From wrinkling to global buckling of a ring on a curved substrate
Name
Reis_From wrinkling to global buckling.pdf
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4.66 MB
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Checksum (MD5)
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Author(s)
Lagrange, Romain
Lopez Jimenez, Francisco
Terwagne, Denis
Brojan, Miha
Reis, Pedro Miguel
Date Issued
February 2016
Journal
Journal of the Mechanics and Physics of Solids
Publisher
Elsevier
Citation
Lagrange, R. et al. “From Wrinkling to Global Buckling of a Ring on a Curved Substrate.” Journal of the Mechanics and Physics of Solids 89 (April 2016): 77–95 © 2016 Elsevier Ltd
Version
Original manuscript
Abstract
We present a combined analytical approach and numerical study on the stability of a ring bound to an annular elastic substrate, which contains a circular cavity. The system is loaded by depressurizing the inner cavity. The ring is modeled as an Euler-Bernoulli beam and its equilibrium equations are derived from the mechanical energy which takes into account both stretching and bending contributions. The curvature of the substrate is considered explicitly to model the work done by its reaction force on the ring. We distinguish two different instabilities: periodic wrinkling of the ring or global buckling of the structure. Our model provides an expression for the critical pressure, as well as a phase diagram that rationalizes the transition between instability modes. Towards assessing the role of curvature, we compare our results for the critical stress and the wrinkling wavelength to their planar counterparts. We show that the critical stress is insensitive to the curvature of the substrate, while the wavelength is only affected due to the permissible discrete values of the azimuthal wavenumber imposed by the geometry of the problem. Throughout, we contrast our analytical predictions against finite element simulations. Keywords: Elasticity; Instability; Buckling; Wrinkling; Ring; Substrate
MIT Department
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/J.JMPS.2016.02.004
