Investigation of static buckling and bending of nanoplates made of new functionally graded materials considering surface effects on an elastic foundation

Abstract

Most research currently is limited to isotropic or porous materials reinforced by graphene platelets (GPLs). However, functionally graded materials (FGMs) made of two different material constituents offer many advantages in terms of durability, strength, high-temperature resistance, and design flexibility. Therefore, a new FGM model reinforced by GPLs (GPL-reinforced FGM) is proposed to enhance the performance of nanoplate structures. This paper presents analytical solutions for buckling and static bending problems of the GPL-reinforced FGM nanoplates with surface stress effects placed on a Pasternak elastic foundation. Three variation laws of the FGM (i.e., P-FGM, E-FGM, and S-FGM) combined with four GPL patterns (i.e., UD, FG-O, FG-X, and FG-V) are studied. The governing equations of the nanoplate resting on the elastic foundation are derived based on the principle of minimum total potential energy, Reddy’s third-order shear deformation theory (TSDT), nonlocal strain gradient (NSG) theory (NSGT), and Gurtin–Murdoch surface elasticity theory (SET). The Navier technique is then utilized to determine the critical buckling load, deflection, and stress components of the nanoplate. The influence of material parameters, NSG parameters, surface energy parameters, and elastic foundation parameters on the static buckling and bending behaviors of the GPL-reinforced FGM nanoplate is investigated.