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

Rita Ferreira; Elvira Zappale

doi:10.3934/cpaa.2020072

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2020, Volume 19, Issue 3: 1747-1793. Doi: 10.3934/cpaa.2020072

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

Rita Ferreira^1, , and
Elvira Zappale^2,

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
^* Corresponding author

Received: March 31, 2019

Revised: June 30, 2019

Published: February 2020

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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.

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Mathematics Subject Classification: Primary: 49J45, 74B20, 74K30.

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