Surface stress effects on the postbuckling behavior of geometrically imperfect cylindrical nanoshells subjected to combined axial and radial compressions

Abstract

Because of surface free energy effects at nanoscale, study of the mechanical behavior of nanostructures including surface stress effects is a topic of substantial interest. Herein, the nonlinear buckling and postbuckling characteristics of geometrically imperfect cylindrical nanoshells under combined axial and radial compressive loads are investigated in the presence of surface stress effects. An efficient size-dependent shell model is proposed based on Gurtin–Murdoch elasticity theory and von Karman–Donnell-type of kinematic nonlinearity. On the basis of variational approach using the principle of virtual work, the non-classical governing differential equations are derived. Afterwards, a boundary layer theory is employed incorporating surface stress effects in conjunction with nonlinear prebuckling deformations, initial geometric imperfections and large postbuckling deflections. Then a two-stepped singular perturbation methodology is put to use in order to solve the size-dependent nonlinear problem corresponding to axial dominated and radial dominated loading cases. It is shown that in the case of radial dominated loading, the combination of hydrostatic pressure with axial compression causes to decrease approximately the effect of surface stress compared to the absence of axial load. However, for the axial dominated loading case, in comparison with no applied radial load, the surface stress effects is more significant in the presence of hydrostatic pressure.