Exact theory for a linearly elastic interior beam

dc.contributorAalto-yliopistofi
dc.contributorAalto Universityen
dc.contributor.authorKarttunen, Anssi T.
dc.contributor.authorvon Hertzen, Raimo
dc.contributor.departmentDepartment of Mechanical Engineering
dc.date.accessioned2017-01-19T11:12:22Z
dc.date.embargoinfo:eu-repo/date/embargoEnd/2018-02-01
dc.date.issued2016-01-01
dc.description.abstractIn 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.en
dc.description.versionPeer revieweden
dc.format.extent6
dc.format.extent125-130
dc.format.mimetypeapplication/pdf
dc.identifier.citationKarttunen , 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.2015.09.010en
dc.identifier.doi10.1016/j.ijsolstr.2015.09.010
dc.identifier.issn0020-7683
dc.identifier.otherPURE UUID: b8d48dfe-37e9-4f8b-90e2-5572764c6558
dc.identifier.otherPURE ITEMURL: https://research.aalto.fi/en/publications/b8d48dfe-37e9-4f8b-90e2-5572764c6558
dc.identifier.otherPURE FILEURL: https://research.aalto.fi/files/7205528/7_IJSS.pdf
dc.identifier.urihttps://aaltodoc.aalto.fi/handle/123456789/24315
dc.identifier.urnURN:NBN:fi:aalto-201701191260
dc.language.isoenen
dc.relation.ispartofseriesINTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURESen
dc.relation.ispartofseriesVolume 78-79en
dc.rightsopenAccessen
dc.subject.keywordPlane beam
dc.subject.keywordElasticity solution
dc.subject.keywordAiry stress function
dc.subject.keywordKinematic variables
dc.subject.keywordClapeyron's theorem
dc.subject.keywordFinite element
dc.subject.keywordFINITE-ELEMENT
dc.subject.keywordPLATES
dc.titleExact theory for a linearly elastic interior beamen
dc.typeA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessäfi
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