### Abstract

A thin cantilever cylindrical shell subjected to a transverse shear force at the free end can experience two distinct modes of buckling, depending on its relative thickness and length. If the former parameter is fixed, then a short cylinder buckles in a diffuse manner, while the eigenmodal deformation of a moderately long shell is localised, both axially and circumferentially, near its fixed end. Donnell-type buckling equations for cylindrical shells are here coupled with a non-symmetric membrane basic state to produce a linear boundary-value problem that is shown to capture the transition between the aforementioned instability modes. The main interest lies in exploring the approximate asymptotic separation of the independent variables in the corresponding stability equations, when the eigen-deformation is doubly localised. Comparisons with direct numerical simulations of the full buckling problem provide further insight into the accuracy and limitations of our approximations.

Original language | English |
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Pages (from-to) | 701-722 |

Number of pages | 22 |

Journal | Mathematics and Mechanics of Solids |

Volume | 24 |

Issue number | 3 |

Early online date | 12 Feb 2018 |

DOIs | |

Publication status | Published - 1 Mar 2019 |

Externally published | Yes |

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### Cite this

*Mathematics and Mechanics of Solids*,

*24*(3), 701-722. https://doi.org/10.1177/1081286517754133

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*Mathematics and Mechanics of Solids*, vol. 24, no. 3, pp. 701-722. https://doi.org/10.1177/1081286517754133

**Eigen-transitions in cantilever cylindrical shells subjected to vertical edge loads.** / Coman, Ciprian D.; Bassom, Andrew P.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Eigen-transitions in cantilever cylindrical shells subjected to vertical edge loads

AU - Coman, Ciprian D.

AU - Bassom, Andrew P.

PY - 2019/3/1

Y1 - 2019/3/1

N2 - A thin cantilever cylindrical shell subjected to a transverse shear force at the free end can experience two distinct modes of buckling, depending on its relative thickness and length. If the former parameter is fixed, then a short cylinder buckles in a diffuse manner, while the eigenmodal deformation of a moderately long shell is localised, both axially and circumferentially, near its fixed end. Donnell-type buckling equations for cylindrical shells are here coupled with a non-symmetric membrane basic state to produce a linear boundary-value problem that is shown to capture the transition between the aforementioned instability modes. The main interest lies in exploring the approximate asymptotic separation of the independent variables in the corresponding stability equations, when the eigen-deformation is doubly localised. Comparisons with direct numerical simulations of the full buckling problem provide further insight into the accuracy and limitations of our approximations.

AB - A thin cantilever cylindrical shell subjected to a transverse shear force at the free end can experience two distinct modes of buckling, depending on its relative thickness and length. If the former parameter is fixed, then a short cylinder buckles in a diffuse manner, while the eigenmodal deformation of a moderately long shell is localised, both axially and circumferentially, near its fixed end. Donnell-type buckling equations for cylindrical shells are here coupled with a non-symmetric membrane basic state to produce a linear boundary-value problem that is shown to capture the transition between the aforementioned instability modes. The main interest lies in exploring the approximate asymptotic separation of the independent variables in the corresponding stability equations, when the eigen-deformation is doubly localised. Comparisons with direct numerical simulations of the full buckling problem provide further insight into the accuracy and limitations of our approximations.

KW - Cylindrical shells

KW - Localised buckling

KW - Multiple-scale asymptotics

KW - Shallow shell equations

UR - http://www.scopus.com/inward/record.url?scp=85045046432&partnerID=8YFLogxK

U2 - 10.1177/1081286517754133

DO - 10.1177/1081286517754133

M3 - Article

VL - 24

SP - 701

EP - 722

JO - Mathematics and Mechanics of Solids

JF - Mathematics and Mechanics of Solids

SN - 1081-2865

IS - 3

ER -