On a lower bound theorem for the buckling load of elastic beams subjected to nonconservative, compressive follower loads

TLDR: In this paper, a modified lower bound theorem for follower loads which monotonically increase over a part or even over the whole length of the beam is presented. But it is not shown that the theorem is valid for all follower loads.

Abstract: For beams loaded withuniformly distributed follower forces, there exists a lower bound theorem, which allows to evaluate the actual buckling load approximately by means of the buckling load of the same beam loaded correspondingly with conservative unidirectional forces of the same magnitude. In this paper it is shown that the theorem remains valid for monotonically decreasing or at least not increasing follower forces. Moreover, a modified lower bound theorem can be formulated for follower loads which monotonically increase over a part or even over the whole length of the beam. In that case, a “lower bound curve” has to be constructed using the eigenvalue curve of the conservatively loaded beam. The intersection of the lower bound curve with the vertical axis yields a lower bound for the buckling load of the nonconservatively loaded beam.