Reference : Finite element analysis on implicitly defined domains: An accurate representation bas...

	Document type :	Scientific journals : Article
	Discipline(s) :	Engineering, computing & technology : Multidisciplinary, general & others
	Focus Areas :	Computational Sciences
	To cite this reference:	http://hdl.handle.net/10993/12915

Title :	Finite element analysis on implicitly defined domains: An accurate representation based on arbitrary parametric surfaces
Language :	English
Author, co-author :	Moumnassi, M. [Centre de Recherche Public Henri Tudor, 29, Avenue John F. Kennedy, G.D. of Luxembourg, L-1855 Luxembourg, Luxembourg, Laboratoire d'Étude des Microstructures et de Mécanique des Matériaux, LEM3, CNRS, Université Paul Verlaine - Metz, Ile du Saulcy, 57045 Metz, France]
	Belouettar, S. [Centre de Recherche Public Henri Tudor, 29, Avenue John F. Kennedy, G.D. of Luxembourg, L-1855 Luxembourg, Luxembourg]
	Béchet, T. [LTAS - Department of Aerospace and Mechanical Engineering, Université de Liège, Chemin des Chevreuils 1, 4000 Liège, Belgium]
	Bordas, Stéphane [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
	Quoirin, D. [Goodyear Innovation Center, L-7750 Colmar-Berg, Luxembourg]
	Potier-Ferry, M. [Laboratoire d'Étude des Microstructures et de Mécanique des Matériaux, LEM3, CNRS, Université Paul Verlaine - Metz, Ile du Saulcy, 57045 Metz, France]
Publication date :	2011
Journal title :	Computer Methods in Applied Mechanics & Engineering
Volume :	200
Issue/season :	5-8
Pages :	774-796
Peer reviewed :	Yes (verified by ORBilu)
Audience :	International
ISSN :	0045-7825
Keywords :	[en] CAD-analysis ; Curved boundary and sharp edges ; Dirichlet ; EXtended Finite Element Method ; Implicit boundary representation ; Level set method ; Boundary representations ; Curved boundary ; Extended finite element method ; Level Set method ; Boundary conditions ; Computer aided analysis ; Computer aided design ; Computer graphics ; Computer simulation ; Convergence of numerical methods ; Curve fitting ; Drop breakup ; Level measurement ; Parametric devices ; Finite element method
Abstract :	[en] In this paper, we present some novel results and ideas for robust and accurate implicit representation of geometric surfaces in finite element analysis. The novel contributions of this paper are threefold: (1) describe and validate a method to represent arbitrary parametric surfaces implicitly; (2) represent arbitrary solids implicitly, including sharp features using level sets and boolean operations; (3) impose arbitrary Dirichlet and Neumann boundary conditions on the resulting implicitly defined boundaries. The methods proposed do not require local refinement of the finite element mesh in regions of high curvature, ensure the independence of the domain's volume on the mesh, do not rely on boundary regularization, and are well suited to methods based on fixed grids such as the extended finite element method (XFEM). Numerical examples are presented to demonstrate the robustness and effectiveness of the proposed approach and show that it is possible to achieve optimal convergence rates using a fully implicit representation of object boundaries. This approach is one step in the desired direction of tying numerical simulations to computer aided design (CAD), similarly to the isogeometric analysis paradigm. © 2010 Elsevier B.V.
Funders :	Royal Academy of Engineering
Target :	Researchers ; Professionals ; Students ; Others
Permalink :	http://hdl.handle.net/10993/12915
DOI :	10.1016/j.cma.2010.10.002

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