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dc.contributor.authorNolde, E-
dc.contributor.authorPichugin, AV-
dc.contributor.authorKaplunov, J-
dc.identifier.citationNolde, E., Pichugin, A.V. and Kaplunov, J. (2018) 'An asymptotic higher-order theory for rectangular beams', Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474(2214), 20180001, pp. 1-20. doi: 10.1098/rspa.2018.0001.en_US
dc.description.abstractA direct asymptotic integration of the full threedimensional 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 classic 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 discusseden_US
dc.format.extent1 - 20-
dc.publisherThe Royal Societyen_US
dc.rights© 2018 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License, which permits unrestricted use, provided the original author and source are credited.-
dc.subjectlong wavesen_US
dc.subjectlow frequencyen_US
dc.subjectbeam theoryen_US
dc.subjectTimoshenko beam theoryen_US
dc.subjectshear correction factoren_US
dc.titleAn asymptotic higher-order theory for rectangular beamsen_US
dc.typeConference Paperen_US
dc.relation.isPartOfProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences-
Appears in Collections:Dept of Mathematics Research Papers

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