Direct method for analysis of flexible cantilever beam subjected to two follower forces

The static analysis of the flexible non-uniform cantilever beams under a tip-concentrated and intermediate follower forces is considered. The angles of inclination of the concentrated forces with respect to the deformed axis of the beam remain unchanged during deformation. The governing non-linear boundary-value problem is reduced to an initial-value problem by change of variables. The resulting problem can be solved without iterations. It is shown that there are no critical loads in the Euler sense (divergence) for any flexural–stiffness distribution and angles of inclination of the follower forces. In particular, if the follower forces are tangential, the rectilinear shape of the non-uniform cantilever beam is the only possible equilibrium configuration. In this paper some equilibrium configurations of the uniform cantilever under normal or tangential follower forces are presented using direct method.