Gregory, A and Lasenby, J and Agarwal, A (2017) *The elastic theory of shells using geometric algebra.* Royal Society Open Science, 4. 170065-. ISSN 2054-5703

## 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.

Item Type: | Article |
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Uncontrolled Keywords: | shells elasticity geometric algebra |

Subjects: | UNSPECIFIED |

Divisions: | Div F > Signal Processing and Communications Div A > Fluid Mechanics |

Depositing User: | Unnamed user with email sms67@cam.ac.uk |

Date Deposited: | 17 Jul 2017 19:11 |

Last Modified: | 09 Sep 2021 03:05 |

DOI: | 10.1098/rsos.170065 |