Abstract
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 post-buckling 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.
Highlights
Thin-walled shell structures are widely employed as mass-efficient means to carry loads
We focus on the mountain-pass solution corresponding to a single dimple located at the mid-length of the cylinder (x/L = 0) as Horák et al [4] showed this deformation mode to be the easiest escape route to postbuckling
Throughout this paper, we have addressed multiple aspects pertaining to the role of localized post-buckling states in axially compressed cylinders
Summary
Thin-walled shell structures are widely employed as mass-efficient means to carry loads. When the pre-buckling equilibrium path is linear, predictions of the first instability load can be based on a linearized eigenproblem This approach provides excellent correlations between theory and experiments for thin-walled beams and flat plates. An important caveat is that the cylinder only restabilizes under controlled end-shortening (rigid loading), whereas in the case of forcecontrolled loading (dead loading), the cylinder undergoes complete collapse once the mountain pass has been crossed With this caveat in mind, consider, for example, the two energy wells depicted, with one valley representing a high-energy pre-buckling equilibrium and the other a restabilized, low-energy post-buckling equilibrium (of localized or periodic form).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
