Exact theory for a linearly elastic interior beam

Thumbnail Image

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)

Authors

Date

2016-01-01

Department

Department of Energy and Mechanical Engineering

Major/Subject

Mcode

Degree programme

Language

en

Pages

6

Series

International Journal of Solids and Structures, Volume 78-79, pp. 125-130

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, exact 1D 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.

Description

Keywords

Plane beam, Elasticity solution, Airy stress function, Kinematic variables, Clapeyron's theorem, Finite element, FINITE-ELEMENT, PLATES

Other note

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

Collections

[article-cris] Insinööritieteiden korkeakoulu / ENG