The initial values method for buckling of nonlocal bars with application in nanotechnology

In this work, the buckling of a bar is investigated by using the method of initial values within the framework of nonlocal elasticity. The principal matrix required for the applicability of the method of initial values is presented. The critical loads for bars with various kind of supports are found. As is well known that nanotechnology is the engineering of functional systems at the molecular scale. Carbon nanotubes are molecular-scale tubes which are figured as hollow cylindrical bars of graphitic carbon at molecular scale with outstanding properties. They are among the stiffest and strongest fibers known, and have remarkable electronic properties and many other unique characteristics. They are widely used in nanotechnological applications. The results are used to display that nonlocal effects could be significant in buckling of carbon nanotubes.