期刊
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
卷 352, 期 -, 页码 561-585出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2019.04.029
关键词
Shell structures; Discontinuous Galerkin method; Nonlinear elasticity; Superconvergence; Finite element; Hybridizable discontinuous Galerkin
资金
- NASA (USA) [NNX16AP15A]
- NASA [NNX16AP15A, 897265] Funding Source: Federal RePORTER
We present a 3D hybridizable discontinuous Galerkin (HDG) method for nonlinear elasticity which can be efficiently used for thin structures with large deformation. The HDG method is developed for a three-field formulation of nonlinear elasticity and is endowed with a number of attractive features that make it ideally suited for thin structures. Regarding robustness, the method avoids a variety of locking phenomena such as membrane locking, shear locking, and volumetric locking. Regarding accuracy, the method yields optimal convergence for the displacements, which can be further improved by an inexpensive postprocessing. And finally, regarding efficiency, the only globally coupled unknowns are the degrees of freedom of the numerical trace on the interior faces, resulting in substantial savings in computational time and memory storage. This last feature is particularly advantageous for thin structures because the number of interior faces is typically small. In addition, we discuss the implementation of the HDG method with arc-length algorithms for phenomena such as snap-through, where the standard load incrementation algorithm becomes unstable. Numerical results are presented to verify the convergence and demonstrate the performance of the HDG method through simple analytical and popular benchmark problems in the literature. (C) 2019 Elsevier B.Y. All rights reserved.
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