Postbuckling analysis of axially loaded nanoscaled shells embedded in elastic foundations based on Ru's surface elasticity theory

Abstract

The nonlinear buckling and postbuckling characteristics of cylindrical nanoshells embedded in elastic foundations are investigated based on a strain-consistent elastic shell model including the both surface tension and the induced residual stress. For this purpose, in contrast to the previous models on the basis of the Gurtin-Murdoch elasticity theory, a new non-classical shell model based on Ru's surface elasticity theory is developed in which the non-strain displacement gradient terms are eliminated from the surface stress-strain relations. Using the virtual work's principle, the governing differential equations incorporating surface effects are derived. After that, the size-dependent governing equations are deduced to a boundary layer type problem which is subsequently solved through employing a two-stepped singular perturbation technique. It is revealed that because the edge supports of nanoshells are movable, before applying the axial compression, surface effects lead to an initial shortening due to induced residual strains, but the terms related to the residual strain and initial surface tension vanish in the size-dependent nonlinear governing equations. As a result, it is observed that before applying the axial compressive load, the surface effects cause an initial end-shortening for very thin nanoshells and these effects quickly diminish by increasing the shell thickness.

Communicated by Krzysztof Kamil Żur

Keywords:

• Nanomechanics
• surface elasticity theory
• nonlinear instability
• size effect
• boundary layer theory