From wrinkling to global buckling of a ring on a curved substrate
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...
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| Format: | Article |
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Elsevier
2018
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| Online Access: | http://hdl.handle.net/1721.1/114878 https://orcid.org/0000-0001-8569-5400 https://orcid.org/0000-0003-3984-828X |
| _version_ | 1811082767469903872 |
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| author | Lagrange, Romain Lopez Jimenez, Francisco Terwagne, Denis Brojan, Miha Reis, Pedro Miguel |
| author2 | Massachusetts Institute of Technology. Department of Civil and Environmental Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Civil and Environmental Engineering Lagrange, Romain Lopez Jimenez, Francisco Terwagne, Denis Brojan, Miha Reis, Pedro Miguel |
| author_sort | Lagrange, Romain |
| collection | MIT |
| description | 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 |
| first_indexed | 2024-09-23T12:08:41Z |
| format | Article |
| id | mit-1721.1/114878 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T12:08:41Z |
| publishDate | 2018 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | mit-1721.1/1148782022-10-01T08:30:08Z From wrinkling to global buckling of a ring on a curved substrate Lagrange, Romain Lopez Jimenez, Francisco Terwagne, Denis Brojan, Miha Reis, Pedro Miguel 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 Lagrange, Romain Lopez Jimenez, Francisco Terwagne, Denis Brojan, Miha Reis, Pedro Miguel 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 National Science Foundation (U.S.) (Grant CMMI-1351449) 2018-04-23T17:32:56Z 2018-04-23T17:32:56Z 2016-02 2015-12 2018-04-20T11:16:52Z Article http://purl.org/eprint/type/JournalArticle 0022-5096 http://hdl.handle.net/1721.1/114878 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 https://orcid.org/0000-0001-8569-5400 https://orcid.org/0000-0003-3984-828X http://dx.doi.org/10.1016/J.JMPS.2016.02.004 Journal of the Mechanics and Physics of Solids Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier arXiv |
| spellingShingle | Lagrange, Romain Lopez Jimenez, Francisco Terwagne, Denis Brojan, Miha Reis, Pedro Miguel From wrinkling to global buckling of a ring on a curved substrate |
| title | From wrinkling to global buckling of a ring on a curved substrate |
| title_full | From wrinkling to global buckling of a ring on a curved substrate |
| title_fullStr | From wrinkling to global buckling of a ring on a curved substrate |
| title_full_unstemmed | From wrinkling to global buckling of a ring on a curved substrate |
| title_short | From wrinkling to global buckling of a ring on a curved substrate |
| title_sort | from wrinkling to global buckling of a ring on a curved substrate |
| url | http://hdl.handle.net/1721.1/114878 https://orcid.org/0000-0001-8569-5400 https://orcid.org/0000-0003-3984-828X |
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