Nonlinear bending analysis of orthotropic nanoscale plates in an elastic matrix based on nonlocal continuum mechanics

In this paper, nonlinear bending behavior of the orthotropic single layered graphene sheet (SLGS) subjected to a transverse uniform load and resting on an elastic matrix as Pasternak foundation model is investigated using the nonlocal elasticity theory. The nanoplate equilibrium equations are derived in terms of the generalized displacements based on first-order shear deformation theory (FSDT) using the nonlocal differential constitutive relations of Eringen and the von Karman nonlinear strains. The differential quadrature (DQ) discretized form of the governing equations with the various types of boundary conditions are derived. The Newton-Raphson iterative scheme is employed to solve the resulting system of nonlinear algebraic equations. Numerical results obtained by the present theory are compared with available solutions in the literature and those developed by finite difference method (FDM) and dynamic relaxation method (DRM) in this work. Excellent agreement between the results of different solution method and presented results is observed. Finally, effects of small scale parameter, width ratio, thickness of plate, elastic foundation properties, load value, boundary conditions and nonlinearity are studied for both nonlocal FSDT and classical plate theory (CPT) in detail.