On the junction of elastic plates and beams
[Sur la jonction des plaques et des poutres élastiques]
Comptes Rendus. Mathématique, Tome 335 (2002) no. 8, pp. 717-722.

On considère le système linéarisé de l'élasticité, dans un multidomaine de R 3 constitué d'une plaque horizontale de section fixée et de faible épaisseur ε et d'une poutre verticale de hauteur fixée et de petite section dont le rayon est rε. La frontière latérale de la plaque et le haut de la poutre sont supposés encastrés. Nous identifions le problème limite quand ε et rε tendent simultanément vers zéro, avec rεε2. Ce problème limite fait intervenir six conditions de jonction.

We consider the linearized elasticity system in a multidomain of R 3 . This multidomain is the union of a horizontal plate with fixed cross section and small thickness ε, and of a vertical beam with fixed height and small cross section of radius rε. The lateral boundary of the plate and the top of the beam are assumed to be clamped. When ε and rε tend to zero simultaneously, with rεε2, we identify the limit problem. This limit problem involves six junction conditions.

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Accepté le :
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DOI : 10.1016/S1631-073X(02)02543-8
Gaudiello, Antonio 1 ; Monneau, Régis 2 ; Mossino, Jacqueline 3 ; Murat, François 4 ; Sili, Ali 5

1 Dipartimento di Automazione, Elettromagnetismo, Ingegneria dell'Informazione e Matematica Industriale, Università di Cassino, Via G. Di Biasio 43, 03043 Cassino (FR), Italy
2 CERMICS, École nationale des ponts et chaussées, 6 et 8, avenue Blaise Pascal, cité Descartes, 77455 Champs-sur-Marne cedex 2, France
3 CMLA, École normale supérieure de Cachan, 61, avenue du Président Wilson, 94235 Cachan cedex, France
4 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, boı̂te courrier 187, 75252 Paris cedex 05, France
5 Département de mathématiques, Université de Toulon et du Var, BP 132, 83957 La Garde cedex, France
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Gaudiello, Antonio; Monneau, Régis; Mossino, Jacqueline; Murat, François; Sili, Ali. On the junction of elastic plates and beams. Comptes Rendus. Mathématique, Tome 335 (2002) no. 8, pp. 717-722. doi : 10.1016/S1631-073X(02)02543-8. http://www.numdam.org/articles/10.1016/S1631-073X(02)02543-8/

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