Nonlinear Stability Analysis of Thin-walled Frames Using Ul–esa Formulation

This work presents a one-dimensional finite element formulation for nonlinear analysis of spaced framed structures with thin-walled cross-sections. Within the framework of updated Lagrangian formulation, the nonlinear displacement field of thin-walled cross-sections, which accounts for restrained warping as well as the second-order displacement terms due to large rotations, the equations of equilibrium are firstly derived for a straight beam element. Due to the nonlinear displacement field, the geometric potential of semitangential moment is obtained for both the torsion and bending moments. In such a way, the joint moment equilibrium conditions of adjacent non-collinear elements are ensured. Force recovering is performed according to the external stiffness approach. Material nonlinearity is introduced for an elastic-perfectly plastic material through the plastic hinge formation at finite element ends and for this a corresponding plastic reduction matrix is determined. The interaction of element forces at the hinge and the possibility of elastic unloading are taken into account. The effectiveness of the numerical algorithm discussed is validated through the test problem.