1308.0732 (Mohamed B Elgindi et al.)

On the Solvability of an Euler Graphene Beam Subject to Axial
Compressive Load    [PDF]

Mohamed B Elgindi, Dongming Wei, Tarek M Elgindi

In this paper we formulate the equilibrium equation of a beam made of graphene material subjected to some boundary conditions and acted upon by axial compression and nonlinear lateral constrains as a fourth-order nonlinear boundary value problem. We also formulate the nonlinear eigenvalue for buckling analysis of the beam. We verify the solvability of the buckling problem as an asymptotic expansion in a ratio of the elastoplastic parameters, that the spectrum is bounded away from zero and contains a discrete infinite sequence of eigenvalues.We also verify, for certain ranges of the lateral forces, the solvability of the general equations using energy methods and a suitable iteration scheme.

View original: http://arxiv.org/abs/1308.0732