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    On the perturbation analysis of interactive buckling in nearly symmetrical structures

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    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

    Interactive buckling of an elastically restrained truss structure

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    Interactive buckling of an elastically restrained truss structure is investigated by using an improved version of the Byskov-Hutchinson perturbation analysis. The mechanical model consists of two horizontal beams connected by rigid diagonals, whose out-of-plane displacements are prevented by a continuous distribution of linear springs. When the two horizontal beams are compressed, three buckling modes are possible: one overall in-plane mode and two local (lateral and torsional) modes which, for a particular choice of the geometry of the structure, may occur nearly simultaneously. Three nonlinear equilibrium equations are derived in the amplitudes of the three buckling modes and solved numerically for given initial imperfections
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