On the Buckling of Euler Graphene Beams Subject to Axial Compressive Load

Mohamed B. M. Elgindi, Dongming Wei, Yeran Soukiassian, Yu Liu

Department of Electrical Engineering, University of New Orleans, Louisiana, USA.
Department of Mathematics, Texas A & M University-Qatar, Doha, Qatar.
Department of Mathematics, University of New Orleans, Louisiana, USA.

DOI: 10.4236/wjet.2014.22016                

Abstract

In this paper, we consider the buckling of an Euler-Bernoulli graphene beam due to an axial compressive load. We formulate the problem as a non-linear (eigenvalue) two-point boundary value problem, prove some properties of the eigenpairs and introduce a suitable numerical shooting method scheme for approximating them. We present the perturbation and the numerical approximations of the first and second buckling loads and the corresponding shapes.

Keywords

Critical Buckling Load, Graphene, Euler-Bernoulli Beam, Non-Linear Eigenvalue Problem, Shooting Method

Conflicts of Interest

The authors declare no conflicts of interest.

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