Buckling of Elastic Circular Plate with Surface Stresses

In the framework of general stability theory for three-dimensional bodies, the buckling analysis has been carried out for a circular plate subjected to the radial compression. It was assumed that the surface stresses are acting on its faces and the behavior of the plate is described by the Gurtin-Murdoch model. For an arbitrary isotropic material, the system of linearized equilibrium equations is derived, which describes the behavior of a plate in a perturbed state. In the case of axisymmetric perturbations, the stability analysis is reduced to solving a linear homogeneous boundary-value problem for a system of three ordinary differential equations. It is shown that for a plate with identical faces, it is sufficient to consider only half of the plate to study its stability. For two specific models of bulk material (Harmonic model and Blatz-Ko model), the buckling analysis has been carried out for a circular plate made of aluminum. It was found, in particular, that the stability of the plate increases with a decrease in its overall size. This effect is due to the influence of surface stresses and is quite significant at the micro- and nanoscale.