Abstract
A novel application of boundary-layer asymptotic techniques to a generalized linear eigenvalue problem is presented. Our investigation is concerned with a bifurcation equation that governs the formation of wrinkles in thin annular plates subjected to in-plane tensile loading on the inner boundary. If η denotes the ratio of the inner and outer radii of the annulus, then the critical wrinkling load satisfies Λ = ΛC(η), where the function ΛC is available only numerically. It is known that there is a critical value ̂η such that Λ → ∞ as η → ̂η but, until now, little has been understood about this singular behaviour. Asymptotic methods enable us to capture accurately and describe the nature of this blow-up phenomenon which we show is sensitive to the forms of the boundary conditions imposed at the edges of the annular plate. Our analytical findings are complemented by a series of comparisons with direct numerical simulations that shed further light on the singular behaviour.
| Original language | English |
|---|---|
| Pages (from-to) | 319-336 |
| Number of pages | 18 |
| Journal | Quarterly Journal of Mechanics and Applied Mathematics |
| Volume | 60 |
| Issue number | 3 |
| Early online date | 6 Jul 2007 |
| DOIs | |
| Publication status | Published - Aug 2007 |
| Externally published | Yes |
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Singular behaviour in a generalized boundary eigenvalue problem for annular plates in tension. / Coman, Ciprian D.; Bassom, Andrew P.
In: Quarterly Journal of Mechanics and Applied Mathematics, Vol. 60, No. 3, 08.2007, p. 319-336.Research output: Contribution to journal › Article
TY - JOUR
T1 - Singular behaviour in a generalized boundary eigenvalue problem for annular plates in tension
AU - Coman, Ciprian D.
AU - Bassom, Andrew P.
PY - 2007/8
Y1 - 2007/8
N2 - A novel application of boundary-layer asymptotic techniques to a generalized linear eigenvalue problem is presented. Our investigation is concerned with a bifurcation equation that governs the formation of wrinkles in thin annular plates subjected to in-plane tensile loading on the inner boundary. If η denotes the ratio of the inner and outer radii of the annulus, then the critical wrinkling load satisfies Λ = ΛC(η), where the function ΛC is available only numerically. It is known that there is a critical value ̂η such that Λ → ∞ as η → ̂η but, until now, little has been understood about this singular behaviour. Asymptotic methods enable us to capture accurately and describe the nature of this blow-up phenomenon which we show is sensitive to the forms of the boundary conditions imposed at the edges of the annular plate. Our analytical findings are complemented by a series of comparisons with direct numerical simulations that shed further light on the singular behaviour.
AB - A novel application of boundary-layer asymptotic techniques to a generalized linear eigenvalue problem is presented. Our investigation is concerned with a bifurcation equation that governs the formation of wrinkles in thin annular plates subjected to in-plane tensile loading on the inner boundary. If η denotes the ratio of the inner and outer radii of the annulus, then the critical wrinkling load satisfies Λ = ΛC(η), where the function ΛC is available only numerically. It is known that there is a critical value ̂η such that Λ → ∞ as η → ̂η but, until now, little has been understood about this singular behaviour. Asymptotic methods enable us to capture accurately and describe the nature of this blow-up phenomenon which we show is sensitive to the forms of the boundary conditions imposed at the edges of the annular plate. Our analytical findings are complemented by a series of comparisons with direct numerical simulations that shed further light on the singular behaviour.
UR - http://www.scopus.com/inward/record.url?scp=34547888012&partnerID=8YFLogxK
U2 - 10.1093/qjmam/hbm009
DO - 10.1093/qjmam/hbm009
M3 - Article
VL - 60
SP - 319
EP - 336
JO - Quarterly Journal of Mechanics and Applied Mathematics
JF - Quarterly Journal of Mechanics and Applied Mathematics
SN - 0033-5614
IS - 3
ER -