Warping and in-plane twist parameters in kinematics of finite rotation shells Original Research Article

The finite rotation shell equations are derived from a 3D mixed formulation with explicit rotations. Constitutive equations are written in terms of the relaxed Biot stress and right stretch strain. The shell kinematics is based on a generalised Reissner hypothesis and rotations depending on the thickness coordinate. The generalized Reissner hypothesis includes a bubble-like term for the warping of a cross-section. The rotations linearly vary over the thickness and are parametrised by a canonical rotation vector. The components of the rotation vector can be identified as the in-plane twist parameter and two warping parameters. Consequences of this new rotation vector for shell equations, especially for rotation constraints and strain measures, are examined, and a comparison with the formulation which includes the in-plane twist parameter is made. The new rotation vector is treated as an implicit kinematical parameter and recovered from the rotation constraint. Hence, a 6-parameter shell formulation, admitting C0 approximations, is retained.