Nonconforming Finite Element Methods for Two-Dimensional Linearly Elastic Shallow Shell Model (Advances in Applied Mathematics and Mechanics, 2024)
A shell whose height is far less than the minimum size covering the bottom is called the shallow shell. As a branch of linear elastic shell, it is a special shellwith large span and has been widely applied in engineering fields. The main aimof this paper is to construct a general nonconforming finite element framework for atwo-dimensional shallow shell model proposed by Ciarlet and Miara. Based on thedifferent regularities of the displacement components, we give the special propertiessatisfied by the general framework and provide several nonconforming finite elementdiscretization schemes. Then, the existence and uniqueness of the numerical solutionsare proved, with the rate of convergence derived. Finally, numerical experiments arecarried out for the paraboloid, spherical dome and cylindrical bridge, which validatesthe theoretical analyses. Moreover, the computing cost of discretizing the shallow shellmodel is evidently less than that of discretizing the general shell model with comparable accuracy when the shell is the large span shell.