On the junction of elastic plates and beams

Abstract

We consider the linearized elasticity system in a multidomain of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi mathvariant="normal">R</mml:mi> <mml:mn>3</mml:mn> </mml:msup> </mml:math> . 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 ε . The lateral boundary of the plate and the top of the beam are assumed to be clamped. When ε and r ε tend to zero simultaneously, with r ε ⪢ ε 2 , we identify the limit problem. This limit problem involves six junction conditions.