A nonlinear Hu—Washizu variational formulation for shells and associated quadrilateral finite element

In the paper a nonlinear quadrilateral shell element for the analysis of thin structures is presented. The variational formulation is based on a Hu—Washizu functional with independent displacement, stress and strain fields. The interpolation matrices for the mid-surface displacements and rotations as well as for the stress resultants and strains are specified. The developed mixed hybrid shell element possesses the correct rank and fulfills the in-plane and bending patch tests. Hence, the approximated stationary condition is iteratively solved using the Newton method. The essential feature of the new element is the robustness in the equilibrium iterations. It allows one to apply very large load steps in comparison to other finite element formulations.