A new approach for bending analysis of bilayer conical graphene panels considering nonlinear van der Waals force

In the present study, the effects of nonlinear van der Waals forces on the bending analysis of orthotropic bilayer conical graphene panels are investigated. In order to model the nano-sized panels, the first-order shear deformation shell theory is used to obtain the governing equations by applying energy method in nonlocal form. Semi-analytical polynomial method (SAPM) is utilized to solve the resulting nonlinear governing equations. Due to cover a wide range of geometric shapes, the geometry is considered as a conical panel, so the results can be simulated for cylindrical panels, annular sectors, and even rectangular plates. The van der Waals force between upper and lower layers of graphene panel is simulated by an extension spring with the linear and nonlinear stiffness. It is easy to obtain the results of single-layer panels by eliminating the van der Waals force, and also for macroscopic plates, with neglecting the nonlocal effects. Finally, the affecting parameters on the results are examined in detail such as the plate size, orthotropic effects of material, nonlocal effects, van der Waals force including its nonlinear term and various types of boundary conditions, even the free edges.