Variational formulation of the static Levinson beam theory

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en
dc.contributor.author Karttunen, Anssi T.
dc.contributor.author von Hertzen, Raimo
dc.date.accessioned 2017-01-19T11:07:37Z
dc.date.issued 2015-06
dc.identifier.citation Karttunen , A T & von Hertzen , R 2015 , ' Variational formulation of the static Levinson beam theory ' MECHANICS RESEARCH COMMUNICATIONS , vol 66 , pp. 15-19 . DOI: 10.1016/j.mechrescom.2015.03.006 en
dc.identifier.issn 0093-6413
dc.identifier.issn 1873-3972
dc.identifier.other PURE UUID: 8c973895-ed3c-4e68-91dd-7e1bb18d7c1b
dc.identifier.other PURE ITEMURL: https://research.aalto.fi/en/publications/variational-formulation-of-the-static-levinson-beam-theory(8c973895-ed3c-4e68-91dd-7e1bb18d7c1b).html
dc.identifier.other PURE LINK: http://dx.doi.org/10.1016/j.mechrescom.2015.03.006
dc.identifier.other PURE FILEURL: https://research.aalto.fi/files/7205521/6_MRC.pdf
dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/24270
dc.description.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. en
dc.format.extent 5
dc.format.extent 15-19
dc.format.mimetype application/pdf
dc.language.iso en en
dc.relation.ispartofseries MECHANICS RESEARCH COMMUNICATIONS en
dc.relation.ispartofseries Volume 66 en
dc.rights openAccess en
dc.subject.other 214 Mechanical engineering en
dc.title Variational formulation of the static Levinson beam theory en
dc.type A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä fi
dc.description.version Peer reviewed en
dc.contributor.department Department of Mechanical Engineering
dc.subject.keyword Levinson beam
dc.subject.keyword Interior beam
dc.subject.keyword Variational formulation
dc.subject.keyword Finite element
dc.subject.keyword PLATES
dc.subject.keyword STABILITY
dc.subject.keyword 214 Mechanical engineering
dc.identifier.urn URN:NBN:fi:aalto-201701191215
dc.identifier.doi 10.1016/j.mechrescom.2015.03.006
dc.date.embargo info:eu-repo/date/embargoEnd/2017-07-01


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