Surface stress effects on the nonlinear postbuckling characteristics of geometrically imperfect cylindrical nanoshells subjected to torsional load

Abstract

The prime aim of the current investigation is to predict the nonlinear torsional buckling and postbuckling behavior of geometrically imperfect cylindrical nanoshells including surface stress effects. To this end, the size-dependent governing differential equations of cylindrical nanoshell based on von Karman–Donnell-type of kinematic nonlinearity are derived using a combination of Gurtin–Murdoch elasticity theory and the classical shell theory, and employing the principle of virtual work. Subsequently, by considering the transverse displacement and Airy stress function as independent variables, a boundary layer theory is put to use which takes surface stress effects into account in conjunction with the nonlinear prebuckling deformations, large postbuckling deflections and initial geometric imperfection. Finally, an efficient solution methodology based on a two-stepped singular perturbation technique is conducted to obtain the size-dependent postbuckling equilibrium paths of nanoshells. It is revealed that after the minimum point of postbuckling load, by increasing the value of applied torsional load, the difference between postbuckling load-deflection curves corresponding to the perfect and imperfect nanoshells tends to decrease.