On the role of localizations in buckling of axially compressed cylinders

Rainer Groh*, Alberto Pirrera

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

60 Citations (Scopus)
266 Downloads (Pure)


The collapse of axially compressed cylinders by buckling instability is a classic problem in engineering mechanics. We revisit the problem by considering fully localized post-buckling states in the form of one or multiple dimples. Using nonlinear finite-element methods and numerical continuation algorithms, we trace the evolution of odd and even dimples into one axially localized ring of circumferentially periodic diamond-shaped waves. The growth of the postbuckling pattern with varying compression is driven by homoclinic snaking with even- and odd-dimple solutions intertwined. When the axially localized ring of diamond-shaped buckles destabilizes, additional circumferential snaking sequences ensue that lead to the Yoshimura buckling pattern. The unstable single-dimple state is a mountain-pass point in the energy landscape and therefore forms the smallest energy barrier between the pre-buckling and post-buckling regimes. The small energy barrier associated with the mountain-pass point means that the compressed, pre-buckled cylinder is exceedingly sensitive to perturbations once the mountain-pass point exists. We parameterize the compressive onset of the single-dimple mountain-pass point with a single non-dimensional parameter, and compare the lower-bound buckling load suggested by this parameter with over 100 experimental data points from the literature. Good correlation suggests that the derived knockdown factor provides a less conservative design load than NASA's SP-8007 guideline.

Original languageEnglish
Article number20190006
Number of pages27
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2224
Publication statusPublished - 17 Apr 2019

Structured keywords

  • Bristol Composites Institute ACCIS


  • buckling
  • cylinders
  • localisation
  • nonlinearities
  • Shell buckling
  • Pattern formation
  • Localization
  • Buckling
  • Snaking


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