Nolde, E, Pichugin, AV and Kaplunov, J (2018) An asymptotic higher-order theory for rectangular beams. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

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Abstract

A direct asymptotic integration of the full three-dimensional problem of elasticity is employed to derive a consistent governing equation for a beam with the rectangular cross section. The governing equation is consistent in the sense that it has the same long-wave low-frequency behaviour as the exact solution of the original three-dimensional problem. Performance of the new beam equation is illustrated by comparing its predictions against the results of direct finite-element computations. Limiting behaviours for beams with large (and small) aspect ratios, which can be established using classical plate theories, are recovered from the new governing equation to illustrate its consistency and also to illustrate the importance of using plate theories with the correctly refined boundary conditions. The implications for the correct choice of the shear correction factor in Timoshenko's beam theory are also discussed.

Item Type: Article
Additional Information: The final published version of this article can be found online at http://rspa.royalsocietypublishing.org/content/474/2214/20180001
Uncontrolled Keywords: asymptoticslong waveslow frequencybeam theoryTimoshenko beam theoryshear correction factor
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Natural Sciences > School of Computing and Maths
Depositing User: Symplectic
Date Deposited: 27 Jun 2018 10:35
Last Modified: 08 Mar 2019 14:38
URI: http://eprints.keele.ac.uk/id/eprint/5063

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