An iterative finite difference scheme for buckling of graphene beam subject to axial compressive load

In this paper buckling loads and modes of an Euler beam made of graphene are considered. An eigenvalue problem is formulated with an additional parameter representing material's elastoplasticity. Analytical approximate solution using the perturbation method is presented. This approximate solution is used as a basis for an iterative finite difference scheme to develop a more accurate solution. Deflection at points along the beam are calculated using this iterative finite difference scheme. Convergence with good accuracy is achieved.