Bending-torsion moments in thin multi-structures in the context of nonlinear elasticity

TL;DR

This paper investigates the asymptotic behavior of thin multi-structures under nonlinear elasticity, deriving limit models and junction conditions as the structure's dimensions shrink, focusing on bending-torsion moments induced by external forces.

Contribution

It introduces a rigorous dimension-reduction analysis for multi-structures with two small parameters, characterizing limit models and junction conditions in the membrane-string regime.

Findings

Derived limit models for thin multi-structures under nonlinear elasticity.

Characterized junction conditions in the membrane-string regime.

Analyzed the effects of two small parameters on the structure's behavior.

Abstract

Here, we address a dimension-reduction problem in the context of nonlinear elasticity where the applied external surface forces induce bending-torsion moments. The underlying body is a multi-structure in $\mathbb{R}^3$ consisting of a thin tube-shaped domain placed upon a thin plate-shaped domain. The problem involves two small parameters, the radius of the cross-section of the tube-shaped domain and the thickness of the plate-shaped domain. We characterize the different limit models, including the limit junction condition, in the membrane-string regime according to the ratio between these two parameters as they converge to zero.