aalto1 untyped-item.component.html
Variational formulation of the static Levinson beam theory
Loading...
Files
Access rights
openAccess
acceptedVersion
URL
Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
This publication is imported from Aalto University research portal.
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Other link related to publication (opens in new window)
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Other link related to publication (opens in new window)
Unless otherwise stated, all rights belong to the author. You may download, display and print this publication for Your own personal use. Commercial use is prohibited.
Date
Major/Subject
Mcode
Degree programme
Language
en
Pages
5
Series
Mechanics Research Communications, Volume 66, pp. 15-19
Abstract
In this communication, we provide a consistent variational formulation for the static Levinson beam theory. First, the beam equations according to the vectorial formulation by Levinson are reviewed briefly. By applying the Clapeyron's theorem, it is found that the stresses on the lateral end surfaces of the beam are an integral part of the theory. The variational formulation is carried out by employing the principle of virtual displacements. As a novel contribution, the formulation includes the external virtual work done by the stresses on the end surfaces of the beam. This external virtual work contributes to the boundary conditions in such a way that artificial end effects do not appear in the theory. The obtained beam equations are the same as the vectorially derived Levinson equations. Finally, the exact Levinson beam finite element is developed. (C) 2015 Elsevier Ltd. All rights reserved.
Description
Other note
Citation
Karttunen, A T & von Hertzen, R 2015, 'Variational formulation of the static Levinson beam theory', Mechanics Research Communications, vol. 66, pp. 15-19. https://doi.org/10.1016/j.mechrescom.2015.03.006