The asymptotic limit of an eigenvalue problem related to the buckling of rolled elastic strips

Research output: Contribution to journalArticle

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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.

LanguageEnglish
Pages826-832
Number of pages7
JournalMechanics Research Communications
Volume36
Issue number7
Early online date30 May 2009
DOIs
Publication statusPublished - Oct 2009
Externally publishedYes

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buckling
Buckling
strip
eigenvalues
cold rolling
metal sheets
traction
Cold rolling
Sheet metal
residual stress
Residual stresses
perturbation
curves

Cite this

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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.",
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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 journalArticle

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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.

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