Buckling of Free-Standing Nanocolumn on an Elastic Substrate with Surface Effect and Self-weight

The buckling behaviors of a nanocolumn on an elastic substrate are studied by using the Euler-Bernoulli beam theory (EBT) and the Timoshenko beam theory (TBT). According the Hamilton’s principle, the governing equations for the buckling of nanocolumn with surface effect and self-weight are derived. The boundary conditions considering the rotational spring stiffness are given, the Galerkin method is adopted to solve the numerical solution of the governing equations, and the convergence and validation of the numerical solution are verified by using the finite element method (FEM). The influences of surface effect and elastic substrate on the critical load parameter are investigated. It is found that comparing with the EBT, the TBT can more accurately describe the buckling behaviors of the nanocolumn on the elastic substrate, and increasing the surface elastic modulus, or increasing the residual stress, can improve the stiffness of nanocolumn.