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The elastic theory of shells using geometric algebra

We present a novel derivation of the elastic theory of shells. We use the language of geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools to express equations in an arbitrary coordinate system, whi...

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Detalles Bibliográficos
Autores principales: Gregory, A. L., Lasenby, J., Agarwal, A.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society Publishing 2017
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5383861/
https://www.ncbi.nlm.nih.gov/pubmed/28405404
http://dx.doi.org/10.1098/rsos.170065
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author Gregory, A. L.
Lasenby, J.
Agarwal, A.
author_facet Gregory, A. L.
Lasenby, J.
Agarwal, A.
author_sort Gregory, A. L.
collection PubMed
description We present a novel derivation of the elastic theory of shells. We use the language of geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools to express equations in an arbitrary coordinate system, which enhances their usefulness. The role of moments and angular velocity, and the apparent use by previous authors of an unphysical angular velocity, has been clarified through the use of a bivector representation. In the linearized theory, clarification of previous coordinate conventions which have been the cause of confusion is provided, and the introduction of prior strain into the linearized theory of shells is made possible.
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spelling pubmed-53838612017-04-12 The elastic theory of shells using geometric algebra Gregory, A. L. Lasenby, J. Agarwal, A. R Soc Open Sci Mathematics We present a novel derivation of the elastic theory of shells. We use the language of geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools to express equations in an arbitrary coordinate system, which enhances their usefulness. The role of moments and angular velocity, and the apparent use by previous authors of an unphysical angular velocity, has been clarified through the use of a bivector representation. In the linearized theory, clarification of previous coordinate conventions which have been the cause of confusion is provided, and the introduction of prior strain into the linearized theory of shells is made possible. The Royal Society Publishing 2017-03-08 /pmc/articles/PMC5383861/ /pubmed/28405404 http://dx.doi.org/10.1098/rsos.170065 Text en © 2017 The Authors. http://creativecommons.org/licenses/by/4.0/ Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
spellingShingle Mathematics
Gregory, A. L.
Lasenby, J.
Agarwal, A.
The elastic theory of shells using geometric algebra
title The elastic theory of shells using geometric algebra
title_full The elastic theory of shells using geometric algebra
title_fullStr The elastic theory of shells using geometric algebra
title_full_unstemmed The elastic theory of shells using geometric algebra
title_short The elastic theory of shells using geometric algebra
title_sort elastic theory of shells using geometric algebra
topic Mathematics
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5383861/
https://www.ncbi.nlm.nih.gov/pubmed/28405404
http://dx.doi.org/10.1098/rsos.170065
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