On Accounting for Surface Effects in Bending of Ultrathin Plates

The equations for axisymmetric bending of a circular plate of the Föppl-von Kármán type that account for surface effects, namely, the presence of a surface layer characterized by its elastic constants and initial stresses, as well as the presence of initial volumetric stresses, are given. An asymptotic solution for large deflections of the problem of a circular uniformly loaded rigidly clamped plate is obtained under the assumption of constant tensile forces. An assessment of the plate parameters at which surface effects become significant has been made.