On the bending and buckling behaviors of Mindlin nanoplates considering surface energies

Due to the high surface to volume ratio of the nanoscale domain, the surface stress effect is a major concern in the analysis of mechanical response of the nanomaterials and nanostructures. This paper is concerned with the applicability of a continuum model including the surface properties for describing the bending and buckling configuration of the nanoscale plates. The Gurtin–Murdoch surface theory of elasticity is first incorporated into Mindlin’s plate theory. Then, the principle of virtual work is applied to derive the size-dependent governing equations along with various boundary conditions. To solve the governing equations, the generalized differential quadrature (GDQ) method is employed. The critical uniaxial and biaxial buckling loads and the maximum deflection of the nanoplate due to a uniform transverse load are calculated in the presence and absence of the surface effects for various edge conditions. It is found that the significance of the surface effects on the response of the nanoplate relies on its size, type of edge support and selected surface constants.