A discontinuous Galerkin method for nonlinear shear-flexible shells
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Radovitzky_A discontinuous.pdf
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1.14 MB
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Author(s)
Talamini, Brandon Louis
Radovitzky, Raul A
Date Issued
January 2016
Journal
Computer Methods in Applied Mechanics and Engineering
Publisher
Elsevier
Citation
Talamini, Brandon L. and Raúl Radovitzky. “A Discontinuous Galerkin Method for Nonlinear Shear-Flexible Shells.” Computer Methods in Applied Mechanics and Engineering 303 (May 2016): 128–162 © 2016 Elsevier B.V.
Version
Original manuscript
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. Keywords: Shells; Discontinuous Galerkin; Locking; Variational
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/j.cma.2016.01.001
