Buckling analysis of micro- and nano-rods/tubes based on nonlocal Timoshenko beam theory

This paper is concerned with the elastic buckling analysis of micro- and nano-rods/tubes based on Eringen's nonlocal elasticity theory and the Timoshenko beam theory. In the former theory, the small scale effect is taken into consideration while the effect of transverse shear deformation is accounted for in the latter theory. The governing equations and the boundary conditions are derived using the principle of virtual work. Explicit expressions for the critical buckling loads are derived for axially loaded rods/tubes with various end conditions. These expressions account for a better representation of the buckling behaviour of micro- and nano-rods/tubes where small scale effect and transverse shear deformation effect are significant. By comparing it with the classical beam theories, the sensitivity of the small scale effect on the buckling loads may be observed.