Some two-mode buckling problems and their relation to catastrophe theory

The asymptotic buckling analysis of semisymmetric, two-degree-of-freedom static systems is presented. The types of behavior which can occur for this class of system are determined and categorized in accordance with the results of catastrophe theory. The expressions for the critical load-initial imperfection surfaces are determined in closed form. Within the context of an asymptotic analysis all possible secondary bifurcations cases are isolated. (The term bifurcation is used here in the sense which is usual in elastic stability analyses and not in the broader sense which is common in catastrophe theory.) In addition, the physical significance of the different critical load-initial imperfection surfaces is determined, and the primary surface is identified for each case. The general results are demonstrated in the example of the two-mode buckling of an axially loaded beam resting on a nonlinear elastic foundation.