Beneficial effects of the precritical nonlinearities on the lateral buckling of extremely flexible beams

The lateral buckling of extremely flexible beams, uniformly or non-uniformly bent in a principal inertia plane, is studied. An exact polar continuum model of an internally constrained 1D straight beam, immersed in the 3D space, is formulated. The model is linearized in the out-of-plane displacement only, so that it is able to capture: (i) the exact planar non-trivial fundamental path, and (ii) the exact critical point along it, at which the beam experiences out-of-plane flexural–torsional buckling. It is proven that the precritical deflections increase the critical load with respect to that evaluated by the classic theory, in which a trivial fundamental path is assumed, thus playing a beneficial role. Moreover, when the beam is extremely flexible, bifurcation disappears, similar to what discussed in literature for axially soft compressed beams, although via a different mechanism of the eigenvalues.