Buckling analysis of a defective annular graphene sheet in elastic medium

In this article, an analytical approach is presented to analyze static stability of defective annular graphene sheet. Due to production process and constrains conditions, graphene sheet may be opposed to structural defect. Some of the defects can be modeled as an eccentric hole. The graphene sheet is elastically restrained at the bottom surface. Nonlocal thin plate theory as well as the translational addition theorem are employed to solve the problem. The stability and accuracy of results are examined by the literature and the finite element analyses. Effects of eccentricity of defects, nonlocality, Winkler and Pasternak foundation parameters and various boundary conditions on the critical buckling load of an annular graphene sheet are investigated. It is observed that the eccentricity and size of defects have significant effect on the critical load.