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

Abstract

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.

A discontinuous Galerkin formulation for nonlinear analysis of multilayered shells refined theories

“…In particular, dG formulations and investigations have been proposed for the linear analysis of: (i) plates, modelled by the Kircchoff [37,38,39] and Mindlin-Reissner [40,41,42] first order theories; (ii) shells studied by using the Kircchoff-Love [43], Koiter [44] and Reissner-Mindlin [45] first order theories. As regard the non-linear regime, dG methods have been employed for the solution of: (i) Kircchoff plates [46,47,48], (ii) Kircchoff-Love shells [49,50,51] and (iii) shear flexible shells modelled with the first order theory [52,53]. Also, refined shell models have been proposed for both the linear [54] and nonlinear [55] analysis, based on finite elements built using a dG approach along the thickness direction.…”