Effects of the Follower Force on the Static Buckling of Beams

The paper discusses the effect of a follower force on the buckling capacities of a beam structure subjected to a non-follower force. The potential of the research is on the application of smart materials in the buckling enhancement of beams, since the follower force is always modeled at the interaction between the smart materials and the substrate. The buckling capacities of beams with different boundary conditions are obtained analytically. Trivial solutions are found for the simply supported beam, beam with two fixed ends, and propped cantilever beam. However, the result from the analysis of a cantilever beam shows that, when the value of follower force is small, the buckling load decreases with the increase of the follower force. Nevertheless, the buckling capacity of the cantilever beam "jumps" to a big value if the follower force on the beam is relative large and beyond a critical value. This observation indicates that by properly applying the follower force with smart materials, the buckling capacities of the beam can be enhanced dramatically for the cantilever beams.

It is hoped that this work will enable designers to capitalize on the effectiveness of using piezoelectric actuators or SMA in enhancing the buckling capacities of beams.