Formulation quasi-symétrique du contact entre corps déformables

(1)

HAL Id: hal-01495638

https://hal.archives-ouvertes.fr/hal-01495638

Submitted on 25 Mar 2017

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Public Domain

Formulation quasi-symétrique du contact entre corps déformables

Lionel Fourment

To cite this version:

Lionel Fourment. Formulation quasi-symétrique du contact entre corps déformables. 8e Colloque

national en calcul des structures, CSMA, May 2007, Giens, France. �hal-01495638�

(2)

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*CEMEF, Ecole des Mines de Paris,

BP 207, 06 904 Sophia Antipolis Cedex, France lionel.fourment@ensmp.fr

RÉSUMÉ . Dans le cadre du contact entre corps déformables 3D ayant des discrétisations éléments finis incompatibles avec des tailles de mailles fort différentes, nous étudions une formulation quasi-symétrique de traitement du contact dans le but d’obtenir des résultats satisfaisants quelque soit le choix du corps HVFODYH et du corps PDvWUH. Cette approche ne repose pas sur l’utilisation d’éléments de mortier, mais sur une formulation symétrique des conditions de contact, cette dernière étant rendue compatible en remplaçant les multiplicateurs de Lagrange du corpsPDvWUH par la projection des multiplicateurs du corps HVFODYH. Les résultats numériques obtenus sur de nombreux cas tests 3D, dans le cadre du contact nodal résolu par pénalisation au sein du logiciel FORGE3®, montrent que cette approche résout avec simplicité les principales difficultés du contact entre corps déformables.

ABSTRACT . In the frame of contact between deformable bodies with non compatible finite element discretisations and with very different mesh sizes, a quasi-symmetric contact treatment is proposed in order to obtain satisfactory results whichever body is selected as PDVWHU or VODYH. This approach is not based on mortar elements, but on a symmetric formulation of the contact conditions. It is made compatible by replacing the Lagrange multipliers of the master body by the projection of the slave body multipliers. Numerical results obtained with numerous 3D test cases, in the frame of a nodal contact formulation solved by a penalty method within the FORGE3® finite element software, show that this approach actually solves the main difficulties of contact between deformable bodies, in a rather simple way.

MOTS-CLÉS :Contact, Maillages Non Compatibles, Mise en Forme, Corps Déformables

KEYWORDS : Contact, Non Compatible Meshes, Metal Forming, Deformable Bodies

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Formulation quasi-symétrique du contact entre corps déformables

HAL Id: hal-01495638

https://hal.archives-ouvertes.fr/hal-01495638

Submitted on 25 Mar 2017

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Public Domain

Formulation quasi-symétrique du contact entre corps déformables

Lionel Fourment

To cite this version:

Lionel Fourment. Formulation quasi-symétrique du contact entre corps déformables. 8e Colloque

national en calcul des structures, CSMA, May 2007, Giens, France. �hal-01495638�

5HYXH9ROXPH;±Q[DQQpHSDJHVj;

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*CEMEF, Ecole des Mines de Paris,

BP 207, 06 904 Sophia Antipolis Cedex, France lionel.fourment@ensmp.fr

MOTS-CLÉS :Contact, Maillages Non Compatibles, Mise en Forme, Corps Déformables

KEYWORDS : Contact, Non Compatible Meshes, Metal Forming, Deformable Bodies

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