Lateral-Torsional Buckling of Non-Prismatic Thin-Walled Beams with Non-Symmetric Cross Section

摘要

A numerical method to evaluate the lateral buckling load of non-prismatic thin-walled straight beams with non-symmetric cross-section is proposed. For this purpose, the potential energy considering the effects of initial stresses, the elastic strain energy, and the work of external forces for non-prismatic thin-walled beam with non-symmetric cross-section are derived. Then equilibrium equations and boundary conditions are obtained from the total potential energy. Power series approximation is used to solve the fourth -order differential equations of non-prismatic thin-walled beam with variable geometric parameters and with generalized end conditions. Based on power series expansions of displacement components explicit expressions for displacement parameters are derived. And also, it is assumed that the functions which describe the beam's variable parameters such as: flexural rigidity and loads can be expanded in to power series form. Finally, the lateral buckling loads are determined by solving eigenvalue problem. Several numerical examples of non-prismatic thin-walled beams have been presented to verify the accuracy and validity of this method, and the obtained results are compared with the finite element solutions using Ansys software and other available numerical or analytical approaches. The method can be applied for the elastic critical buckling load of prismatic members as well as non prismatic members.