Développement d'un nouvel élément fini « SHB6 » de type solide-coque

HAL Id: hal-01504291

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Développement d’un nouvel élément fini “ SHB6 ” de type solide-coque

Vuong-Dieu Trinh, Farid Abed-Meraim, Alain Combescure

To cite this version:

Vuong-Dieu Trinh, Farid Abed-Meraim, Alain Combescure. Développement d’un nouvel élément fini “

SHB6 ” de type solide-coque. 8e Colloque national en calcul des structures, CSMA, May 2007, Giens,

France. �hal-01504291�

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* Laboratoire de Physique et Mécanique des Matériaux, ENSAM CER de Metz UMR CNRS 7554

4 rue Augustin Fresnel, 57078 Metz

vuong-dieu.trinh@metz.ensam.fr, farid.abed-meraim@metz.ensam.fr

** Laboratoire de Mécanique des Contacts et des Solides, INSA de Lyon UMR CNRS 5514

18-20 rue des Sciences, 69621 Villeurbanne alain.combescure@insa-lyon.fr

RÉSUMÉ . Cet article décrit le développement d’un nouvel élément fini prismatique SHB6 de type solide-coque, obtenu à partir d’une formulation purement tridimensionnelle. Cet élément possède six nœuds et cinq points d’intégration répartis selon la direction de l’épaisseur.

L’objectif étant d’avoir des éléments à géométrie volumique capables de modéliser des structures minces, tout en prenant correctement en compte les différents phénomènes à travers l’épaisseur. Afin d’améliorer ses performances de calcul et d’éviter certains blocages, l’intégration réduite a été employée. On montre d’abord que cette sous-intégration ne génère pas de modes de hourglass. Ensuite, on met en évidence que l’élément SHB6, sans aucune modification ou projection de son opérateur gradient discrétisé, peut souffrir de certains verrouillages de type cisaillement transverse ou membrane.

ABSTRACT . This paper presents the development of a new solid-shell finite element “SHB6”

derived from a purely three-dimensional formulation. It has six nodes as well as five integration points, all distributed along the “thickness” direction. The main goal of this research is to develop low-order solid elements that are able to model thin structures while correctly taking into account the various through-thickness phenomena. In order to improve its calculation performances and to prevent some locking phenomena, reduced integration was used. We demonstrate first that there are no hourglass modes generated by the reduced integration. On the other hand, we show that, without any modification or projection of its discrete gradient operator, the SHB6 element could suffer from some membrane and shear locking phenomena.

MOTS-CLÉS : Coque massive SHB6, Hourglass, Verrouillage en membrane et cisaillement.

KEYWORDS : SHB6 solid-shell, Hourglass, Shear and membrane locking.

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