Junction of elastic plates and beams

¹ 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
² 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
³ CMLA, École Normale Supérieure de Cachan, 61 Avenue du Président Wilson, 94235 Cachan Cedex, France; mossino@cmla.ens-cachan.fr
⁴ Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Boîte courrier 187, 75252 Paris Cedex 05, France; murat@ann.jussieu.fr
⁵ Département de Mathématiques, Université de Toulon et du Var, BP 132, 83957 La Garde Cedex, France; sili@univ-tln.fr

Received: 14 July 2005

Abstract

We consider the linearized elasticity system in a multidomain of . 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 . The lateral boundary of the plate and the top of the beam are assumed to be clamped. When ε and tend to zero simultaneously, with , we identify the limit problem. This limit problem involves six junction conditions.