Buckling of nonlocal columns with allowance for selfweight

This paper presented new analytical solutions for the elastic buckling of Eringen's nonlocal columns with allowance for selfweight. A discrete column model on the basis of the central finite difference formulation and the equivalent Hencky bar-chain model also were presented for this buckling problem. The discrete column model allows one to determine the buckling solutions of columns constructed from repetitive cells. In addition, one may use the discrete buckling solutions to calibrate the small-length scale coefficient e0 in the Eringen's nonlocal column model. It was found that e0 values varied from 0.289 to 0.373 with respect to increasing selfweight for clamped-free column case, from 0.289 to 0.276 for the pinned-pinned column case, and from 0.289 to 0.281 for the clamped-clamped column case.