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Junction of elastic plates and beams

Published online by Cambridge University Press:  26 July 2007

Antonio Gaudiello ,
Régis Monneau ,
Jacqueline Mossino ,
François Murat  and
Ali Sili
Antonio Gaudiello
Affiliation:
Dipartimento di Automazione, Elettromagnetismo, Ingegneria dell'Informazione e Matematica Industriale, Università di Cassino, via G. Di Biasio 43, 03043 Cassino (FR), Italia; gaudiell@unina.it
Régis Monneau
Affiliation:
CERMICS, École Nationale des Ponts et Chaussées, 6 et 8 Avenue Blaise Pascal, Cité Descartes, 77455 Champs-sur-Marne Cedex 2, France; monneau@cermics.enpc.fr
Jacqueline Mossino
Affiliation:
CMLA, École Normale Supérieure de Cachan, 61 Avenue du Président Wilson, 94235 Cachan Cedex, France; mossino@cmla.ens-cachan.fr
François Murat
Affiliation:
Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Boîte courrier 187, 75252 Paris Cedex 05, France; murat@ann.jussieu.fr
Ali Sili
Affiliation:
Département de Mathématiques, Université de Toulon et du Var, BP 132, 83957 La Garde Cedex, France; sili@univ-tln.fr
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Abstract

We consider the linearized elasticity system in a multidomain of ${\bf R}^3$. 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 $r^{\varepsilon}$. The lateral boundary of the plate and the top of the beam are assumed to be clamped. When ε and $r^{\varepsilon}$ tend to zero simultaneously, with $r^{\varepsilon}\gg \varepsilon^2$, we identify the limit problem. This limit problem involves six junction conditions.

Keywords

Junctionsthin structuresplatesbeamslinear elasticityasymptotic analysis
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 13 , Issue 3 , July 2007 , pp. 419 - 457
Copyright
© EDP Sciences, SMAI, 2007

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