### Abstract

This work addresses a generalization of Dean's classical problem, which sought to explain how an annular thin elastic plate buckles under uniform shearing forces applied around its edges. We adapt the original setting by assuming that the outer edge is radially stretched while the inner rim undergoes in-plane rotation through some small angle. Boundary-layer methods are used to investigate analytically the deformation pattern which is set up and localized around the inner hole when this angle reaches a well-defined critical wrinkling value. Linear stability theory enables us to identify both the critical load and the preferred number of wrinkles appearing in the deformed configuration. Our asymptotic results are compared with a number of direct numerical simulations.

Language | English |
---|---|

Pages | 3037-3053 |

Number of pages | 17 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 463 |

Issue number | 2087 |

Early online date | 4 Sep 2007 |

DOIs | |

Publication status | Published - 8 Nov 2007 |

Externally published | Yes |

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*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, vol. 463, no. 2087, pp. 3037-3053. https://doi.org/10.1098/rspa.2007.0106

**Boundary layers and stress concentration in the circular shearing of annular thin films.** / Coman, Ciprian D.; Bassom, Andrew P.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Boundary layers and stress concentration in the circular shearing of annular thin films

AU - Coman, Ciprian D.

AU - Bassom, Andrew P.

PY - 2007/11/8

Y1 - 2007/11/8

N2 - This work addresses a generalization of Dean's classical problem, which sought to explain how an annular thin elastic plate buckles under uniform shearing forces applied around its edges. We adapt the original setting by assuming that the outer edge is radially stretched while the inner rim undergoes in-plane rotation through some small angle. Boundary-layer methods are used to investigate analytically the deformation pattern which is set up and localized around the inner hole when this angle reaches a well-defined critical wrinkling value. Linear stability theory enables us to identify both the critical load and the preferred number of wrinkles appearing in the deformed configuration. Our asymptotic results are compared with a number of direct numerical simulations.

AB - This work addresses a generalization of Dean's classical problem, which sought to explain how an annular thin elastic plate buckles under uniform shearing forces applied around its edges. We adapt the original setting by assuming that the outer edge is radially stretched while the inner rim undergoes in-plane rotation through some small angle. Boundary-layer methods are used to investigate analytically the deformation pattern which is set up and localized around the inner hole when this angle reaches a well-defined critical wrinkling value. Linear stability theory enables us to identify both the critical load and the preferred number of wrinkles appearing in the deformed configuration. Our asymptotic results are compared with a number of direct numerical simulations.

KW - Boundary layers

KW - Circular shearing

KW - Thin films

KW - Wrinkling

UR - http://www.scopus.com/inward/record.url?scp=36349023336&partnerID=8YFLogxK

U2 - 10.1098/rspa.2007.0106

DO - 10.1098/rspa.2007.0106

M3 - Article

VL - 463

SP - 3037

EP - 3053

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

T2 - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0080-4630

IS - 2087

ER -