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

Research paper by Rita Ferreira, Elvira Zappale

Indexed on: 07 Dec '17Published on: 07 Dec '17Published in: arXiv - Mathematics - Analysis of PDEs



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.