TY - JOUR

T1 - Asymptotics of cellular buckling close to the Maxwell load

AU - Budd, C. J.

AU - Hunt, G. W.

AU - Kuske, R.

N1 - ID number: ISI:000172976900008

PY - 2001

Y1 - 2001

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.

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.

UR - http://dx.doi.org/10.1098/rspa.2001.0843

U2 - 10.1098/rspa.2001.0843

DO - 10.1098/rspa.2001.0843

M3 - Article

SN - 1364-5021

VL - 457

SP - 2935

EP - 2964

JO - Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences

JF - Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences

IS - 2016

ER -