Shell deformation states and the finite element method: A benchmark study of cylindrical shells Original Research Article

We demonstrate some of the basic mathematical characteristics of shell deformation states and shell models from the point of view of finite element approximation. As benchmark cases, we analyze in detail three simple cylindrical shell problems. These problems are seemingly similar but turn out to be quite different. We (1) compute the exact displacement and strain fields in the model problems both numerically and symbolically using two variants of classical shell models, (2) for comparison, compute numerically the displacements and strains corresponding to certain higher-order dimension reduction models derived from the energy principle, (3) demonstrate the dissimilarity of the three benchmark problems as to their asymptotic behaviour in the limit of zero thickness and (4) show, both theoretically and experimentally, how this diversity is reflected in the accuracy of standard finite element approximations of both low and high order.