Size-dependent nonlinear instability of shear deformable cylindrical nanopanels subjected to axial compression in thermal environments

In this work, modeling and analysis for size-dependent buckling and postbuckling behavior of cylindrical nanopanels under axial compression in thermal environments are presented. To this end, a non-classical panel model based upon the Gurtin–Murdoch elasticity theory in conjunction with the first-order shear deformation shell theory is developed which considers efficiently the effects of surface free energy. In order to capture the large deflections, the von Kármán geometrical nonlinearity is taken into account. The size-dependent governing differential equations are deduced to a boundary layer type that incorporates the nonlinear prebuckling deformations and the large postbuckling deflections. Afterwards, by means of an efficient solution methodology using a perturbation solving process, the size-dependent critical buckling loads and associated postbuckling equilibrium paths are obtained corresponding to various geometrical parameters and thermal environments. It is seen that for the both classical and non-classical panel models, the wide of snap-through phenomenon is larger for nanopanels with higher ratio of length to width. Also, it is found that thermal environment has no influence on the value of minimum load of the postbuckling domain and associated maximum deflection.