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.

On the perturbation analysis of interactive buckling in nearly symmetrical structures

LUONGO, Angelo;
1992

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/18593
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