Abstract
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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: The Quarterly Journal of Mechanics and Applied Mathematics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
