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Title: An asymptotic higher-order theory for rectangular beams
Authors: Nolde, E
Pichugin, AV
Kaplunov, J
Keywords: asymptotics;long waves;low frequency;beam theory;Timoshenko beam theory;shear correction factor
Issue Date: 13-Jun-2018
Publisher: The Royal Society
Citation: Nolde, 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.
Abstract: A 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 discussed
ISSN: 1364-5021
Other Identifiers: 20180001
Appears in Collections:Dept of Mathematics Research Papers

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