A $C^0$ discontinuous Galerkin formulation for thin shells

Abstract

This paper presents a C 0 discontinuous Galerkin formulation for the simulation of thin shells. The method is based on Koiter’s shell model and allows finite element solutions to be obtained by using standard $C^0$ Lagrange basis functions in terms of the displacement only. It invokes a curvature-like term by applying a lifting operation which transforms jumps in the normal rotation across element boundaries into a field defined on element interiors. This procedure enforces weak continuity of normal derivative across element boundaries and a special term is added to enhance stability of the formulation. Benchmark tests using various-order elements are presented and conclusions are drawn as to the computational efficiency of the method.