A one-field discontinuous Galerkin formulation of non-linear Kirchhoff-Love shells

Spatially-discontinuous Galerkin methods constitute a generalization of weak formulations, which allow for discontinuities of the problem unknowns in its domain interior. This is particularly appealing for problems involving high-order derivatives, since discontinuous Galerkin (DG) methods can also be seen as a means of enforcing higher-order continuity requirements. Recently, DG formulations of linear and non-linear Kirchhoff-Love shell theories have been proposed. This new one-field formulations take advantage of the weak enforcement in such a way that the displacements are the only discrete unknowns, while the C1 continuity is enforced weakly. The Resulting one field formulation is a simple and efficient method to model thin structures and can be applied to various computational methods.