Size dependent stability analysis of circular ultrathin films in elastic medium with consideration of surface energies

In this article, analytical framework is developed for size dependent symmetric stability and self-instability of circular nanoplates including surface effects using modified Kirchhoff plate theory. The surrounding elastic medium is modeled as Winkler elastic foundation and its effect is comprehensively studied on self-instability problems. The derived explicit solutions contain Bessel functions with modified arguments reflecting the size dependency of the buckling loads. In order to check the results an inverse formulation is presented for effective Youngʹs modulus using the buckling loads to be verified by previous experimental results for nanowires. Several numerical examples are given for two types of materials with positive and negative surface properties to show the general trends of size dependencies. Some problems and limitations are explored for consistency of results with experiments and suggestions for future works.