Abstract
We examine the structure of the marginal stability curves of an eigenvalue problem related to the buckling deformations observed during cold rolling of sheet metal. The instability in question is characterised by a centre "wave" pattern and arises as the interplay between the self-equilibrating residual stresses associated with the rolling process, on the one hand, and the traction force acting on the strip, on the other. When the latter effect dominates, we show that singular perturbation methods can be used to unravel a number of novel mathematical features of the linear bifurcation equation. We also provide simple quantitative formulae that facilitate an easy interpretation of the corresponding physical phenomena.
| Original language | English |
|---|---|
| Pages (from-to) | 826-832 |
| Number of pages | 7 |
| Journal | Mechanics Research Communications |
| Volume | 36 |
| Issue number | 7 |
| Early online date | 30 May 2009 |
| DOIs | |
| Publication status | Published - Oct 2009 |
| Externally published | Yes |
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The asymptotic limit of an eigenvalue problem related to the buckling of rolled elastic strips. / Coman, Ciprian D.
In: Mechanics Research Communications, Vol. 36, No. 7, 10.2009, p. 826-832.Research output: Contribution to journal › Article
TY - JOUR
T1 - The asymptotic limit of an eigenvalue problem related to the buckling of rolled elastic strips
AU - Coman, Ciprian D.
PY - 2009/10
Y1 - 2009/10
N2 - We examine the structure of the marginal stability curves of an eigenvalue problem related to the buckling deformations observed during cold rolling of sheet metal. The instability in question is characterised by a centre "wave" pattern and arises as the interplay between the self-equilibrating residual stresses associated with the rolling process, on the one hand, and the traction force acting on the strip, on the other. When the latter effect dominates, we show that singular perturbation methods can be used to unravel a number of novel mathematical features of the linear bifurcation equation. We also provide simple quantitative formulae that facilitate an easy interpretation of the corresponding physical phenomena.
AB - We examine the structure of the marginal stability curves of an eigenvalue problem related to the buckling deformations observed during cold rolling of sheet metal. The instability in question is characterised by a centre "wave" pattern and arises as the interplay between the self-equilibrating residual stresses associated with the rolling process, on the one hand, and the traction force acting on the strip, on the other. When the latter effect dominates, we show that singular perturbation methods can be used to unravel a number of novel mathematical features of the linear bifurcation equation. We also provide simple quantitative formulae that facilitate an easy interpretation of the corresponding physical phenomena.
KW - Boundary layers
KW - Buckling
KW - Elastic plates
KW - WKB analysis
UR - http://www.scopus.com/inward/record.url?scp=68149114392&partnerID=8YFLogxK
U2 - 10.1016/j.mechrescom.2009.05.008
DO - 10.1016/j.mechrescom.2009.05.008
M3 - Article
AN - SCOPUS:68149114392
VL - 36
SP - 826
EP - 832
JO - Mechanics Research Communications
JF - Mechanics Research Communications
SN - 0093-6413
IS - 7
ER -