Nonconforming Finite Element Methods for Two-Dimensional Linearly Elastic Shallow Shell Model

A shell whose height is far less than the minimum size covering the bot -tom is called the shallow shell. As a branch of linear elastic shell, it is a special shell with large span and has been widely applied in engineering fields. The main aim of this paper is to construct a general nonconforming finite element framework for a two-dimensional shallow shell model proposed by Ciarlet and Miara. Based on the different regularities of the displacement components, we give the special properties satisfied by the general framework and provide several nonconforming finite element discretization schemes. Then, the existence and uniqueness of the numerical solutions are proved, with the rate of convergence derived. Finally, numerical experiments are carried out for the paraboloid, spherical dome and cylindrical bridge, which validates the theoretical analyses. Moreover, the computing cost of discretizing the shallow shell model is evidently less than that of discretizing the general shell model with comparable accuracy when the shell is the large span shell.