Nonlinear bending analysis of orthotropic nanoplates based on nonlocal model of Eringen using DQM

In this paper، nonlinear bending of rectangular nanoplates of Graphene subjected to a transverse uniform load، with incorporation of the nonlocal effect of Eringen based on the first-order shear deformation theory (FSDT) of orthotropic plates and Von Karman nonlinear strains is investigated using differential quadrature method (DQM). In order to validate of the solution accuracy، the simplified results have been compared with results of two developed numerical solution methods and other available results. Comparisons show an excellent agreement between the results. Finally، effects of small scale parameter، aspect ratio، thickness of plate، load value، boundary conditions and efficacy of large deflection، on the maximum deflection and different deflections ratio for nonlocal theory of thin plate and nonlocal FSDT are investigated. Results reveal that among the considered parameters، just aspect of plate is the parameter of difference between two employed nonlocal theories and the small scale parameter has not any effect on the mentioned difference. Also، it is found that the small scale parameter has a noticeable effect on the decrease of deflection of nonlinear solution; so that، unlike the larger values of mechanical load، this parameter has less effect for long length of square plate.