Buckling Analysis of Thin-Walled Beams by Two-Phase Local-Nonlocal Integral Model

A mathematical model is developed based on the thin-walled beam theory for buckling analysis of beams showing nonlocal properties. Constitutive equations of the thin-walled beams are defined by using two-phase local-nonlocal integral formulation. The developed model accounts for flexural-torsional coupling and warping effects as well as nonlocal elasticity. Governing equations of the nonlocal thin-walled beams which may have arbitrary open or closed cross-sections are derived by using the principle of minimum potential energy. Both local and nonlocal parts of the model are solved by a displacement-based finite element method, and formulation is given in detail. The effects of nonlocal parameters on the critical buckling force and buckling modes of nonlocal thin-walled beams are investigated for both open and closed cross-sections.