Nonlocal buckling analysis of functionally graded annular nanoplates in an elastic medium with various boundary conditions

In this article, buckling of functionally graded (FG) single-layered annular graphene sheets embedded in a Pasternak elastic medium is investigated using the nonlocal elasticity theory. The material properties of the FG graphene sheets are assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. Using the principle of virtual work, the governing equations are derived based on first-order shear deformation theory and the nonlocal differential constitutive relations of Eringen. Differential quadrature method is also utilized to solve the equilibrium equations for various combinations of free, simply supported and clamped boundary conditions. In order to assure the accuracy of the results, convergence properties of the critical buckling load are examined in detail. To verify the present study, some comparison studies are carried out between the obtained results and the available solutions in the literature. A parametric study is then conducted to investigate the influences of small scale effects, grading index, surrounding elastic medium, boundary conditions, buckling mode and geometrical parameters on the critical buckling load.