On dynamically and kinematically exact theory of shells

In the dynamically and kinematically exact theory of shells, the shell is represented by a base surface with an attached structure tensor. The gross deformation of the shell cross sections is described by the translation vector and the rotation tensor which are fields work-averaged through the shell thickness. Some relations between 3D fields in the shell-like body and 2D fields modelling the shell behaviour are discussed. We show, in particular, that the exact resultant stress power of the shell does not coincide with the 2D effective stress power following from the exact resultant balance laws. The difference expressed through an intrinsic deformation vector field is responsible for approximations in the shell constitutive description. We sketch how to refine the shell model in the case of a simple equilibrium problem of the non-linearly elastic shell.