Reference : On the approximation in the smoothed finite element method (SFEM)
Scientific journals : Letter to the editor
Engineering, computing & technology : Multidisciplinary, general & others
Computational Sciences
http://hdl.handle.net/10993/11866
On the approximation in the smoothed finite element method (SFEM)
English
Bordas, Stéphane mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
Natarajan, S. [Department of Civil Engineering, University of Glasgow, Glasgow G12 8LT, Scotland, United Kingdom]
2010
International Journal for Numerical Methods in Engineering
81
5
660-670
Yes (verified by ORBilu)
International
00295981
[en] Boundary integration ; Distorted meshes ; Isoparametric ; Non-mapped shape functions ; Rational basis finite elements ; SFEM ; Smoothed finite element method ; Strain smoothing ; Wachspress interpolants ; Finite Element ; Interpolants ; Shape functions ; Function evaluation ; Interpolation ; Rational functions ; Finite element method
[en] This letter aims at resolving the issues raised in the recent short communication (Int. J. Numer. Meth. Engng 2008; 76(8):1285-1295. DOI: 10.1002/nme.2460) and answered by (Int. J. Numer. Meth. Engng 2009; DOI: 10.1002/nme.2587) by proposing a systematic approximation scheme based on non-mapped shape functions, which both allows to fully exploit the unique advantages of the smoothed finite element method (SFEM) (Comput. Mech. 2007; 39(6):859-877. DOI: 10.1007/s00466-006-0075-4; Commun. Numer. Meth. Engng 2009; 25(1):19-34. DOI: 10.1002/cnm.1098; Int. J. Numer. Meth. Engng 2007; 71(8):902-930; Comput. Meth. Appl. Mech. Engng 2008; 198(2):165-177. DOI: 10.1016/j.cma.2008.05.029; Comput. Meth. Appl. Mech. Engng 2007; submitted; Int. J. Numer. Meth. Engng 2008; 74(2):175-208. DOI: 10.1002/nme.2146; Comput. Meth. Appl. Mech. Engng 2008; 197 (13-16):1184-1203. DOI: 10.1016/j.cma.2007.10.008) and resolve the existence, linearity and positivity deficiencies pointed out in (Int. J. Numer. Meth. Engng 2008; 76(8):1285-1295). We show that Wachspress interpolants (A Rational Basis for Function Approximation. Academic Press, Inc.: New York, 1975) computed in the physical coordinate system are very well suited to the SFEM, especially when elements are heavily distorted (obtuse interior angles). The proposed approximation leads to results that are almost identical to those of the SFEM initially proposed in (Comput. Mech. 2007; 39(6):859-877. DOI: 10.1007/s00466-006-0075-4). These results suggest that the proposed approximation scheme forms a strong and rigorous basis for the construction of SFEMs. © 2009 John Wiley & Sons, Ltd.
Researchers ; Professionals ; Students
http://hdl.handle.net/10993/11866
10.1002/nme.2713

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