The Clamped-Free Rod Under Inclined End Forces and Transitions Between Equilibrium Confi gurations

Journal article


Singh, P. and Goss, V.G.A. (2019). The Clamped-Free Rod Under Inclined End Forces and Transitions Between Equilibrium Confi gurations. Journal of Engineering Mathematics. 117 (1), pp. 65-78.
AuthorsSingh, P. and Goss, V.G.A.
Abstract

We investigate the problem of the straight, inextensible and unshearable clamped-free elastic rod subjected to an inclined end force. Exact analytic solutions representing all equi-
librium con figurations of the deformed rod are presented in elliptic integral form. Those exact solutions, for a given angle of inclination of the end force and number of inflection points, are characterised by two quantities; the end force and the elliptic modulus. Critical points are discussed and analytic conditions for determining their location are presented. Certain critical points where transitions between two equilibrium confi gurations whose numbers of inflection points differs by one are pointed out. Simple formulae for the total number of equilibrium confi gurations for a given end force are given. Applying arguments based on the elastic strain energy of the rod, we discuss scenarios where highly inflectional equilibrium con figurations can transition to equilibrium con figurations with fewer inflection points.

Keywordsclamped-free, elastica, elliptic integrals, equilibrium con figurations, inclined end forces, transitions.
Year2019
JournalJournal of Engineering Mathematics
Journal citation117 (1), pp. 65-78
PublisherSpringer
ISSN0022-0833
Digital Object Identifier (DOI)doi:10.1007/s10665-019-10009-7
Publication dates
Online16 Aug 2019
Publication process dates
Accepted26 Jul 2019
Deposited28 Aug 2019
Accepted author manuscript
License
CC BY 4.0
File Access Level
Open
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https://openresearch.lsbu.ac.uk/item/87x16

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