Summary: A higher-order shell theory is proposed for arbitrary shell geometries, which allows the cross-section to rotate with respect to the middle surface and to warp into a non-planar surface. This new kinematic assumption satisfies the shear-free surface boundary condition (BC) automatically. We derive a new expression for internal forces based on this kinematic assumption. A new functional for arbitrary shell geometries is obtained employing Gâteaux differential method. During this variational process, we are able to construct BC and to introduce the functional in a systematic way. Two different mixed elements, PRSH 52 and CRSH52, are derived for parabolic and circular cylindrical shells, respectively, using the functional. The element does not suffer from shear locking. The performance of the elements is verified by test problems.
Y. et al. (Sun,) studied this question.