On the solvability of euler graphene beam subject to axial compressive load

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dc.contributor.authorElgindi, Mohamed B. M.
dc.contributor.authorWei, Dongming
dc.contributor.authorElgindi, T.M.
dc.date.accessioned2016-11-23T09:49:51Z
dc.date.available2016-11-23T09:49:51Z
dc.date.issued2014
dc.description.abstractIn this paper we formulate the equilibrium equation for a beam made of graphene sub- jected to some boundary conditions and acted upon by axial compression and nonlinear lateral constrains as a fourth-order nonlinear boundary value problem. We first study the nonlinear eigenvalue problem for buckling analysis of the beam. We show the solvability of the eigen- value problem as an asymptotic expansion in a ratio of the elastoplastic parameters. We verify that the spectrum is a closed set bounded away from zero and contains a discrete in- finite sequence of eigenvalues. In particular, we prove the existence of a minimal eigenvalue for the graphene beam corresponding to a Lipschitz continuous eigenfunction, providing a lower bound for the critical buckling load of the graphene beam column. We also proved that the eigenfunction corresponding to the minimal eigenvalue is positive and symmetric. For a certain range of lateral forces, we demonstrate the solvability of the general equation by using energy methods and a suitable iteration scheme.ru_RU
dc.identifier.citationMohamed B. Elgindi, Dongming Wei and Tarek M. Elgindi; 2014; On the solvability of euler graphene beam subject to axial compressive load; arXiv.org; http://nur.nu.edu.kz/handle/123456789/1932ru_RU
dc.identifier.urihttp://nur.nu.edu.kz/handle/123456789/1932
dc.language.isoenru_RU
dc.publisherarXiv.orgru_RU
dc.rightsAttribution-NonCommercial-ShareAlike 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/us/*
dc.subjectMaterials Scienceru_RU
dc.subjectAnalysis of PDEsru_RU
dc.titleOn the solvability of euler graphene beam subject to axial compressive loadru_RU
dc.typeArticleru_RU

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