Size-dependent axial buckling and postbuckling characteristics of cylindrical nanoshells in different temperatures

• Development an efficient size-dependent shell model incorporating surface free energy effects.
• Using a boundary layer theory to obtain the size-dependent nonlinear buckling and postbuckling behavior of nanoshells.
• Prediction the influence of thermal environment on the nonlinear buckling and postbuckling of nanoshells.

One of the most important reasons that give rise to the extraordinary behaviors of nanostructures is the free surface energy. In the current investigation, a size-dependent shell model is introduced which has an excellent capability to take surface energy effects into account. To this end, Gurtin–Murdoch elasticity theory is implemented into the classical shell theory. Using virtual work׳s principle, the non-classical governing differential equations related to the cylindrical nanoshell subjected to axial compressive load are derived. Subsequently, a boundary layer theory is extended to solve the problem with considering the effects of surface free energy in addition to the nonlinear prebuckling deformations and the large postbuckling deflections. Finally, a solution methodology based on a two-stepped perturbation technique is put to use in order to obtain the size-dependent critical buckling loads and related postbuckling equilibrium paths corresponding to different surface properties and various sets of thermal environments. It is found that for all sets of thermal environment, the surface free energy has significant influence on the postbuckling strength of nanoshell. Also, it is seen that thermal environment causes to decrease the both critical buckling load and critical end-shortening, but it has a negligible influence on the value of minimum postbuckling load.