On the solvability of euler graphene beam subject to axial compressive load
Loading...
Date
2014
Authors
Elgindi, Mohamed B. M.
Wei, Dongming
Elgindi, T.M.
Journal Title
Journal ISSN
Volume Title
Publisher
arXiv.org
Abstract
In 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.
Description
Keywords
Materials Science, Analysis of PDEs
Citation
Mohamed 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/123456789/1932