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

TL;DR

This paper investigates the asymptotic behavior of a nonlinear elastic junction between a plate and a rod of similar thickness, deriving the limit energy as the thickness approaches zero using advanced decomposition techniques.

Contribution

It introduces a new asymptotic analysis framework for nonlinear elastic junctions between plates and rods of comparable thickness, extending previous linear models.

Findings

Derived the limit energy functional for the junction as thickness tends to zero

Established the asymptotic behavior of large deformations in the structure

Provided a mathematical foundation for nonlinear elasticity in multi-structure junctions

Abstract

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.