Free access article

ESAIM: Proc., 2009, Vol. 27, pp. 240-253
DOI: 10.1051/proc/2009030

A numerical approach for modelling thin cracked plates with XFEM

Jérémie Lasry¹, Yves Renard² and Michel Salaün<sup>3

1</sup>  MIP-IMT, CNRS UMR 5219, INSAT, Complexe scientifique de Rangueil, 31077 Toulouse, France,
²  Université de Lyon, CNRS INSA-Lyon, ICJ UMR5208, LaMCoS UMR5259, F-69621, Villeurbanne, France,
³  Université de Toulouse, ISAE, 10 av. Edouard Belin, 31055 Toulouse cedex, France,

Published online: 25 June 2009

Abstract
The modelization of bending plates with through the thickness cracks is investigated. We consider the Kirchhoff-Love plate model which is valid for very thin plates. We apply the eXtended Finite Element Method (XFEM) strategy: enrichment of the finite element space with the asymptotic bending and with the discontinuity across the crack. We present two variants and their numerical validations and also a numerical computation of the stress intensity factors.

Résumé
Cet article traite de l'approximation numérique des plaques en flexion en présence d'une fissure traversante. Nous considérons un modèle de Kirchhoff-Love, valide pour les plaques très minces, et des éléments finis de type triangles HCT et quadrangles FVS réduits. La stratégie de la méthode des éléments finis étendue (XFEM) est alors appliquée : enrichissement de l'espace élément fini par le déplacement de flexion asymptotique en fond de fissure et par la discontinuité à la traversée de la fissure. Nous présentons deux variantes que nous validons numériquement ainsi que des calculs de facteurs d'intensité de contrainte.

© EDP Sciences, ESAIM 2009

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