Imperfection sensitivity of the nonlinear axial buckling behavior of FGM nanoshells in thermal environments based on surface elasticity theory

Abstract

A size-dependent shell model which accounts for geometrical imperfection sensitivity of the axial postbuckling characteristics of a cylindrical nanoshell made of functionally graded material (FGM) is proposed within the framework of the surface elasticity theory. In accordance with a power law, the material properties of the FGM nanoshell are supposed to vary through the shell thickness. In order to eliminate the stretching-bending coupling terms, the change in the position of physical neutral plane corresponding to different volume fractions is taken into account. Based upon the virtual work’s principle, the non-classical governing differential equations are derived and then deduced to boundary layer-type ones. After that, a perturbation-based solution methodology is employed to predict the size dependency in the nonlinear instability of perfect and imperfect axially loaded FGM nanoshells with various values of shell thickness, material property gradient index and different uniform temperature changes. It was seen that for thicker FGM nanoshells in which the surface free energy effects diminish, the influence of the initial geometric imperfection on the critical buckling load is higher than its influence on the minimum load of the postbuckling domain. It is also found that through reduction of the surface free energy effects, the influence of material property gradient index on the critical end-shortening of FGM nanoshell decreases.