Effect of nonlocal parameters and Kerr foundation on nonlinear static and dynamic stability of micro/nano plate with graphene platelet reinforcement

Abstract

It is a fact that size effects appear when studying the mechanical behavior of nano/microscopic materials. This paper, for the first time, applies an analytical method to determine the size effect dependence and Kerr foundation on nonlinear static and dynamic stability of micro/nano plate with graphene platelet reinforcement. For this purpose, the nonlocal elasticity theory along with classical plate theory is used to derive the basic equations. Both motion and geometric compatibility equations of the plate are deduced by introducing the Von Kármán strain–displacement relationship. Applying the analytical method (Bubnov–Galerkin and the stress function methods), the nonlinearity of buckling and postbuckling, the vibration and the dynamic response of micro/nano plate with graphene platelet reinforcement are analyzed. The fourth-order Runge–Kutta methods are implemented to solve the governing equation of the dynamic system. To prove the reliability of the formulas, the results of the present study in specific cases are compared with those of relevant published papers in the reference and good agreements are observed. In the final part, the effects of nonlocal parameters, Kerr foundation, initial imperfection, GPL weight fraction and geometrical parameters on the overall nonlinear static and dynamic stability of the micro/nano plate with graphene platelet reinforcement are evidently demonstrated.