Asymptotics of cellular buckling close to the Maxwell load


Budd, C. J., Hunt, G. W. and Kuske, R., 2001. Asymptotics of cellular buckling close to the Maxwell load. Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences, 457 (2016), pp. 2935-2964.

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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.


Item Type Articles
CreatorsBudd, C. J., Hunt, G. W. and Kuske, R.
DepartmentsFaculty of Science > Mathematical Sciences
Faculty of Engineering & Design > Mechanical Engineering
Research CentresBath Institute for Complex Systems (BICS)
ID Code7483
Additional InformationID number: ISI:000172976900008


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