Surface stress effects on the nonlinear postbuckling characteristics of geometrically imperfect cylindrical nanoshells subjected to axial compression

Abstract

For structures at nanoscale, the surface effects can be important due to the high ratio of surface area to volume. In the current investigation, the nonlinear axial postbuckling behavior of geometrically imperfect cylindrical nanoshells is studied including surface stress effects. For this purpose, Gurtin–Murdoch continuum elasticity theory in conjunction with von Karman–Donnell-type geometric nonlinearity is implemented into the classical shell theory. By the developed size-dependent shell model, the surface effects which include surface elasticity and residual surface stress are taken into account. In order to satisfy balance conditions on the surfaces of nanoshell, a linear variation through the thickness is considered for the normal stress component of the bulk. Based on the variational approach using virtual work's principle, the non-classical governing differential equations are derived. In order to solve the nonlinear problem, a boundary layer theory is employed which contains simultaneously the nonlinear prebuckling deformations, initial geometric imperfections and large deflections corresponding to the postbuckling domain. Subsequently, a two-stepped singular perturbation methodology is utilized to predict the nonlinear critical buckling loads as well as the postbuckling equilibrium paths. It is observed that by taking surface stress effects into account, the both critical buckling load and critical end-shortening of a cylindrical nanoshell made of Silicon increase.