stress resultants. Within the second part independent thickness strains are considered. This allows incorporation of arbitrary non-linear 3d constitutive equations without further modifications. The developed mixed hybrid shell element possesses the correct rank and fulfills the in-plane and bending patch test. The essential feature of the new element is the robustness in the equilibrium iterations. It allows very large load steps in comparison with other element formulations. We present results for finite strain elasticity, inelasticity, bifurcation and post-buckling problems. Copyright (C) 2007 John Wiley & Sons, Ltd.