Asymptotic deformation modes of benchmark problems suitable for evaluating shell elements

An analytical approach introduced recently concerning the definition of the limiting cases of the asymptotic behaviour of shell elements is critically reviewed. A simple analytical approach for defining the asymptotic behaviour of shell elements is proposed. This approach is employed to define and analyse the asymptotic deformation modes of selected benchmark problems suitable for the evaluation of the asymptotic behaviour of shell elements. A new limit test problem, the hyperbolic paraboloid shell problem, proposed as a strong test for the pure bending asymptotic behaviour of shell elements, is analysed in the context of the proposed approach. Explicit expressions for characteristic asymptotic displacements are derived for the shell benchmark problems considered. These expressions are proposed for testing the asymptotic behaviour of finite shell elements in membrane-dominated, bending-dominated and mixed membrane-bending mode shell problems.