Postbuckling behavior of circular higher-order shear deformable nanoplates including surface energy effects

The effects of surface energy are generally ignored in traditional continuum elasticity. However, due to the high surface to volume ratio in nanostructures, this is not the case for them. In this work, the nonlinear postbuckling characteristics of circular nanoplates are predicted in the presence of surface energy effects including surface elasticity and residual surface tension. For this objective, Gurtin–Murdoch elasticity theory is implemented into the classical higher-order shear deformation plate theory. In order to satisfy the balance conditions on the surfaces of nanoplate, it is assumed the normal stress of the bulk is distributed cubically through the thickness of nanoplate. Virtual work’s principle in conjunction with von Karman geometric nonlinearity is utilized to derive non-classical nonlinear governing differential equations of motion and related boundary conditions. Afterwards, an efficient numerical methodology based generalized differential quadrature (GDQ) method is carried out using the shifted Chebyshev–Gauss–Lobatto grid points to discretize the governing partial differential equations. Then, the Galerkin’s method is employed to reduce the set of nonlinear equations into a time-varying set of ordinary differential equations of Duffing type. At the end, the pseudo arc-length continuation technique is utilized in order to obtain the solution of the parameterized equation.