Implementation of Discontinuous Galerkin Kirchhoff-Love Shells

Abstract

This technical report describes an implementation of the discontinuous Galerkin (DG) finite element method for thin shells presented by [Noels and Radovitzky 2008]. After a short summary of the Kirchhoff-Love shell theory, the DG weak form is reviewed and the assembly of the stiffness matrix is described in detail. We also present a co-rotational extension to the method which allows us to simulate large rotational deformations without the typical linearization artifacts of a linear shell model. The proposed model has been successfully applied to the simulation of cutting and fracturing of thin shells by means of harmonic enrichments [Kaufmann et al. 2009].