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References 8 and 13 are:
8 R. M. J. Groh and A. Pirrera, On the role of localisations in buckling of axially compressed cylinders, Proc. R. Soc. A 475, 20190006 (2019).
13 R. V. Southwell, On the general theory of elastic stability, Philos. Trans. R. Soc. Lond. A 213, 187 (1914)
FROM:
Rainer M. J. Groh and Alberto Pirrera [Bristol Composites Institute (ACCIS), Department of Aerospace Engineering, University of Bristol, United Kingdom],
“Spatial chaos as a governing factor for imperfection sensitivity in shell buckling”, Phys. Rev. E 100, 032205, 6 September 2019, https://doi.org/10.1103/PhysRevE.100.032205
ABSTRACT: Shell buckling is known for its extreme sensitivity to initial imperfections. It is generally understood that this sensitivity is caused by subcritical (unstable) buckling, whereby initial geometric imperfections rapidly erode the idealized buckling load of the perfect shell. However, it is less appreciated that subcriticality also creates a strong proclivity for spatially localized buckling modes. The spatial multiplicity of localizations implies a large set of possible trajectories to instability—also known as spatial chaos—with each trajectory affine to a particular imperfection. Using a toy model, namely a link system on a softening elastic foundation, we show that spatial chaos leads to a large spread in buckling loads even for seemingly indistinguishable random imperfections of equal amplitude. By imposing a dominant imperfection, the strong sensitivity to random imperfections is ameliorated. The ability to control the equilibrium trajectory to buckling via dominant imperfections or elastic tailoring creates interesting possibilities for designing imperfection-insensitive shells.
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