Buckling analysis of cylindrical thin-shells using strain gradient elasticity theory

Abstract

The stability problem of cylindrical shells is addressed using higher-order continuum theories in a generalized framework. The length-scale effect which becomes prominent at microscale can be included in the continuum theory using gradientbased nonlocal theories such as the strain gradient elasticity theories. In this work, expressions for critical buckling stress under uniaxial compression are derived using an energy approach. The results are compared with the classical continuum theory, which can be obtained by setting the length-scale parameters to zero. A special case is obtained by setting two length scale parameters to zero. Thus, it is shown that both the couple stress theory and classical continuum theory forms a special case of the strain gradient theory. The effect of various parameters such as the shell-radius, shell-length, and length-scale parameters on the buckling stress are investigated. The dimensions and constants corresponding to that of a carbon nanotube, where the length-scale effect becomes prominent, is considered for this investigation.

Buckling of Eccentrically Loaded Carbon Nanotubes

“…Eringen's Nonlocal Elasticity Theory has been widely used in modeling of nanobeam [8][9][10][11][12]. Also different gradient beam models have been used by researchers [13][14][15]. van der Waals interaction between the nanotubes has been considered in buckling on multi-walled nanotube structures [16][17][18].…”

Two-dimensional bending behavior of the three-layered shear deformable nanoshells: Electro-elastic size-dependent

“…Some nonlocal analyses of structures were presented based on the nonlocal elasticity theory by Arefi and Zenkour [19,20]. Krishnan and Ghosh [21] presented the critical buckling loads of cylindrical thin shell using the strain gradient theory in terms of the effect of small scale parameter, length, radius and thickness of shell. The effect of small scale parameter was studied on the free vibration and buckling analyses of nano shells and nano beams [22,23].…”