Branching Analysis at Coincident Buckling Loads of Nonconservative Elastic Systems

Abstract

Discrete nonconservative elastic systems which lose stability by buckling (divergence) are considered. Simple (distinct) critical points were treated previously, and the case of coincident buckling loads is analyzed here. An asymptotic procedure in the neighborhood of the critical point is used to determine postbuckling behavior and imperfection-sensitivity. It is shown that the system may exhibit no bifurcation at all. In other cases postbuckling paths may be tangential to the fundamental path at the critical point. The sensitivity to imperfections is shown to be more severe than for systems with distinct buckling loads (e.g., one-third, one-fourth, and one-fifth power laws are obtained for certain cases).