E. Nolde
An asymptotic higher-order theory for rectangular beams
Nolde, E.; Pichugin, A.V.; Kaplunov, J.
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 |
Files
NoldePichuginKaplunov_RS2018.pdf
(464 Kb)
PDF
Publisher Licence URL
https://creativecommons.org/licenses/by/4.0/
You might also like
Asymptotic corrections to the low-frequency theory for a cylindrical elastic shell
(2023)
Journal Article
Some aspects of wave propagation in a fluid-loaded membrane
(2022)
Book Chapter
Dispersion of the Bending Wave in a Fluid-loaded Elastic Layer
(2022)
Book Chapter
The effect of contact conditions on the performance of flexural seismic metasurfaces
(2022)
Journal Article
Downloadable Citations
About Keele Repository
Administrator e-mail: research.openaccess@keele.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search