Small scale effect on the buckling analysis of single-layered graphene sheet embedded in an elastic medium based on nonlocal plate theory

Nonlocal elasticity theory is implemented to investigate the buckling behavior of single-layered graphene sheet (SLGS) embedded in an elastic medium. Nonlocal elasticity theory accounts for the small-size effects when dealing with nanostructures such as graphene sheets. Both Winkler-type and Pasternak-type foundation models are employed to simulate the interaction between the graphene sheet and the surrounding elastic medium. Based on principle of virtual work, governing differential equations for the aforementioned problem are derived. Differential quadrature method is being employed and numerical solutions for the buckling loads of SLGS are obtained. Numerical results show that the buckling loads of SLGS are strongly dependent on the small scale coefficients and the stiffness of the surrounding elastic medium. With elastic medium modeled as Winkler-type foundation, the nonlocal effects are found to have decrease–increase–decrease pattern with increase in stiffness of elastic medium.