A discontinuous Galerkin formulation of non‐linear Kirchhoff–Love shells

Discontinuous Galerkin (DG) methods provide a means of weakly enforcing the continuity of the unknown‐field derivatives and have particular appeal in problems involving high‐order derivatives. This feature has previously been successfully exploited (Comput. Methods Appl. Mech. Eng. 2008; 197 :2901–2929) to develop a formulation of linear Kirchhoff–Love shells considering only the membrane and bending responses. In this proposed one‐field method—the displacements are the only unknowns, while the displacement field is continuous, the continuity in the displacement derivative between two elements is weakly enforced by recourse to a DG formulation. It is the purpose of the present paper to extend this formulation to finite deformations and non‐linear elastic behaviors. While the initial linear formulation was relying on the direct linear computation of the effective membrane stress and effective bending couple‐stress from the displacement field at the mid‐surface of the shell, the non‐linear formulation considered implies the evaluation of the general stress tensor across the shell thickness, leading to a reformulation of the internal forces of the shell. Nevertheless, since the interface terms resulting from the discontinuous Galerkin method involve only the resultant couple‐stress at the edges of the shells, the extension to non‐linear deformations is straightforward. Copyright © 2008 John Wiley & Sons, Ltd.