Reference : Addressing volumetric locking and instabilities by selective integration in smoothed ...
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Computational Sciences
Addressing volumetric locking and instabilities by selective integration in smoothed finite elements
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 mailto [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]
Communications in Numerical Methods in Engineering
Yes (verified by ORBilu)
[en] 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
[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.
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