### Abstract

Short-wavelength wrinkles that appear on an initially stretched thin elastic plate under transverse loading are examined. As the degree of loading is increased, wrinkles appear and their structure at the onset of buckling takes on one of three distinct forms depending on the size of the imposed stretching. With relatively little stretching, the wrinkles sit off the rim of the plate at a location which is not known a priori, but which is determined via a set of consistency conditions. These take the form of constraints on the solutions of certain coupled nonlinear differential equations that are solved numerically. As the degree of stretching grows, an asymptotic solution of the consistency conditions is possible, which heralds the structure that governs a second regime. Now the wrinkle sits next to the rim, where its detailed structure can be described by the solution of suitably scaled Airy equations. In each of these first two regimes the F oppl-von K arman bifurcation equations remain coupled, but as the initial stretching becomes stronger the governing equations separate. Further use of singular perturbation arguments allows us to identify the wavelength wrinkle which is likely to be preferred in practice.

Original language | English |
---|---|

Pages (from-to) | 1009-1029 |

Number of pages | 21 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 78 |

Issue number | 2 |

DOIs | |

Publication status | Published - 29 Mar 2018 |

Externally published | Yes |

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### Cite this

*SIAM Journal on Applied Mathematics*,

*78*(2), 1009-1029. https://doi.org/10.1137/17M1155193

}

*SIAM Journal on Applied Mathematics*, vol. 78, no. 2, pp. 1009-1029. https://doi.org/10.1137/17M1155193

**Wrinkling Structures at the Rim of an Initially Stretched Circular Thin Plate Subjected to Transverse Pressure.** / Coman, Ciprian D.; Bassom, Andrew P.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Wrinkling Structures at the Rim of an Initially Stretched Circular Thin Plate Subjected to Transverse Pressure

AU - Coman, Ciprian D.

AU - Bassom, Andrew P.

PY - 2018/3/29

Y1 - 2018/3/29

N2 - Short-wavelength wrinkles that appear on an initially stretched thin elastic plate under transverse loading are examined. As the degree of loading is increased, wrinkles appear and their structure at the onset of buckling takes on one of three distinct forms depending on the size of the imposed stretching. With relatively little stretching, the wrinkles sit off the rim of the plate at a location which is not known a priori, but which is determined via a set of consistency conditions. These take the form of constraints on the solutions of certain coupled nonlinear differential equations that are solved numerically. As the degree of stretching grows, an asymptotic solution of the consistency conditions is possible, which heralds the structure that governs a second regime. Now the wrinkle sits next to the rim, where its detailed structure can be described by the solution of suitably scaled Airy equations. In each of these first two regimes the F oppl-von K arman bifurcation equations remain coupled, but as the initial stretching becomes stronger the governing equations separate. Further use of singular perturbation arguments allows us to identify the wavelength wrinkle which is likely to be preferred in practice.

AB - Short-wavelength wrinkles that appear on an initially stretched thin elastic plate under transverse loading are examined. As the degree of loading is increased, wrinkles appear and their structure at the onset of buckling takes on one of three distinct forms depending on the size of the imposed stretching. With relatively little stretching, the wrinkles sit off the rim of the plate at a location which is not known a priori, but which is determined via a set of consistency conditions. These take the form of constraints on the solutions of certain coupled nonlinear differential equations that are solved numerically. As the degree of stretching grows, an asymptotic solution of the consistency conditions is possible, which heralds the structure that governs a second regime. Now the wrinkle sits next to the rim, where its detailed structure can be described by the solution of suitably scaled Airy equations. In each of these first two regimes the F oppl-von K arman bifurcation equations remain coupled, but as the initial stretching becomes stronger the governing equations separate. Further use of singular perturbation arguments allows us to identify the wavelength wrinkle which is likely to be preferred in practice.

KW - Asymptotic methods

KW - Föppl-von Kármán plate equations

KW - Thin films

KW - Wrinkling

UR - http://www.scopus.com/inward/record.url?scp=85047740743&partnerID=8YFLogxK

U2 - 10.1137/17M1155193

DO - 10.1137/17M1155193

M3 - Article

VL - 78

SP - 1009

EP - 1029

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 2

ER -