Calculus of Variations and Geometric Measure Theory
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R. Ferreira - E. Zappale

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

created by ferreira on 10 Dec 2017
modified on 25 Oct 2020

[BibTeX]

Published Paper

Inserted: 10 dec 2017
Last Updated: 25 oct 2020

Journal: Comm. Pure Appl. Anal.
Year: 2019
Doi: http://dx.doi.org/10.3934/cpaa.2020072

ArXiv: 1712.02598 PDF

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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