A non-linear finite element formulation for shells of arbitrary geometry

Based on a total Lagrangian approach, the shell element formulation developed by two of the authors is extended to non-linear field. The proposed shell element belongs to the degenerated 3D type, with a Mindlin-Reissner approach and five effective degrees of freedom per node. A detailed description of the geometry and kinematics characterisation of the element, as well as of the stress-strain relationship is presented. Numerical testing of the non-linear model indicates excellent performance of the proposed finite element shell, both in simulating large displacement and rotations, and in the buckling analysis of some classical test examples, e.g., cylinder and sphere.