On the role of localised post-buckling equilibria in axially compressed cylinders

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We revisit buckling of axially compressed cylinders by considering fully localised post-buckling states in the form of one or multiple dimples. Using a combination of nonlinear quasi-static finite element methods and numerical continuation algorithms, we trace the evolution of odd and even dimples into one ring of circumferential diamond waves. The growth of the post-buckling pattern with varying compression is driven by a homoclinic snaking sequence, with even and odd dimple solutions intertwined. The initially stable and axially localised ring of circumferential diamonds destabilises at a pitchfork bifurcation to produce a second circumferential snaking sequence that results in the Yoshimura pattern. Localised dimple solutions represent saddle points in the energy landscape providing an exponentially decreasing energy barrier between the stable pre-buckling and re-stabilised post-buckling wells. The significance of the Maxwell load as a measure for quantifying the onset of mountain-pass solutions and the reduced resilience of the pre-buckling state is assessed. Finally, conservative buckling loads for design are inferred by tracing critical boundaries of the snaking set.
Original languageEnglish
Number of pages13
Publication statusPublished - 8 Mar 2019
EventAmerican Physical Society March Meeting 2019 - Boston, United States
Duration: 4 Mar 20198 Mar 2019


ConferenceAmerican Physical Society March Meeting 2019
Abbreviated titleAPS March Meeting
Country/TerritoryUnited States


  • localisation
  • buckling
  • shells
  • instability


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