Buckling analysis of biaxially compressed double-layered graphene sheets with various boundary conditions based on nonlocal elasticity theory

Abstract

This paper investigates the buckling behavior of biaxially compressed orthotropic double-layered graphene sheet (DLGS) embedded in an elastic medium based on nonlocal elasticity theory. The DLGS is modeled as a nonlocal double-layered plate which contains small scale effect and van der Waals interaction forces. The van der Waals interactions between the graphene layers are simulated as a set of linear springs using the Lennard-Jones potential model. Using the principle of virtual work, equilibrium equations are derived based on first order shear deformation theory and the nonlocal differential constitutive relations of Eringen. Differential quadrature method is employed to solve the governing equations for various combinations of free, simply supported or clamped boundary conditions. The present formulation and method of solution are validated by comparing the results, in the limit cases, with those available in the open literature. Finally, the effects of nonlocal parameter, geometric properties, elastic medium, compression ratio, mode numbers and boundary conditions are investigated on the buckling load of DLGS in detail. It is observed that in DLGSs with width of 20 nm and lengthes larger than 30 nm, the buckling load is independent of aspect ratios and boundary conditions.