Junction between a plate and a rod of comparable thickness in nonlinear elasticity.

We analyze the asymptotic behavior of a junction problem between a plate and a perpendicular rod made of a nonlinear elastic material. The two parts of this multi-structure have small thicknesses of the same order $\delta$. We use the decomposition techniques obtained for the large deformations and the displacements in order to derive the limit energy as $\delta$ tends to $0$.