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A hybridizable discontinuous Galerkin method for both thin and 3D nonlinear elastic structures

A hybridizable discontinuous Galerkin method for both thin and 3D nonlinear elastic structures

Terrana, S., Nguyen, N.C. ORCID: 0000-0001-9167-5780, Bonet, J. ORCID: 0000-0002-0430-5181 and Peraire, J. (2019) A hybridizable discontinuous Galerkin method for both thin and 3D nonlinear elastic structures. Computer Methods in Applied Mechanics and Engineering, 352. pp. 561-585. ISSN 0045-7825 (doi:https://doi.org/10.1016/j.cma.2019.04.029)

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Abstract

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 snapthrough, 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.

Item Type: Article
Uncontrolled Keywords: Shell structures; Discontinuous Galerkin method; Nonlinear elasticity; Superconvergence; Finite element; Hybridizable discontinuous Galerkin
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
T Technology > TK Electrical engineering. Electronics Nuclear engineering
Faculty / Department / Research Group: Vice-Chancellor's Group
Last Modified: 01 May 2020 01:38
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: None
Selected for REF2021: None
URI: http://gala.gre.ac.uk/id/eprint/23898

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