Asymptotic analysis of layered elastic beams

Michele Serpilli

doi:10.1016/j.crme.2005.07.001

Asymptotic analysis of layered elastic beams

Presented by: Évariste Sanchez-Palencia

Michele Serpilli ¹

¹ Dipartimento di Architettura, Costruzioni e Strutture, Università Politecnica delle Marche, via Brecce Bianche, 60131 Ancona, Italy

Comptes Rendus. Mécanique, Volume 333 (2005) no. 8, pp. 593-598.

Abstract
Résumé

We consider an elastic beam formed by three layers, fixed at one end and loaded at the free end. We call adherents the upper and lower layers $Ω_{+}^{ɛ}$ and $Ω_{-}^{ɛ}$ and an adhesive layer $Ω_{m}^{ɛ}$ . We denote by $ɛ h_{\pm, m}$ the thickness of each layer and we suppose that the stiffness of the adhesive layer is $ɛ^{2}$ , with respect to that of the adherents. By an asymptotic analysis we obtain the zeroth order limit problem and the form of the second order displacements.

Si l'on considère une poutre élastique constituée de trois couches, fixée à une extrémité. La strate supérieure et inférieure sont indiquées de la sorte $Ω_{+}^{ɛ}$ et $Ω_{-}^{ɛ}$ , alors que la partie centrale, ou adhésive $Ω_{m}^{ɛ}$ . Nous prendrons $ɛ h_{\pm, m}$ comme l'épaisseur de chaque strate et supposerons que la rigidité du adhésive et de l'ordre de $ɛ^{2}$ , par rapport avec les strates supérieures et inférieures. Par la méthode de l'expansion asymptotique on obtient le problème limite de l'ordre zéro et les fonctions de déplacement de l'ordre 2.

Received: 2005-06-01
Accepted: 2005-06-07
Published online: 2005-08-01

DOI: 10.1016/j.crme.2005.07.001

Keywords: Computational solid mechanics, Asymptotic analysis, Layered beams, Bonding
Mots-clés : Mécanique des solides numérique, Analyse asymptotique, Poutres multicouche, Collage

Author's affiliations:

Michele Serpilli ¹

¹ Dipartimento di Architettura, Costruzioni e Strutture, Università Politecnica delle Marche, via Brecce Bianche, 60131 Ancona, Italy

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     title = {Asymptotic analysis of layered elastic beams},
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Michele Serpilli. Asymptotic analysis of layered elastic beams. Comptes Rendus. Mécanique, Volume 333 (2005) no. 8, pp. 593-598. doi : 10.1016/j.crme.2005.07.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2005.07.001/

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