Stability estimates for a twisted rod under terminal loads: A three-dimensional study

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-se...

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Principais autores: Majumdar, A, Prior, C, Goriely, A
Formato: Journal article
Idioma:English
Publicado em: 2012
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author Majumdar, A
Prior, C
Goriely, A
author_facet Majumdar, A
Prior, C
Goriely, A
author_sort Majumdar, A
collection OXFORD
description 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.
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spelling oxford-uuid:65e5ac90-bc92-41a9-b67a-d5d815e057b02022-03-26T18:28:29ZStability estimates for a twisted rod under terminal loads: A three-dimensional studyJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:65e5ac90-bc92-41a9-b67a-d5d815e057b0EnglishSymplectic Elements at Oxford2012Majumdar, APrior, CGoriely, AThe 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.
spellingShingle Majumdar, A
Prior, C
Goriely, A
Stability estimates for a twisted rod under terminal loads: A three-dimensional study
title Stability estimates for a twisted rod under terminal loads: A three-dimensional study
title_full Stability estimates for a twisted rod under terminal loads: A three-dimensional study
title_fullStr Stability estimates for a twisted rod under terminal loads: A three-dimensional study
title_full_unstemmed Stability estimates for a twisted rod under terminal loads: A three-dimensional study
title_short Stability estimates for a twisted rod under terminal loads: A three-dimensional study
title_sort stability estimates for a twisted rod under terminal loads a three dimensional study
work_keys_str_mv AT majumdara stabilityestimatesforatwistedrodunderterminalloadsathreedimensionalstudy
AT priorc stabilityestimatesforatwistedrodunderterminalloadsathreedimensionalstudy
AT gorielya stabilityestimatesforatwistedrodunderterminalloadsathreedimensionalstudy