Closed-form solutions, extremality and nonsmoothness criteria in a large deformation elasticity problem

Gao, D.Y. and Ogden, R.W. (2008) Closed-form solutions, extremality and nonsmoothness criteria in a large deformation elasticity problem. Zeitschrift für Angewandte Mathematik und Physik, 59(3), pp. 498-517. (doi:10.1007/s00033-007-7047-1)

Full text not currently available from Enlighten.

Abstract

The pure azimuthal shear problem for a circular cylindrical tube of nonlinearly elastic material, both isotropic and anisotropic, is examined on the basis of a complementary energy principle. For particular choices of strain-energy function, one convex and one non-convex, closed-form solutions are obtained for this mixed boundary-value problem, for which the governing differential equation can be converted into an algebraic equation. The results for the non-convex strain energy function provide an illustration of a situation in which smooth analytic solutions of a nonlinear boundary-value problem are not global minimizers of the energy in the variational statement of the problem. Both the global minimizer and the local extrema are identified and the results are illustrated for particular values of the material parameters.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Ogden, Professor Raymond
Authors: Gao, D.Y., and Ogden, R.W.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Zeitschrift für Angewandte Mathematik und Physik
Journal Abbr.:ZAMP
ISSN:0044-2275
ISSN (Online):1420-9039
Published Online:05 August 2007

University Staff: Request a correction | Enlighten Editors: Update this record