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Investigation of a locking‐free hybrid discontinuous Galerkin element that is very easy to implement into FE‐codes
Author(s) -
Wulfinghoff Stephan,
Bayat Hamid Reza,
Alipour Atefeh,
Reese Stefanie
Publication year - 2017
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201710026
Subject(s) - quadrilateral , finite element method , element (criminal law) , simple (philosophy) , degrees of freedom (physics and chemistry) , discontinuous galerkin method , bilinear interpolation , convergence (economics) , mathematics , geometry , mathematical analysis , physics , structural engineering , engineering , law , political science , philosophy , statistics , epistemology , quantum mechanics , economics , economic growth
In this work, a hybrid discontinuous Galerkin (dG) quadrilateral element formulation is investigated. In hybrid formulations, the elements' interior is treated independently from the skeleton (the element boundaries). The global degrees of freedom (dofs) are located on the element corners. This makes the implementation into existing finite element codes simple. The dofs in the element interior are condensed out. The deformation gradient is taken homogeneous within the element instead of using bilinear shape funcitons. The result is a very simple formulation and numerical implementation. The element has been shown to be free of volumetric locking and shear locking. Moreover, the mesh convergence is close to well‐known formulations like the Q1E4‐, Q1P0‐ or Q1SP‐element. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)