RT Journal Article
SR Electronic
T1 Asymptotics of cellular buckling close to the Maxwell load
JF Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
FD The Royal Society
SP 2935
OP 2964
DO 10.1098/rspa.2001.0843
VO 457
IS 2016
A1 Budd, C. J.
A1 Hunt, G. W.
A1 Kuske, R.
YR 2001
UL http://rspa.royalsocietypublishing.org/content/457/2016/2935.abstract
AB 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.