Design and development of a discontinuous Galerkin method for shells

Abstract

The design and development of a discontinuous Galerkin (DG) formulation for linear shell problems is presented in this paper. Discontinuous approximations for displacement and stress fields are employed as independent unknowns. Through the properties associated with the inter-element discontinuities the present class of DG methods provide an additional mechanism to alleviate locking in shells. These properties are introduced by means of a suitable definition of numerical fluxes at the element interfaces. Degenerated bilinear quadrilateral element is used as an example, however, the formulation presented here is quite general and easily extendible to elements of other type and order. To demonstrate the effects of the DG approach to shell problems two different formulations of the elements themselves are considered, one with equal order approximations for displacement and stresses and the other with modified stresses (used in continuous finite element approach to eliminate locking). These two element formulations are then used within the DG framework. The results indicate that the DG approach can lead to significant improvements if the inter-element interface properties are selected properly, and several numerical examples are presented to support this feature. However, a rational method of selecting these interface attributes and the associated error estimates are still under investigation.