A review of shell finite elements and corotational theories

The development of shell finite elements is reviewed. As a background for these discussions, some of the controversies and difficulties in classical shell theories are reviewed and the features of shell bending behavior which were elucidated analytically are recalled. The description of shell elements focuses on three types of methods: mixed methods, assumed strain methods and discrete Kirchhoff methods. In Section 4, a corotational theory and its application to shells are presented; as part of this development, the kinematics of degenerated continuum formulations are compared to the Koiter-Sanders theory.