A novel nonlocal refined plate theory for stability response of orthotropic single-layer graphene sheet resting on elastic medium

This work presents the buckling investigation of embedded orthotropic nanoplates such as graphene by employing a new refined plate theory and nonlocal small-scale effects. The elastic foundation is modeled as two parameter Pasternak foundation. The proposed two-variable refined plate theory takes account of transverse shear influences and parabolic variation of the transverse shear strains within the thickness of the plate by introducing undetermined integral terms, hence it is unnecessary to use shear correction factors. Nonlocal governing equations for the single layered graphene sheet are obtained from the principle of virtual displacements. The proposed theory is compared with other plate theories. Analytical solutions for buckling loads are obtained for single-layered graphene sheets with isotropic and orthotropic properties. The results presented in this study may provide useful guidance for design of orthotropic graphene based nanodevices that make use of the buckling properties of orthotropic nanoplates.