Buckling analysis of graphene nanosheets by the finite element method

Abstract

The paper is devoted to the problems related to buckling analysis of graphene sheets without and with vacancies in the structure under different boundary conditions. The analysis was performed by the classical numerical treatment – the finite element method (FEM). The graphene sheets were modelled by beam elements. Interatomic relations between carbon atoms in the structure were represented by the beams connecting individual atoms. The behaviour of the beam as structural element was based on the properties that were established from relations of molecular mechanics. The vacancies in single layer graphene sheets (SLGSs) were created by elimination of randomly chosen atoms and corresponding beam elements connected to the atoms in question. The computations were accomplished for different percentage of atom vacancies and the results represent an obvious fact that the critical buckling force decreases for increased percentage of vacancies in the structure. The numerical results are represented in form of graphs.