A structure exhibiting localized buckle patterns is analysed asymptotically to reveal how such solutions are limited by a restabilizing non-linearity. The calculation reveals the fashion in which solutions become periodic (heteroclinic) in the vicinity of a critical coefficient by way of the propagation of a front, which is found to be a boundary layer linking the two distinct regions (flat and periodic). The predictions are compared against direct numerical solutions and excellent agreement between the two independent methods is found.
History
Publication title
Quarterly Journal of Mechanics and Applied Mathematics
Volume
65
Pagination
141-160
ISSN
0033-5614
Department/School
School of Natural Sciences
Publisher
Oxford Univ Press
Place of publication
Great Clarendon St, Oxford, England, Ox2 6Dp
Rights statement
Copyright The author 2011. Published by Oxford University Press; all rights reserved.