Out-of-plane buckling in two-dimensional glass drawing
We derive a mathematical model for the drawing of a two-dimensional thin sheet of viscous fluid in the direction of gravity. If the gravitational field is sufficiently strong, then a portion of the sheet experiences a compressive stress and is thus unstable to transverse buckling. We analyse the dep...
| Main Authors: | , , , , |
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| Format: | Journal article |
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Cambridge University Press
2019
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| _version_ | 1826260362571284480 |
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| author | O'Kiely, D Breward, C Griffiths, I Howell, P Lange, U |
| author_facet | O'Kiely, D Breward, C Griffiths, I Howell, P Lange, U |
| author_sort | O'Kiely, D |
| collection | OXFORD |
| description | We derive a mathematical model for the drawing of a two-dimensional thin sheet of viscous fluid in the direction of gravity. If the gravitational field is sufficiently strong, then a portion of the sheet experiences a compressive stress and is thus unstable to transverse buckling. We analyse the dependence of the instability and the subsequent evolution on the process parameters, and the mutual coupling between the weakly nonlinear buckling and the stress profile in the sheet. Over long time scales, the sheet centreline ultimately adopts a universal profile, with the bulk of the sheet under tension and a single large bulge caused by a small compressive region near the bottom, and we derive a canonical inner problem that describes this behaviour. The large-time analysis involves a logarithmic asymptotic expansion, and we devise a hybrid asymptotic–numerical scheme that effectively sums the logarithmic series. |
| first_indexed | 2024-03-06T19:04:26Z |
| format | Journal article |
| id | oxford-uuid:14a55d59-2620-41c0-82aa-c3cded943166 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:04:26Z |
| publishDate | 2019 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | oxford-uuid:14a55d59-2620-41c0-82aa-c3cded9431662022-03-26T10:21:02ZOut-of-plane buckling in two-dimensional glass drawingJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:14a55d59-2620-41c0-82aa-c3cded943166Symplectic Elements at OxfordCambridge University Press2019O'Kiely, DBreward, CGriffiths, IHowell, PLange, UWe derive a mathematical model for the drawing of a two-dimensional thin sheet of viscous fluid in the direction of gravity. If the gravitational field is sufficiently strong, then a portion of the sheet experiences a compressive stress and is thus unstable to transverse buckling. We analyse the dependence of the instability and the subsequent evolution on the process parameters, and the mutual coupling between the weakly nonlinear buckling and the stress profile in the sheet. Over long time scales, the sheet centreline ultimately adopts a universal profile, with the bulk of the sheet under tension and a single large bulge caused by a small compressive region near the bottom, and we derive a canonical inner problem that describes this behaviour. The large-time analysis involves a logarithmic asymptotic expansion, and we devise a hybrid asymptotic–numerical scheme that effectively sums the logarithmic series. |
| spellingShingle | O'Kiely, D Breward, C Griffiths, I Howell, P Lange, U Out-of-plane buckling in two-dimensional glass drawing |
| title | Out-of-plane buckling in two-dimensional glass drawing |
| title_full | Out-of-plane buckling in two-dimensional glass drawing |
| title_fullStr | Out-of-plane buckling in two-dimensional glass drawing |
| title_full_unstemmed | Out-of-plane buckling in two-dimensional glass drawing |
| title_short | Out-of-plane buckling in two-dimensional glass drawing |
| title_sort | out of plane buckling in two dimensional glass drawing |
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