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Buckling of Long Elastic Structures

The phenomenon of localized buckling gives rise to many interesting nonlinear-mechanics problems. Localized Buckling is the engineering term for a situation where the deformation in a buckled structure does not extend throughout the structure, but remains confined to a small part of it. The concept is most simply demonstrated on the Euler strut: the classical Euler strut buckles in a sinusoid profile:
unconfined Euler strut
If we encase the strut between two elastic media (`strut on a foundation') then under certain conditions the deformation remains restricted to a small section of the length of the strut:
Euler strut on a foundation
Other well-known examples of such localization are the axially loaded cylinder and a strut (or rod) under torsion; you also see it if you replace the elastic foundation by a viscous one.

The strut-on-foundation model leads to the ODE
u'''' + p u'' + F'(u) = 0
where F is a single- or multiple-well potential. This equation, known also as the stationary Extended Fisher-Kolmogorov Equation or the stationary Swift-Hohenberg equation, has many solutions that are bounded on the real line.

All activity described on this page is in collaboration with the Center for Nonlinear Mechanics in Bath, and most importantly Giles Hunt and Chris Budd.

Last modified on March 25, 2012 by Mark Peletier