Nonlinear Analysis of a Cantilever Elastic Beam under Non-conservative Distributed Load

Based on the large deflection theory for the extensible elastic beams, the governing equations of post-buckling of a cantilever elastic beam subjected to a non-conservative distributed tangential follower force along the central axis were established. They consist of a boundary value problem of ordinary differential equations with strong non-linearity, in which seven unknown functions were included and the arc length of the deformed axis is considered as one on the basic unknown functions. By using shooting method and analytical continuation, the nonlinear boundary-value problem was numerically solved as well as the post-buckling configurations of the deformed beam were obtained. The results show that the features of the equilibrium paths of the cantilever beam subjected to a non-conservative load are evidently different from those to a conservative one.