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.

Bending-torsion moments in thin multi-structures in the context of nonlinear elasticity / Ferreira, Rita; Zappale, Elvira. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - 19:(2020), pp. 1747-1793. [10.3934/cpaa.2020072]

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

Elvira Zappale
2020

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.
multi-structures; dimension reduction; nonlinear elasticity; bendingtorsionmoments; Γ-convergence; relaxation
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Bending-torsion moments in thin multi-structures in the context of nonlinear elasticity / Ferreira, Rita; Zappale, Elvira. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - 19:(2020), pp. 1747-1793. [10.3934/cpaa.2020072]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1458138
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