Analytical GNI Analysis for Lateral-torsional Behavior of Thin-walled Beams with Doubly-symmetric I-Sections

In this paper elastic lateral-torsional behavior of simple beams is discussed. The motivation of the presented research is the observation that classic analytical prediction and finite element prediction are, typically, considerably different, when the second-order nonlinear behavior of beams with initial imperfections is analyzed. In order to understand and explain the observed differences, a novel analytical solution is presented for the geometrically nonlinear analysis of beams with initial geometric imperfection. The presented analytical solution is derived for doubly-symmetric cross-sections, but with the novelty that it takes into consideration the changing geometry as the load is increasing. The most important steps of the derivations are summarized, and the resulted formulae are briefly discussed. Numerical studies are performed, too: the results of the new analytical formulae are compared to those from shell finite element analysis. The results suggest that the new formulae are able to capture the most important elements of the behavior. By the analytical and numerical results, it is proved that classic analytical solutions for the geometrically nonlinear analysis of beams with geometric imperfections are necessarily different from the numerical results obtained by incremental-iterative procedures