Buckling of a stretched nanoplate with a nanohole incorporating surface energy

Abstract

The effect of a nanoplate buckling at a circular nanohole under the remote uniaxial tension is studied incorporating the surface energy in accordance with the Gurtin–Murdoch surface elasticity model. The hole surface within the framework of the plane problem and the faces of the plate within the framework of the Kirchhoff theory of the plate bending are characterized by both the surface elasticity properties and the residual surface tension. The full potential energy of the plate containing the surface tension with non-strain terms of the surface displacement gradient is derived. Based on the principle of virtual displacements, critical values of the load, corresponding symmetrical and asymmetrical forms of the buckling are found by the Ritz method. Numerical investigations reveal that allowing for the non-strain terms of the surface displacement gradient in the Gurtin–Murdoch constitutive relation leads to the essential increasing the rigidity of the plate and the critical Euler load. Two types of the size effect are detected. The nanoplate thickness and the ratio of the hole radius to the thickness influence independently the value of the critical load.