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Publication - Dr Alberto Pirrera

    On the role of localisations in buckling of axially compressed cylinders

    Citation

    Groh, R & Pirrera, A, 2019, ‘On the role of localisations in buckling of axially compressed cylinders’. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol 475.

    Abstract

    The collapse of axially compressed cylinders by buckling instability is a classic problem in engineering mechanics. We revisit the problem by considering fully localised 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 localised 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 localised ring of diamond-shaped buckles destabilises, 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 parametrise the compressive onset of the singledimple mountain-pass point with a single nondimensional parameter, and compare the lowerbound 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.

    Full details in the University publications repository