The generic nature of homoclinic snaking has been identified in various structural mechanics problems, e.g. the buckling collapse of an axially compressed, thin-walled cylinder. In early studies on the cylinder, the applied load was found to fluctuate about the periodic Maxwell load with end-displacement growing accordingly, i.e. pattern formation occurs in the direction of the applied load. More recent finite element simulations have uncovered snaking around the cylinder circumference with pattern formation propagating orthogonal to the direction of loading, so-called transverse snaking. This phenomenon begins with a single or two adjacent dimples that multiply circumferentially in odd or even series to connect to a periodic solution of one ring of dimples. The fully localised nature of the single and two adjacent dimples means that many multi-dimple solutions also exist that lead to different periodic solutions. Interestingly, the addition of internal pressure changes the pattern formation, with multiplication of the single dimple now occurring at a diagonal across the cylinder domain. As the single dimple corresponds to a mountain-pass point above a critical threshold of compression, the single dimple is of critical importance from a structural design point of view as it requires significantly less triggering energy than its periodic counterparts. The contemporary understanding of snaking therefore provides opportunities to influence the design of engineering structures.
|Publication status||Published - 2021|
|Event||2021 SIAM Conference on Dynamical Systems - |
Duration: 23 May 2021 → 27 May 2021
|Conference||2021 SIAM Conference on Dynamical Systems|
|Period||23/05/21 → 27/05/21|