The elastic theory of shells using geometric algebra
Published version
Peer-reviewed
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Repository DOI
Type
Article
Change log
Authors
Gregory, Alastair https://orcid.org/0000-0003-0667-5861
Lasenby, Joan https://orcid.org/0000-0002-0571-0218
Agarwal, Anurag https://orcid.org/0000-0002-0332-2166
Abstract
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.
Description
Keywords
shells, elasticity, geometric algebra
Journal Title
Royal Society Open Science
Conference Name
Journal ISSN
2054-5703
2054-5703
2054-5703
Volume Title
4
Publisher
Royal Society
Publisher DOI
Sponsorship
EPSRC (1463167)
The authors would like to acknowledge funding from the EPSRC, the IMechE Postgraduate Research Scholarship, and Engineering for Clinical Practice (http://divf.eng.cam.ac.uk/ecp/Main/EcpResearch).