Abstract
Experiments have shown that long cylinders buckle into localized patterns axially. It is argued that traditional linear or nonlinear analysis is unlikely to capture such modes, nor the effective buckling load at which such responses stabilise. However, the inherent translational indeterminacy of localised buckling is well captured by considering infinitely long cylinders and seeking homoclinic solutions of the von Kármán-Donnell equations. This exploits the dynamical analogy of such structural problems, so that symmetry arguments and numerical techniques developed for dynamical systems may be used. The method is illustrated by successful application to a cylinder which has well documented experimental results.
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Lord, G.J., Champneys, A.R., Hunt, G.W. (1999). The Role of Homoclinic Bifurcations in Understanding the Buckling of Long Thin Cylindrical Shells. In: Moon, F.C. (eds) IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics. Solid Mechanics and its Applications, vol 63. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5320-1_17
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DOI: https://doi.org/10.1007/978-94-011-5320-1_17
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