Nonlinear bending analysis of Graphene nanoplate embedded in elastic matrix, via nonlocal continuum models

In this paper، static bending behavior of square orthotropic nanoplate of Graphene، embedded in elastic matrix has been investigated. Based on first-order shear deformation theory of plates and strain-displacement relationships for small deflection theory the equilibruim equatuions are derived. Also، nonlocal continuum theory of Eringen is employed as implementation the small scale effect. Then equilibrium equations are rewrite at displacement parameter and after normalizing، are discretized and solved by differential quadrature and finite difference methods. with comparison study between the results of the mentioned theories، the accuracy and reliability of the present soulotion methodology is verified. Finally، maximum value of deflection has been peresented and influences of the small scale coefficient، width ratio، thickness of plate، load value، elastic matrix properties and mesh point numbers are investigated based on of first-order shear deformation and classical theories. It is concluded that with increase of small scale effects، the values of deflections decrease significantly.