[en] This paper is devoted to the imposition of Dirichlet-type conditions within the extended finite element method (X-FEM). This method allows one to easily model surfaces of discontinuity or domain boundaries on a mesh not necessarily conforming to these surfaces. Imposing Neumann boundary conditions on boundaries running through the elements is straightforward and does preserve the optimal rate of convergence of the background mesh (observed numerically in earlier papers). On the contrary, much less work has been devoted to Difichlet boundary conditions for the X-FEM (or the limiting case of stiff boundary conditions). In this paper, we introduce a strategy to impose Dirichlet boundary conditions while preserving the optimal rate of convergence. The key aspect is the construction of the correct Lagrange multiplier space on the boundary. As an application, we suggest to use this new approach to impose precisely zero pressure on the moving resin front in resin transfer moulding (RTM) process while avoiding remeshing. The case of inner conditions is also discussed as well as two important practical cases: material interfaces and phase-transformation front capturing. Copyright (c) 2006 John Wiley & Sons, Ltd.
Disciplines :
Mathematics Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Moes, Nicolas; GeM Institute, Ecole Centrale de Nantes, Université de Nantes, CNRS, 1 Rue de la Noe, 44321 Nantes, France
Béchet, Eric ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Conception géométrique assistée par ordinateur
Tourbier, Matthieu; GeM Institute, Ecole Centrale de Nantes, Université de Nantes, CNRS, 1 Rue de la Noe, 44321 Nantes, France
Language :
English
Title :
Imposing Dirichlet boundary conditions in the extended finite element method
Publication date :
2006
Journal title :
International Journal for Numerical Methods in Engineering
ISSN :
0029-5981
eISSN :
1097-0207
Publisher :
John Wiley & Sons, Inc, Chichester, United Kingdom
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