Kinematics of finite rotation shells with in-plane twist parameter

Abstract

The paper concerns shell equations derived from a 3D mixed formulation with explicit rotations. The constitutive equation is postulated in terms of the relaxed Biot stress and right stretch strain. The shell kinematics is based on the Reissner hypothesis and on a constant/linear approximation of the rotation tensor with respect to the thickness coordinate. The rotation around the shell director is parametrized by the drill and in-plane twist parameters, with the latter one associated with the linear approximation. The in-plane twist parameter is new, and hence consequences of its presence for the shell rotation constrains and strain measures are examined, and compared to the formulation with the drill rotation only. In the presented formulation, the drill rotation is retained explicitly, and can be recovered from the drill rotation constraint, while the in-plane twist parameter is an internal parameter of the theory. In this way the enhanced shell kinematics does not increase the number of degrees of freedom of a discrete model.