Nonlocal Bending Analysis of Bilayer Annular/Circular Nano Plates Based on First Order Shear Deformation Theory

In this paper, nonlinear bending analysis of bilayer orthotropic annular/circular graphene sheets is studied based on the nonlocal elasticity theory. The equilibrium equations are derived in terms of generalized displacements and rotations considering the first-order Shear deformation theory (FSDT). The nonlinear governing equations are solved using the differential quadrature method (DQM) which is a highly accurate numerical method and a new semi-analytical polynomial method (SAPM). The ordinary differential equations (ODE’s) are converted to the nonlinear algebraic equations applying DQM or SAPM. Then, the Newton–Raphson iterative scheme is applied. The obtained results of DQM and SAPM are compared. It is concluded that although, the SAPM’s formulation is considerably simple in comparison with DQM, however, the results of two methods are so close to each other. The results are validated with available researches. The effects of small scale parameter, the value of van der Waals interaction between the layers, different values of elastic foundation and loading, the comparison between the local and nonlocal deflections and linear to nonlinear        analysis are investigated.

کلیدواژه ها:

Bilayer orthotropic annular/circular graphene sheets ، Eringen nonlocal elasticity theory ، Winkler-Pasternak elastic foundation ، Differential quadrature method (DQM) ، Semi analytical polynomial method (SAPM)