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Birdcaging and the collapse of rods and cables in fixed-grip compression. (English) Zbl 0989.74041

Summary: Wound cables and straight rods exhibit lateral instabilities when loaded under compression and rotation in fixed-grip conditions. In a multi-strand cable made from helically wound strands, this produces a “bird cage” structure where the constituent strands separate to leave a central void region. For a straight rod, a similar instability occurs when the planar elastica becomes unstable under significant axial compression. Here we use the large deflection theory of linear elastic rods to explain these behaviours in terms of standard concepts of the theory of buckling, post-buckling, and imperfection sensitivity. The problem allows an excellent use of Euler parameters (quaternions) which remove the singularities normally associated with Euler angle formulation.

MSC:

74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74G60 Bifurcation and buckling
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
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