A discontinuous Galerkin method for nonlinear shear-flexible shells

Abstract

In this paper, a discontinuous Galerkin method for a nonlinear shear-flexible shell theory is proposed that is suitable for both thick and thin shell analysis. The proposed method extends recent work on Reissner–Mindlin plates to avoid locking without the use of projection operators, such as mixed methods or reduced integration techniques. Instead, the flexibility inherent to discontinuous Galerkin methods in the choice of approximation spaces is exploited to satisfy the thin plate compatibility conditions a priori. A benefit of this approach is that only generalized displacements appear as unknowns. We take advantage of this to craft the method in terms of a discrete energy minimization principle, thereby restoring the Rayleigh–Ritz approach. In addition to providing a straightforward and elegant derivation of the discrete equilibrium equations, the variational character of the method could afford numerous advantages in terms of mesh adaptation and available solution techniques. The proposed method is exercised on a set of benchmarks and example problems to assess its performance numerically, and to test for shear and membrane locking.