In this paper, the buckling behavior of arbitrary straight-sided quadrilateral nanoscale plates is studied based on a surface elastic model. The nanoplate is considered to be made from functionally graded materials (FGMs) whose properties are estimated using power-law functions. The plate model is developed within the frameworks of the Gurtin–Murdoch's (GM) surface and the Mindlin's plate theories so, it accounts for both the surface stress and the shear deformation effects. A mapping-differential quadrature methodology is used in the context of variational formulation to obtain discretized governing equations of a weak form. The solution algorithm makes it possible to bypass the transformation and discretization of the high order derivatives involved in the strong form of the governing equations. The reliability of the developed model is first verified by comparing the present results with those previously reported in the literature. Afterward, the surface effects on the buckling response of the functionally graded (FG) quadrilateral nanoplates with respect to different geometric parameters are investigated. It is found that skew nanoplates are of higher buckling strength and less sensitive to the surface stress effect than rectangular ones.
