Heriot-Watt Mathematics Report Series
HWM97-56, 18 Jan 2000
Localization and solitary waves in solid mechanics
G J Lord, A R Champneys and G W Hunt
Buckling is investigated of a long thin cylindrical shell under longitudinal compression as modelled by the von Karman-Donnell equations.
Evidence is reviewed for the buckling being localised to some of the axial length. In accordance with this observed behaviour the equations are first approximated circumferentially by a Galerkin proceedure, whereupon cross-symmetric homoclininc solutions of the resulting system of ordinary differential equations are saught in the axial direction.
Results are compared with experimental and other numerical data. Excellent agreement with experiments is achieved with fewer circumferential modes than other methods.
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