On the perturbation analysis of interactive buckling in nearly symmetrical structures

Different perturbation methods for the analysis of non-linear interaction between simultaneous buckling modes of nearly symmetric structures are discussed. First, the perturbation method employed by Budiansky for a single buckling mode, is extended to consider modes interaction of a perfect structure, by determining both the slope and the curvature of the bifurcated paths. It is shown that the solution diverges, when a properly defined parameter which characterizes the asymmetry of the structure approaches zero, thus preventing to recover results of symmetric systems. A modified perturbation method which permits to surmount this drawback is then suggested; this method applies only to a class of structures and furnishes asymptotic series valid in a wide region around bifurcation. The two methods are applied to investigate the post-buckling behavior of a two-degree-of-freedom system. Finally, a novel perturbation method which follows to some extent the lines of the Galerkin method and is particularly powerful in the investigation of nearly symmetric systems is presented.