Enhanced model including moment-rotation dependency for stability of thin-walled structures

Abstract

Adopting an updated Lagrangian approach, a “general” and “exact” framework for the geometrically non-linear analysis of thin-walled framed structures are developed. The generality of such framework stands for the wide range of its applicability for different types of beam cross-sections, support conditions, and loading patterns including configuration-dependent behavior of applied moments; while the exactness stands for the utilization of a number of closed-form solutions of a class of torsionally loaded thin-walled beams to formulate a two-node element for spatial buckling analysis. The key in this formulation relates to the use of the “exact” solution for the displacement fields as opposed to the more conventional finite element approach in which polynomial/Lagrangian-type interpolation function is employed. Further, emphasizes are given to the effect of finite rotations in space on the non-linear kinematic descriptions as well as the configuration-dependent behavior of externally applied moment vector of the conservative/non-conservative type. Results obtained in a number of numerical simulations of beam assemblages subjected to different loading patterns illustrated the usefulness, robustness and fast convergence of the developed model in predicting the lateral torsional buckling.