Buckling analysis of nanoscale beams based on nonlocal Timoshenko beam theory

Abstract Eigen-buckling problems of nanoscale beams continue to be of great research interest, and the nonlocal theory is widely used. However, the existing research generally adopted some simplified assumptions of nonlocal effects. This article studies the buckling behaviors of the nonlocal Timoshenko beam, where the nonlocal effects are considered both on the governing equations and boundary conditions. The variational principle is adopted to obtain the nonlocal governing equations and boundary conditions. The buckling solutions for nanoscale beams are obtained analytically. Numerical comparisons validate the correctness of the present results. Parameter study shows that the buckling characteristic of nonlocal beams is different from that of classical beams, and the nonlocal effect is dependent on boundary conditions and geometry size of nanoscale beams.