Out-of-plane buckling in two-dimensional glass drawing
| Autor: | Ian M. Griffiths, Chris Breward, Peter Howell, Doireann O'Kiely, Ulrich Lange |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Coupling
Physics Tension (physics) Mechanical Engineering 020207 software engineering 02 engineering and technology Mechanics Viscous liquid Condensed Matter Physics 01 natural sciences Instability 010305 fluids & plasmas Transverse plane Buckling Gravitational field Mechanics of Materials 0103 physical sciences 0202 electrical engineering electronic engineering information engineering Asymptotic expansion |
| Zdroj: | Journal of Fluid Mechanics. 869 |
| ISSN: | 1469-7645 0022-1120 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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