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Analysis and computations for a model of quasi-static deformation of a thinning sheet arising in superplastic forming

Published online by Cambridge University Press:  25 September 2002

KLAUS DECKELNICK ,
CHARLES M. ELLIOTT  and
VANESSA STYLES
KLAUS DECKELNICK
Affiliation:
Centre for Mathematical Analysis and Its Applications, School of Mathematical Sciences, University of Sussex, Falmer, Brighton BN1 9QH, UK
CHARLES M. ELLIOTT
Affiliation:
Centre for Mathematical Analysis and Its Applications, School of Mathematical Sciences, University of Sussex, Falmer, Brighton BN1 9QH, UK
VANESSA STYLES
Affiliation:
Centre for Mathematical Analysis and Its Applications, School of Mathematical Sciences, University of Sussex, Falmer, Brighton BN1 9QH, UK
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Abstract

We consider a mathematical model for the quasi-static deformation of a thinning sheet. The model couples a first-order equation for the thickness of the sheet to a prescribed curvature equation for the displacement of the sheet. We prove a local in time existence and uniqueness theorem for this system when the sheet can be written as a graph. A contact problem is formulated for a sheet constrained to be above a mould. Finally we present some computational results.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 13 , Issue 4 , August 2002 , pp. 403 - 429
Copyright
2002 Cambridge University Press

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