Contact frottant avec X-FEM: formulation 3D et stabilisation

HAL Id: hal-01495829

https://hal.archives-ouvertes.fr/hal-01495829 Submitted on 26 Mar 2017

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Contact frottant avec X-FEM: formulation 3D et

stabilisation

Samuel Geniaut, Patrick Massin, Nicolas Moës

To cite this version:

Samuel Geniaut, Patrick Massin, Nicolas Moës. Contact frottant avec X-FEM: formulation 3D et stabilisation. 8e Colloque national en calcul des structures, CSMA, May 2007, Giens, France. �hal-01495829�

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RÉSUMÉ. L’enjeu de ce travail est de proposer une nouvelle méthodologie, basée sur la

méthode des éléments finis étendue (X-FEM), pour l’étude de structures fissurées lorsque des conditions de contact (sans frottement, ou avec frottement adhérant) sont prises en compte sur les lèvres de la fissure. L’utilisation de X-FEM nous a conduit à formuler le problème de contact de manière continue, puis à le discrétiser au sens éléments finis. Un Lagrangien Augmenté est utilisée pour le traitement des équations de contact frottement. Afin de résoudre des problèmes de stabilité liés à la satisfaction de la condition LBB, un algorithme de construction de l’espace des multiplicateurs de Lagrange est également proposé. Un exemple numérique traité par Code_Aster vient illustrer l’emploi de cette approche pour résoudre un problème tridimensionnel de contact avec frottement.

ABSTRACT. This work presents a new method, based on the extended finite element method

(X-FEM), for the survey of frictional contact cracks. Because of X-FEM, a continuum mechanics formulation of contact is used, with an Augmented Lagrangian method. In order to satisfy the LBB condition, we propose an algorithm for building an appropriate Lagrange multiplier space. A detailed numerical example with the finite element software Code_Aster illustrates this approach while solving a three-dimensional frictional contact problem.

MOTS-CLÉS: X-FEM, contact frottant, 3D, condition LBB. KEYWORDS: X-FEM, frictional contact, 3D, LBB condition.

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