# Exact theory for a linearly elastic interior beam

No Thumbnail Available
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
This publication is imported from Aalto University research portal.
View publication in the Research portal
View/Open full text file from the Research portal
2016-01-01
en
6
125-130
##### Series
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, Volume 78-79
##### Abstract
In this paper, an elasticity solution for a two-dimensional (2D) plane beam is derived and it is shown that the solution provides a complete framework for exact one-dimensional (1D) presentations of plane beams. First, an interior solution representing a general state of any 2D linearly elastic isotropic plane beam under a uniform distributed load is obtained by employing a stress function approach. The solution excludes the end effects of the beam and is valid sufficiently far away from the beam boundaries. Then, three kinematic variables defined at the central axis of the plane beam are formed from the 2D displacement field. Using these central axis variables, the 2D interior elasticity solution is presented in a novel manner in the form of a 1D beam theory. By applying the Clapeyron's theorem, it is shown that the stresses acting as surface tractions on the lateral end surfaces of the interior beam need to be taken into account in all energy-based considerations related to the interior beam. Finally, exact1D rod and beam finite elements are developed by the aid of the axis variables from the 2D solution. (C) 2015 Elsevier Ltd. All rights reserved.
##### Keywords
Plane beam, Elasticity solution, Airy stress function, Kinematic variables, Clapeyron's theorem, Finite element, FINITE-ELEMENT, PLATES
##### DOI
10.1016/j.ijsolstr.2015.09.010
##### Citation
Karttunen , A T & von Hertzen , R 2016 , ' Exact theory for a linearly elastic interior beam ' , International Journal of Solids and Structures , vol. 78-79 , pp. 125-130 . https://doi.org/10.1016/j.ijsolstr.2015.09.010
##### Permanent link to this item
https://urn.fi/URN:NBN:fi:aalto-201701191260