Abstract: In this paper, we construct a Galerkin nonconforming finite element method for the linear elastic flexural shell model proposed by Ciarlet-Lods-Miara. First, we discretize the integral domain with Delaunay triangulation. We approximate the first two component of the displacement by the first-order Lagrangian polynomial, whereas we approximate the third component of the displacement, i.e., the normal displacement, by the nonconforming Morley element. Secondly, we discuss the existence, uniqueness, and a priori error estimate of the numerical solution. Finally, we run numerical experiments for the conical shell with special boundary conditions. We derive the displacements of the conical middle surface under the different meshes. We analyze the numerical results which show that the finite element method is convergent and effective.

Key words: linear elastic flexural shell, nonconforming finite element method, Lagrangian polynomial, Moley element, conical shell