Lateral-torsional buckling analysis of a doubly symmetric thin-walled beam under axial force and bending moment

Abstract

A co-rotational formulation of second order beam theory is employed for the lateral-torsional buckling analysis of an elastic Euler beam under axial force and bending moment. The beam structure is divided into several segments. A set of segment coordinate system is constructed at the current configuration of the deformed beam segment. The principle of virtual work and the consistent second order linearization of the nonlinear beam theory are used to derive the equilibrium equations and constitutive equation of the beam segment. The exact solution of the primary path is solved using an analytical and numerical combined method. Disturbance is applied to the primary path of beam segments to derive the governing equations for buckling analysis using the first order linearization. A power series solution method is used to solve the buckling moment. Numerical examples are studied to demonstrate the accuracy of the present method.