Stability Estimates for a Twisted Rod Under Terminal Loads: A Three-dimensional Study

Handle URI:
http://hdl.handle.net/10754/599708
Title:
Stability Estimates for a Twisted Rod Under Terminal Loads: A Three-dimensional Study
Authors:
Majumdar, Apala; Prior, Christopher; Goriely, Alain
Abstract:
The stability of an inextensible unshearable elastic rod with quadratic strain energy density subject to end loads is considered. We study the second variation of the corresponding rod-energy, making a distinction between in-plane and out-of-plane perturbations and isotropic and anisotropic cross-sections, respectively. In all cases, we demonstrate that the naturally straight state is a local energy minimizer in parameter regimes specified by material constants. These stability results are also accompanied by instability results in parameter regimes defined in terms of material constants. © 2012 Springer Science+Business Media B.V.
Citation:
Majumdar A, Prior C, Goriely A (2012) Stability Estimates for a Twisted Rod Under Terminal Loads: A Three-dimensional Study. Journal of Elasticity 109: 75–93. Available: http://dx.doi.org/10.1007/s10659-012-9371-8.
Publisher:
Springer Nature
Journal:
Journal of Elasticity
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
1-Mar-2012
DOI:
10.1007/s10659-012-9371-8
Type:
Article
ISSN:
0374-3535; 1573-2681
Sponsors:
This publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). AG is a Wolfson Royal Society Merit Holder. AM is also supported by an EPSRC Career Acceleration Fellowship EP/J001686/1. We also would like to thank John Maddocks for comments on an earlier version of this manuscript, and bringing to our attention important references.
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Full metadata record

DC FieldValue Language
dc.contributor.authorMajumdar, Apalaen
dc.contributor.authorPrior, Christopheren
dc.contributor.authorGoriely, Alainen
dc.date.accessioned2016-02-28T06:08:01Zen
dc.date.available2016-02-28T06:08:01Zen
dc.date.issued2012-03-01en
dc.identifier.citationMajumdar A, Prior C, Goriely A (2012) Stability Estimates for a Twisted Rod Under Terminal Loads: A Three-dimensional Study. Journal of Elasticity 109: 75–93. Available: http://dx.doi.org/10.1007/s10659-012-9371-8.en
dc.identifier.issn0374-3535en
dc.identifier.issn1573-2681en
dc.identifier.doi10.1007/s10659-012-9371-8en
dc.identifier.urihttp://hdl.handle.net/10754/599708en
dc.description.abstractThe stability of an inextensible unshearable elastic rod with quadratic strain energy density subject to end loads is considered. We study the second variation of the corresponding rod-energy, making a distinction between in-plane and out-of-plane perturbations and isotropic and anisotropic cross-sections, respectively. In all cases, we demonstrate that the naturally straight state is a local energy minimizer in parameter regimes specified by material constants. These stability results are also accompanied by instability results in parameter regimes defined in terms of material constants. © 2012 Springer Science+Business Media B.V.en
dc.description.sponsorshipThis publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). AG is a Wolfson Royal Society Merit Holder. AM is also supported by an EPSRC Career Acceleration Fellowship EP/J001686/1. We also would like to thank John Maddocks for comments on an earlier version of this manuscript, and bringing to our attention important references.en
dc.publisherSpringer Natureen
dc.subjectCosserat rodsen
dc.subjectStability of straight axis solutionen
dc.subjectVariational criterionen
dc.titleStability Estimates for a Twisted Rod Under Terminal Loads: A Three-dimensional Studyen
dc.typeArticleen
dc.identifier.journalJournal of Elasticityen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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