An investigation on effect of surface stress in buckling stability of a nanotube using modified nonlocal theory of elasticity

In this paper, buckling analysis of an Euler-Bernoulli nanotube with simply support boundary condion is investigated using modified nonlocal elasticity theory considering the surface elasticity, surface tension effect and nonlocal parameter. Using Hamilton principle in conjuctre with modified nonlocal elasticity theory considering surface effect the governing dynamic equations of motion for nanotube has been derived. Th critical buckling load for nanotube considerng surface tension effect is analytically obtained based on Navier’s series soltion. Then, rearrenging of serie solution for nanotube buckling load to eliminate effect of recocnized terms of soltion, the modofied governing equations are rewritten and derived. Effect of changes of various parameters such as mode coefficent of buckling, nanotube length and diameter, surface tension and nonlocal paprameter on the critical buckling load are all investigated. finally, the obtained results for critical bucklinf load from modified nonlocal theory of elasticity are compared with those from nonlocal and classic beam theories.