A rational derivation of a tube law from shell theory

Whittaker, Robert J. ORCID: https://orcid.org/0000-0001-9598-5938, Heil, Matthias, Jensen, Oliver E. and Waters, Sarah L. (2010) A rational derivation of a tube law from shell theory. Quarterly Journal of Mechanics and Applied Mathematics, 63 (4). pp. 465-496. ISSN 0033-5614

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We consider small-amplitude deformations of a long thin-walled elastic tube having an initially axially uniform elliptical cross section. The tube is subject to an axial pre-stress, and the deformations result from an applied transmural pressure. An approximate tube law (linking the transmural pressure with the cross-sectional area and its axial derivatives) is derived from shell theory in the distinguished asymptotic limit in which the tube's behaviour is dominated by the restoring forces from the axial pre-stress and azimuthal bending. This is possible because the deformations of the tube induced by both the transmural pressure and the axial forces can be described, to very good approximation, by a single azimuthal mode of deformation of axially varying amplitude. The resulting tube law is compared with numerical solutions of the full shell equations and good agreement is found (provided the tube is sufficiently long and the wall not too thin so that in-plane shearing is negligible). We discuss the applications of our results to the modelling of flow in collapsible tubes.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Fluid and Solid Mechanics
Depositing User: Robert Whittaker
Date Deposited: 10 Mar 2011 12:47
Last Modified: 15 Dec 2022 01:29
URI: https://ueaeprints.uea.ac.uk/id/eprint/20901
DOI: 10.1093/qjmam/hbq020

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