Effect of an elastic substrate on buckling of free-standing nanocolumns

This paper studies the buckling problem of nanowires (NWs) and carbon nanotubes (CNTs) freely standing on a substrate and subjected to distributed axial loads. NWs and CNTs are modeled as elastic nanocolumns and due to their high Young's modulus, the substrate is reasonably considered as an elastic foundation. The junction between the nanocolumn and substrate is described by a rotational spring. A new approach is suggested to solve the stability of axially-loaded nanocolumns with a rotational spring junction. An approximation expression for the critical load with high accuracy is derived in closed form. The results are confirmed for a rectangular Ag NW by FEM. Numerical results of the critical length of NWs and CNTs under their own weight are presented in graphs and tables. Obtained results indicate that the critical length is sensitive to small Young's modulus of the elastic substrate and becomes insensitive for enough large Young's modulus of the elastic substrate. When the rotational spring stiffness is sufficiently large, the case reduces to a free-standing NW on a rigid foundation.