Chapman, S. J. (1999) Vacuum moulding of a superplastic in two dimensions. IMA Journal of Applied Mathematics, 63 (3). pp. 217246. ISSN 14643634

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Abstract
A mathematical model is proposed for the process of vacuum superplastic forming. The model exploits the fact that in most industrial applications the sheet aspect ratio (thickness/sheet width) is small. After an initial consideration of some of the more general properties and the literature of superplastic materials, the elastic/plastic deformation of an internallyinflated thinwalled cylinder is examined. Plates of arbitrary geometry are then considered. A quasisteady model in which the sheet moves through a sequence of steady states is developed. Some simplified closedform solutions are examined, but for general cases a system of nonlinear partial differential equations must be solved numerically. An efficient and accurate semiexplicit numerical scheme is proposed and a simplified stability analysis is presented; the method is then used to compute properties of superplastic vacuum moulded sheets in a number of practically motivated cases.
Item Type:  Article 

Subjects:  H  N > Mechanics of deformable solids O  Z > Partial differential equations 
Research Groups:  Oxford Centre for Industrial and Applied Mathematics 
ID Code:  596 
Deposited By:  Jon Chapman 
Deposited On:  18 May 2007 
Last Modified:  29 May 2015 18:25 
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