Publication:
Bending of Euler-Bernoulli beams using Eringen's integral formulation: A paradox resolved

dc.affiliation.areaUC3M. Área de Ingeniería Mecánicaes
dc.affiliation.dptoUC3M. Departamento de Ingeniería Mecánicaes
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Tecnologías de Fabricación y Diseño de Componentes Mecánicos y Biomecánicoses
dc.contributor.authorFernández-Sáez, José
dc.contributor.authorZaera, Ramón
dc.contributor.authorLoya Lorenzo, José Antonio
dc.contributor.authorReddy, JN
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.date.accessioned2022-10-05T12:37:19Z
dc.date.available2022-10-05T12:37:19Z
dc.date.issued2016-02-01
dc.description.abstractThe Eringen nonlocal theory of elasticity formulated in differential form has been widely used to address problems in which size effect cannot be disregarded in micro- and nano-structured solids and nano-structures. However, this formulation shows some inconsistencies that are not completely understood. In this paper we formulate the problem of the static bending of Euler-Bernoulli beams using the Eringen integral constitutive equation. It is shown that, in general, the Eringen model in differential form is not equivalent to the Eringen model in integral form, and a general method to solve the problem rigorously in integral form is proposed. Beams with different boundary and load conditions are analyzed and the results are compared with those derived from the differential approach showing that they are different in general. With this integral formulation, the paradox that appears when solving the cantilever beam with the differential form of the Eringen model (increase in stiffness with the nonlocal parameter) is solved, which is one of the main contributions of the present work.es
dc.description.sponsorshipThis work was supported by the Ministerio de Economía y Competitividad de España (grants numbers DPI2011-23191 and DPI2014-57989-P). Prof. J.N. Reddy acknowledges the support of Universidad Carlos III de Madrid with a Cátedra de Excelencia funded by Banco Santander during academic year 2014–2015.en
dc.format.extent10
dc.identifier.bibliographicCitationFernández-Sáez, J., Zaera, R., Loya, J. A., & Reddy, J. N. (2016). Bending of Euler–Bernoulli beams using Eringen’s integral formulation: A paradox resolved. In International Journal of Engineering Science (Vol. 99, pp. 107–116). Elsevier BV.en
dc.identifier.doihttps://doi.org/10.1016/j.ijengsci.2015.10.013
dc.identifier.issn0020-7225
dc.identifier.publicationfirstpage107
dc.identifier.publicationlastpage116
dc.identifier.publicationtitleInternational Journal of Engineering Scienceen
dc.identifier.publicationvolume99
dc.identifier.urihttps://hdl.handle.net/10016/35850
dc.identifier.uxxiAR/0000017699
dc.language.isoengen
dc.publisherElsevier BV.en
dc.relation.projectIDGobierno de España. DPI2011-23191es
dc.relation.projectIDGobierno de España. DPI2014-57989-Pes
dc.rights© 2015 Elsevier Ltd. All rights reserved.en
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España
dc.rights.accessRightsopen accessen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.ecienciaIngeniería Mecánicaes
dc.subject.otherNonlocalen
dc.subject.otherEringen Integral Modelen
dc.subject.otherBendingen
dc.subject.otherNanobeamsen
dc.subject.otherParadoxen
dc.titleBending of Euler-Bernoulli beams using Eringen's integral formulation: A paradox resolveden
dc.typeresearch article*
dc.type.hasVersionVoR*
dspace.entity.typePublication
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