Analysis of large deflections of a curved cantilever subjected to a tip-concentrated follower force

Abstract

The paper addresses the issue of effectively using the direct numerical method for static analysis of the flexible curved uniform cantilever beam under a tip-concentrated follower force. The angle of inclination of the follower force with respect to the deformed axis of the beam remains unchanged during deformation. After changing the variables, the original non-linear boundary value problem transforms into the initial-value problem for pendulum equation. The resulting initial value problem is solved numerically using a modified Numerov's method. In contrast to the usually used iteration methods (e.g. shooting technique), the problem is solved without iterations by direct numerical method. Some qualitative conclusions were made using Kirchhoff's kinetic analogy. It is shown that there are no critical loads in the Euler sense (divergence) for any values of the initial curvature and angle of inclination of the follower force. An extension of direct numerical method to curved spring-hinged cantilever subjected to follower force is also proposed. The paper presents some equilibrium configurations of the uniform curved fixed and spring-hinged cantilevers under normal and tangential follower force obtained by direct method.