## Abstract

The authors consider the two-point boundary-value problem resulting from the equations of nonlinear elastostatics for azimuthal shear of a Blatz-Ko tube. Previous work on this problem by Simmonds and Warne includes a numerical study of these equations and indicates that smooth radial deformation solutions (no kinks) should exist regardless of the aspect ratio of the tube, provided that the dimensionless applied torque τ is small enough (τ <≈ 0.72). The numerics of Simmonds and Warne also indicated that the existence of smooth solutions for τ >≈ 0.72 depends on the geometry of the tube, and that for τ = √3, no smooth solution exists. Motivated by this numerical work, the authors prove via a topological shooting argument the existence and uniqueness of smooth solutions to this problem for τ ≤ τ_{cr} = √3/4^{4/3} ≈ 0.69, and the nonexistence of smooth solutions for τ = √3.

Original language | English (US) |
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Pages (from-to) | 53-69 |

Number of pages | 17 |

Journal | Mathematics and Mechanics of Solids |

Volume | 3 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1998 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Materials Science(all)
- Mechanics of Materials