Radial postbuckling of nanoscaled shells embedded in elastic foundations based on Ru's surface stress elasticity theory

In this article, the nonlinear buckling and postbuckling response of cylindrical nanoshells under radial compressive load is investigated on the basis of a new surface elasticity theory. To this point, in contrast to the previous models based on the Gurtin-Murdoch elasticity theory, a new non-classical shell model based on the Ru's surface elasticity theory is developed in which the non-strain displacement gradient terms are eliminated from the surface stress-strain relations. The non-classical governing equations are derived using the principle of virtual work. Then they are deduced to boundary layer-type equations including simultaneously the nonlinear prebuckling deformations and the large postbuckling deflections. By using a singular perturbation technique, the new size-dependent problem is solved. It is indicated that due to the immovable edge supports and in the absence of the hydrostatic pressure, surface effects lead to an initial shortening caused by the induced residual strains. Additionally, the residual strain and initial surface tension terms vanish in the size-dependent nonlinear governing equations. Moreover, it is observed that this initial shortening diminishes quickly for thicker nanoshells.