Nonlocal Mechanical Buckling Analysis of Nano Single Layer Sheets Using Differential Quadrature method

Abstract

The following article investigates buckling of moderately thick circular Nano plates with an orthotropic property under uniform radial compressive in-plane mechanical load. Taking into account nonlocal elasticity theory (Eringen), principle of virtual work, first order shear deformation plate theory (FSDT) and nonlinear Von-Karman strains, the governing equations are obtained based on displacements. The stability equations are derived from the neighbor equilibrium estate. The differential quadrature method (DQM) as a numerical procedure is applied to discretize the derivatives equations with a non-uniform mesh point distribution (Chebyshev-Gauss-Lobatto). The accuracy of the present results is validated by comparing the solutions with those reported by the available literatures. The effect of nonlocal parameter, thickness and radius are investigated on non-dimension buckling loads. From the results, it can be seen that the non-dimension buckling load of Graphene sheets increases by decreasing flexibility of boundary condition and increasing the rate of nonlocal parameter. It can be observed that with increasing the non-dimensional thickness of plate, the non-dimension buckling loa reduces