Junction of elastic plates and beams

Gaudiello, Antonio; Monneau, Régis; Mossino, Jacqueline; Murat, François; Sili, Ali

ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 3, pp. 419-457

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 $\epsilon$, and of a vertical beam with fixed height and small cross section of radius $r^{\epsilon }$. The lateral boundary of the plate and the top of the beam are assumed to be clamped. When $ϵ$ and $r^{\epsilon }$ tend to zero simultaneously, with $r^{\epsilon }\gg {ϵ}^2$, we identify the limit problem. This limit problem involves six junction conditions.

Classification : 35B40, 74B05, 74K30
Keywords: junctions, thin structures, plates, beams, linear elasticity, asymptotic analysis

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