# American Institute of Mathematical Sciences

March  2020, 19(3): 1747-1793. doi: 10.3934/cpaa.2020072

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

 1 King Abdullah University of Science and Technology, 4700 KAUST, CEMSE Division, Thuwal 23955-6900, Saudi Arabia 2 Università degli Studi di Salerno, Dipartimento di Ingegneria Industriale, Via Giovanni Paolo II, 132 Fisciano (SA), Italy

* Corresponding author

Received  April 2019 Revised  July 2019 Published  November 2019

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.

Citation: Rita Ferreira, Elvira Zappale. Bending-torsion moments in thin multi-structures in the context of nonlinear elasticity. Communications on Pure & Applied Analysis, 2020, 19 (3) : 1747-1793. doi: 10.3934/cpaa.2020072
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##### References:
ε - reference configuration
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