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The deformation of rubber cylinders and tubes by rotation

Published online by Cambridge University Press:  17 February 2009

P. Chadwick ,
C. F. M. Creasy  and
V. G. Hart
P. Chadwick
Affiliation:
School of Mathematics and Physics, University of East Anglia, Norwich, England
C. F. M. Creasy
Affiliation:
Department of Mathematics, University of Queenland, St Lucia, Q. 4067, Australia
V. G. Hart
Affiliation:
Department of Mathematics, University of Queenland, St Lucia, Q. 4067, Australia
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Abstract

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A detailed analytical and numerical study is made of the deformation of highly elastic circular cylinders and tubes produced by steady rotation about the axis of symmetry. Explicit results are obtained through the use of Ogden's strain–energy function for incompressible isotropic elastic materials which, as well as being analytically convenient, is capable of reproducing accurately the observed isothermal behaviour of vulcanized rubber over a wide range of deformations. The three problems of steady rotation considered here concern (i) a tube shrink-fitted to a rigid spindle, (ii)an unconstrained tube, and (iii) a solid cylinder. In each case a set of restictions on the material constans appearing in the strain–energy function is stated which ensures that a tubular of cylindrical shape-preserving deformation exists for all angular spees and that, for problems (i) and (iii), there is no other solution. In connection with problems (ii) and (iii) values of the material constans are also given which correspond to the bifuraction or non-existence of soultions. Enegry consideration are used to determine the local stability of the various solutions obtained.

Type
Research Article
Information
The ANZIAM Journal , Volume 20 , Issue 1 , June 1977 , pp. 62 - 96
Copyright
Copyright © Australian Mathematical Society 1977

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