Article (Scientific journals)
Addressing volumetric locking and instabilities by selective integration in smoothed finite elements
Hung, Nguyen-Xuan; Bordas, Stéphane; Hung, Nguyen-Dang
2009In Communications in Numerical Methods in Engineering, 25 (1), p. 19-34
Peer reviewed
 

Files


Full Text
Addressing volumetric locking and instabilities.pdf
Publisher postprint (293.14 kB)
Request a copy

All documents in ORBilu are protected by a user license.

Send to



Details



Keywords :
Accuracy; Convergence; Finite element method; Instabilities; Non-local strain; Rank deficiency; Reduced integration; Selective integration; Smoothed strains; Stabilized conforming nodal integration; Volumetric locking; Incompressible flow; Integration; Standards; Strain; Vibration measurement
Abstract :
[en] This paper promotes the development of a novel family of finite elements with smoothed strains, offering remarkable properties. In the smoothed finite element method (FEM), elements are divided into subcells. The strain at a point is defined as a weighted average of the standard strain field over a representative domain. This yields superconvergent stresses, both in regular and singular settings, as well as increased accuracy, with slightly lower computational cost than the standard FEM. The one-subcell version that does not exhibit volumetric locking yields more accurate stresses but less accurate displacements and is equivalent to a quasi-equilibrium FEM. It is also subject to instabilities. In the limit where the number of subcells goes to infinity, the standard FEM is recovered, which yields more accurate displacements and less accurate stresses. The specific contribution of this paper is to show that expressing the volumetric part of the strain field using a one-subcell formulation is sufficient to get rid of volumetric locking and increase the displacement accuracy compared with the standard FEM when the single subcell version is used to express both the volumetric and deviatoric parts of the strain. Selective integration also alleviates instabilities associated with the single subcell element, which are due to rank deficiency. Numerical examples on various compressible and incompressible linear elastic test cases show that high accuracy is retained compared with the standard FEM without increasing computational cost.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Hung, Nguyen-Xuan;  Division of Computational Mechanics, Department of Mathematics and Informatics, University of Natural Sciences-VNU-HCM, 227 Nguyen Van Cu, Viet Nam
Bordas, Stéphane ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
Hung, Nguyen-Dang;  LTAS-Division of Fracture Mechanics, University of Liège, Bâtiment B52/3 Chemin des Chevreuils 1, B-4000 Liège 1, Belgium
External co-authors :
yes
Language :
English
Title :
Addressing volumetric locking and instabilities by selective integration in smoothed finite elements
Publication date :
2009
Journal title :
Communications in Numerical Methods in Engineering
ISSN :
1069-8299
Volume :
25
Issue :
1
Pages :
19-34
Peer reviewed :
Peer reviewed
Focus Area :
Computational Sciences
Available on ORBilu :
since 17 February 2018

Statistics


Number of views
82 (0 by Unilu)
Number of downloads
0 (0 by Unilu)

Scopus citations®
 
49
Scopus citations®
without self-citations
31
OpenCitations
 
28
WoS citations
 
30

Bibliography


Similar publications



Contact ORBilu