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An asymptotic higher-order theory for rectangular beams

Nolde, E.; Pichugin, A.V.; Kaplunov, J.

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Authors

E. Nolde

A.V. Pichugin



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.

Journal Article Type Article
Acceptance Date Apr 30, 2018
Online Publication Date Jun 13, 2018
Publication Date 2018-06
Publicly Available Date Mar 28, 2024
Journal Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Print ISSN 1364-5021
Publisher The Royal Society
Peer Reviewed Peer Reviewed
Volume 474
Issue 2214
DOI https://doi.org/10.1098/rspa.2018.0001
Keywords asymptoticslong waveslow frequencybeam theoryTimoshenko beam theoryshear correction factor
Publisher URL https://doi.org/10.1098/rspa.2018.0001

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