title: The elastic theory of shells using geometric algebra.
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.
authors.affiliation: Cambridge University Engineering Department , Trumpington Street, Cambridge CB2 1PZ, UK.
authors.forename: A L
authors.identifier: 0000-0003-0667-5861
authors.initials: AL
authors.lastname: Gregory
authors.affiliation: Cambridge University Engineering Department , Trumpington Street, Cambridge CB2 1PZ, UK.
authors.forename: J
authors.initials: J
authors.lastname: Lasenby
authors.affiliation: Cambridge University Engineering Department , Trumpington Street, Cambridge CB2 1PZ, UK.
authors.forename: A
authors.initials: A
authors.lastname: Agarwal
keywords: elasticity; geometric algebra; shells