TY - JOUR
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
SP - 2935
LP - 2964
M3 - 10.1098/rspa.2001.0843
VL - 457
IS - 2016
AU - Budd, C. J.
AU - Hunt, G. W.
AU - Kuske, R.
Y1 - 2001/12/08
UR - http://rspa.royalsocietypublishing.org/content/457/2016/2935.abstract
N2 - 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.
ER -