Boundary layer modeling of surface residual tension in postbuckling behavior of axially loaded silicon panels at nanoscale embedded in elastic foundations

Here, nonlinear buckling and postbuckling properties of cylindrical silicon nanopanels of finite length resting on elastic foundation exposed to axial compression have been studied by taking into account surface free energy (SFE) effect. Size-dependent governing equations were constructed by integrating classical shell theory and Gurtin-Murdoch elasticity theory. Surrounding elastic media were considered as Pasternak foundations. Using shell buckling boundary layer theory, the influences of large deflections and SFE were extended to nonlinear instability analysis of nanopanels under axial loads. Finally, a perturbation-based solution procedure was applied to extract explicit equations for nanopanel postbuckling equilibrium paths at different surface elastic constants and geometric parameter values. It was revealed that surface effect related to positive surface elastic constant values shifted the minimum postbuckling domain point to lower maximum deflection while materials with negative surface values of elastic constant, SFE effect shifted the minimum point of postbuckling domain to higher maximum deflections.

Automated summary

This study investigates the nonlinear buckling and postbuckling properties of cylindrical silicon nanopanels of finite length under axial compression. The surface free energy effect is taken into account, and the size-dependent governing equations are derived. It is found that the surface effect shifts the minimum point of postbuckling domain to lower or higher maximum deflections, depending on the surface elastic constant values.