Large deflections of a cantilever beam subjected to a follower force

The large-deflection problem of a non-uniform spring-hinged cantilever beam under a tip-concentrated follower force is considered. The angle of inclination of the force with respect to the deformed axis of the beam remains unchanged during deformation. The mathematical formulation of this problem yields a nonlinear two-point boundary-value problem which is reduced to an initial-value problem by change of variables. The resulting problem can be solved without iterations. It is shown that there exist no critical loads in the Euler sense (divergence) for any flexural-stiffness distribution and angle of inclination of the follower force. The load–displacement characteristics of a uniform cantilever under a follower force normal to the deformed beam axis are presented.