Surface stress size dependency in postbuckling characteristics of nanoshells under lateral and hydrostatic pressures

Abstract

The prime aim of the current study is to predict the nonlinear buckling and postbuckling behavior of cylindrical nanoshells subjected to two different radial compressive loads including lateral pressure and hydrostatic pressure with the presence of surface stress effects. The Gurtin-Murdoch elasticity theory in conjunction with von Karman geometrical nonlinearity relations is implemented into the classical shell theory to develop size-dependent shell model incorporating the effects of surface stress. Consequently, to satisfy the balance conditions on the free surfaces of nanoshell, a linear variation through the thickness is considered for the normal stress component of the bulk in such a way that it diminishes on mid-plane and is equal to shear surface stress components on the free surfaces. Afterwards, a boundary layer theory is employed which considers both nonlinear prebuckling deformations and large deflections in the postbuckling domain. Finally, a singular perturbation technique is utilized to obtain the critical buckling loads and the postbuckling equilibrium paths of nanoshells including surface stress effects and corresponding to both loading cases. It is revealed that surface stress effect has a more significant influence on the postbuckling behavior of nanoshells with lower thicknesses. Also, it is found that this pattern is some deal more considerable for the hydrostatic pressure loading case compared to the lateral pressure one.