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On p-harmonic functions, convex duality and an asymptotic formula for injection mould filling

Published online by Cambridge University Press:  26 September 2008

Gunnar Aronsson
Gunnar Aronsson
Affiliation:
Department of Mathematics, Linköping University, S-581 83 Linköping, Sweden
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Abstract

This work treats the injection of certain thermoplastics into a planar mould cavity. The problem is to determine the filling pattern. It is assumed that the thermoplastic can be modelled as a non-Newtonian fluid of power-law type whose power-law exponent is relatively small (the pseudo-plastic case). The dependence of the viscosity on thermal variations is neglected. The mathematical description leads to a moving boundary problem, for which an asymptotic solution is found. According to this solution, the expansion of the polymer melt follows the level sets of an interior distance function, which is determined by the geometry of the mould, and the position of the injection point. The solution is easily computed and results of numerical experiments are given.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 7 , Issue 5 , October 1996 , pp. 417 - 437
Copyright
Copyright © Cambridge University Press 1996

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