Exact theory for a linearly elastic interior beam

dc.contributorAalto-yliopistofi
dc.contributorAalto Universityen
dc.contributor.authorKarttunen, Anssi T.en_US
dc.contributor.authorvon Hertzen, Raimoen_US
dc.contributor.departmentDepartment of Energy and Mechanical Engineeringen
dc.contributor.groupauthorMarine Technologyen
dc.contributor.groupauthorSolid Mechanicsen
dc.date.accessioned2017-01-19T11:12:22Z
dc.date.embargoinfo:eu-repo/date/embargoEnd/2018-02-01en_US
dc.date.issued2016-01-01en_US
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, 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.en
dc.description.versionPeer revieweden
dc.format.extent6
dc.format.extent125-130
dc.format.mimetypeapplication/pdfen_US
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.2015.09.010en_US
dc.identifier.issn0020-7683
dc.identifier.otherPURE UUID: b8d48dfe-37e9-4f8b-90e2-5572764c6558en_US
dc.identifier.otherPURE ITEMURL: https://research.aalto.fi/en/publications/b8d48dfe-37e9-4f8b-90e2-5572764c6558en_US
dc.identifier.otherPURE FILEURL: https://research.aalto.fi/files/7205528/7_IJSS.pdfen_US
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 beamen_US
dc.subject.keywordElasticity solutionen_US
dc.subject.keywordAiry stress functionen_US
dc.subject.keywordKinematic variablesen_US
dc.subject.keywordClapeyron's theoremen_US
dc.subject.keywordFinite elementen_US
dc.subject.keywordFINITE-ELEMENTen_US
dc.subject.keywordPLATESen_US
dc.titleExact theory for a linearly elastic interior beamen
dc.typeA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessäfi

Files