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Contribution à l’automatisation des analyses par éléments-finis multidimensionnelles

Published online by Cambridge University Press:  06 January 2012

Jean-Christophe Cuillière ,
Sylvain Bournival  and
Vincent François
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Abstract

La réduction du nombre de degrés de liberté d’une étude par éléments-finis peut être obtenue en utilisant l’analyse par éléments-finis multidimensionnelle, c’est-à-dire le mélange d’éléments-finis de poutre, de coque et de volume. Cette approche multidimensionnelle permet de réduire considérablement le temps de maillage et de résolution du système. Malheureusement, la connexion d’éléments de différentes dimensions entraîne certains problèmes au niveau de la modélisation géométrique ainsi qu’au niveau de l’incompatibilité des degrés de liberté entre éléments et de la continuité entre différentes parties de maillage réalisées séparément. Cet article présente une solution complètement automatisée à ces problèmes, utilisant uniquement des éléments-finis classiques et sans recourir à l’ajout d’équations de contraintes aux interfaces entre éléments de dimensions différentes.

Keywords

Multi-dimensional analysisfinite elementsmesh generationshell elementsbeam elementsAnalyse multidimensionnelleéléments-finismaillageéléments de coqueéléments de poutre
Type
Research Article
Information
Mechanics & Industry , Volume 12 , Issue 6 , 2011 , pp. 513 - 531
Copyright
© AFM, EDP Sciences 2011

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References

Références

C.G. Armstrong, S. Bridgett, R. Donaghy, W. Mc Cune, R. McKeag, D. Robinson, Techniques for interactive and automatic idealisation of cad models, numerical grid generation in computational field simulations, Greenwich, UK, 1998, pp. 643–662
Chong, C.S., Kumar, A.S., Lee, K.H., Automatic solid decomposition and reduction for non-manifold geometric model generation, Comput. Aided Design 36 (2004) 1357–1369 CrossRefGoogle Scholar
R.J. Donaghy, W. McCune, S.J. Bridgett, C.G. Armstrong, D.J. Robinson, R.M. McKeag, Dimensional Reduction of Analysis Models, in: S.N. Laboratories (éd.), International Meshing Roundtable, Pittsburgh, Pennsylvania, 1996, pp. 307–320
D.J. Monaghan, I.W. Doherty, D. McCourt, C.G. Armstrong, Coupling 1D Beams to 3D Bodies, International Meshing Roundtable, Dearborn, USA, 1998, pp. 1–8
K. Suresh, Generalization of the Kantorovich Method of Dimensional Reduction, International Meshing Roundtable, Santa Fe, New Mexico, 2003, pp. 261–270
M. Mantyla, An introduction to solid modeling, 1988
M.E. Mortenson, Geometric Modeling, 1985
Mc Cune, W., Armstrong, C.G., Robinson, D., Mixed-dimensional coupling in finite element models, Int. J. Numer. Methods Eng. 49 (2000) 725–750 3.0.CO;2-W>CrossRefGoogle Scholar
K. Shim, D.J. Monaghan, A. CG, Mixed dimensional coupling in finite element stress analysis, International Meshing Roundtable Newport Beach, California 2001, pp. 269–277
H. Ben Dhia, Approches Locales-Globales Méthode Arlequin, 5e Colloque National de Calcul des Structures, Giens, France, 2005, pp. 21–32
J.-C. Craveur, D. Marceau, De la CAO au calcul, Dunod, Paris, 2001
Allman, D.J., A compatible triangular element including vertex rotations for plane elasticity analysis, Comput. Struct. 19 (1984) 1–8 CrossRefGoogle Scholar
Pawlak, T.P., Yunus, S.M., Solid elements with rotational degrees of freedom: Part II – tetrahedron elements, Int. J. Numer. Methods Eng. 31 (1991) 593–610 CrossRefGoogle Scholar
Sze, K.Y., Pan, Y.S., Hybrid stress tetrahedral elements with Allman’s rotational D.O.F.s, Int. J. Numer. Methods Eng. 48 (2000) 1055–1070 3.0.CO;2-P>CrossRefGoogle Scholar
S. Bournival, J.-C. Cuilliere, V. Francois, A mesh-based method for coupling 1D and 3D finite elements, Design and Modelling of Mechanical Systems, Monastir, Tunisia, 2007
P.J. Frey, P.-L. George, Maillages applications aux elements finis, Hermes Sciences, Paris, 1999
Cuilliere, J.-C., An adaptive method for the automatic triangulation of 3D parametric surfaces, Comput. Aided Design 30 (1998) 139–149 CrossRefGoogle Scholar
V. Francois, J.-C. Cuilliere, An a priori adaptive 3D advancing front mesh generator integrated to solid modeling, Recent Advances in Integrated Design and Manufacturing in Mechanical Engineering. (2003) 337–346
Bournival, S., Cuillière, J.-C., François, V., A mesh-geometry based method for coupling 1D and 3D elements, Adv. Eng. Softw. 41 (2010) 838–858 CrossRefGoogle Scholar
Cuillière, J.-C., Bournival, S., François, V., A mesh-geometry-based solution to mixed-dimensional coupling, Comput. Aided Design 42 (2010) 509–522 CrossRefGoogle Scholar