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

Rita Ferreira; Elvira Zappale

doi:10.3934/cpaa.2020072

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

Rita Ferreira, Elvira Zappale

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 R3 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.

Original language	English (US)
Pages (from-to)	1747-1793
Number of pages	47
Journal	Communications on Pure and Applied Analysis
Volume	19
Issue number	3
DOIs	https://doi.org/10.3934/cpaa.2020072
State	Published - Dec 12 2019

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The authors thank Professors F. Murat for having suggested to target the model proposed in Section 6.2 and R. Alicandro and M.G. Mora for insights on the double-well case. E. Zappale is a member of GNAMPA- INdAM whose support is gratefully acknowledged.

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10.3934/cpaa.2020072

https://repository.kaust.edu.sa/bitstream/10754/660543/1/1712.02598.pdf

Cite this

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AU - Zappale, Elvira

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N2 - 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 R3 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.

AB - 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 R3 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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Bending-torsion moments in thin multi-structures in the context of nonlinear elasticity

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