A numerical approach for the stability analysis of open thin-walled beams

A finite differences procedure is used to study the buckling of non-trivial equilibrium solutions for open thin-walled beams in a dynamic setting. A direct one-dimensional model with a coarse descriptor of warping is adopted. The algorithm describes non-trivial equilibrium paths by integrating discretized field equations, suitably written in terms of velocities. Some benchmark cases under conservative loading are discussed. Known results for the first critical loads are found to validate the procedure. New results are found accounting for non-trivial equilibrium paths, thus providing an estimate for the error made by linearizing around trivial equilibrium paths. The effect of warping on the critical loads is also investigated.