An exact finite rotation shell theory, its mixed variational formulation and its finite element implementation

TLDR: In this paper, a non-linear shell theory, including transverse shear strains, with exact description of the kinematical fields is developed, and the strain measures are derived via the polar decomposition theorem allowing for an explicit use of a three parametric rotation tensor.

Abstract: A non-linear shell theory, including transverse shear strains, with exact description of the kinematical fields is developed. The strain measures are derived via the polar decomposition theorem allowing for an explicit use of a three parametric rotation tensor. Thus in-plane rotations, also called drilling degrees of freedom, are included in a natural way. Various alternatives of the theory are derived. For a special version of the theory, with altogether six kinematical fields, different mixed variational principles are given. A hybrid finite element formulation, which does not exhibit locking phenomena, is developed. Numerical examples of shell deformation at finite rotations, with excellent element performance, are presented. Comparison with results reported in the literature demonstrates the features of the theory as well as the proposed finite element formulation.