%0 Journal Article
%A Budd, C. J.
%A Hunt, G. W.
%A Kuske, R.
%T Asymptotics of cellular buckling close to the Maxwell load
%D 2001
%R 10.1098/rspa.2001.0843
%J Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
%P 2935-2964
%V 457
%N 2016
%X We study the deformation of an elastic strut on a nonlinear Winkler foundation subjected to an axial compressive load P. Using multi–scale analysis and numerical methods we describe the localized, cellular, post–buckled state of the system when P is removed from the critical load P = 2. The solutions, and their modulation frequencies, differ significantly from those predicted by weakly nonlinear analysis very close to P = 2. In particular, when P approaches the Maxwell load PM , the localized solutions approach a large–amplitude heteroclinic connection between an unbuckled solution and a periodic solution. An asymptotic description of PM in terms of the system parameters is given. The agreement between the numerical calculations and the asymptotic approximations is striking.
%U http://rspa.royalsocietypublishing.org/content/royprsa/457/2016/2935.full.pdf