Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-05-13T01:27:31.276Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)