In this article, the element free Galerkin (EFG) method and Carrera’s Unified Formulation (CUF) are employed as the CUF–EFG method for the buckling analysis of multilayer GPLs–CNTs-reinforced functionally graded (FG) plates with cutout. The radial basis shape functions which possess the Kronecker delta function property are used as the shape functions. In CUF, a Taylor expansion with first to 4th order is employed as the thickness function. In the proposed method, the stretching effect (effect of thickness extension ‘ezz 6¼ 0’) is taken into account. The plate is under axial, biaxial, shear and combined loadings and composed of a number of layers stacked up in the thickness direction. The carbon nanotubes (CNTs) and graphene platelets (GPLs) uniformly distributed in each individual layer but their weight fractions gradually vary in each layer to achieve functionally graded properties. Four types of distribution patterns with the same average GPLs and CNTs weight fraction are considered in the problem. The mechanical properties of plates with various grading patterns of GPLs and CNTs distributions are estimated using the modified Halpin- Tsai method and the rule of mixture. A comparison between the obtained results with both analytical solution and other shear deformation theories given in the published literatures is performed to show the accuracy and efficiency of the proposed CUF–EFG method. A parametric study is carried out to evaluate the influences of the boundary conditions, aspect ratio, CNT and GPLs weight fraction, number of layers, stacking sequences of layers, dimension and location of circular cutout on the buckling capacity of plates.

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