Nonlinear Bending of a Cantilever Beam Subjected to a Tip Concentrated Follower Force

By using shooting method, large deflection bending of the Euler-Bernoulli beam with fixed-free ends subjected to a tip follower force is investigated. Based on geometrically non-linear theory for extensible elastic beams, the governing nonlinear governing equations of elastic beam subjected to a tip-concentrated follower force along the central axis are established. They consist of a boundary value problem of ordinary differential equations with strong non-linearity, in which seven unknown functions are included and the arc length of the deformed axis is considered as one of the basic unknown functions. By using shooting method and analytical continuation, the nonlinear boundary-value problem is numerically solved as well as the non-linear bending characteristic curves of the deformed beam versus the load are presented and the effects of load parameters on the deformation are also discussed. The results show that the load and the relevant physical quantities are evidently non-linearity.