The influence of surface tension on the effective stiffness of nanosize plates

The problem of bending of a nanosize plate, taking into account the action of the surface effects, is considered, and the influence of surface tension on the effective stiffness of nanosize plates is found. The deformation of a linearly elastic body is considered and the action of the surface effects on the upper and lower surfaces are taken into account. An approximation for the field of displacements that is linear in thickness is assumed to describe the deformations of the plates. The equations of state allows the determination of the equilibrium equations for the plate, with the surface tension being taken into account, in terms of the displacements and rotations. The dependence of the transverse shear forces and momentum tensors on deformations is defined by the four elastic constant.