Modeling of the junction between a plate and a rod in nonlinear elasticity

Abstract

The asymptotic expansions method is used to study the limit behaviour of a system made of a plate of small thickness 2ε in which one partly inserted a rod of cross section equal to 4ε². When the free extremity of the rod is clamped and when the materials are nonlinearly elastic, it turns out that the transverse displacement of the rod around the junction is “almost” rigid. Moreover, the plate, which is somehow held by the rod, has a torsion equal to zero around the junction, which makes impossible any free rotation around the axis of the rod.