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...
Principais autores: | , , |
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Formato: | Journal article |
Idioma: | English |
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2012
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_version_ | 1826276326641762304 |
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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. |
first_indexed | 2024-03-06T23:12:16Z |
format | Journal article |
id | oxford-uuid:65e5ac90-bc92-41a9-b67a-d5d815e057b0 |
institution | University of Oxford |
language | English |
last_indexed | 2024-03-06T23:12:16Z |
publishDate | 2012 |
record_format | dspace |
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 |
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