Skip Navigation


IMA Journal of Applied Mathematics Advance Access originally published online on December 17, 2004
IMA Journal of Applied Mathematics 2005 70(1):53-63; doi:10.1093/imamat/hxh059
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
70/1/53    most recent
hxh059v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Aron, M.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

IMA Journal of Applied Mathematics Vol. 70 No. 1 © Institute of Mathematics and its Applications 2005; all rights reserved.

Combined axial shearing, extension, and straightening of elastic annular cylindrical sectors*

M. Aron

School of Mathematics and Statistics, University of Plymouth, Drake Circus, Plymouth PL4 8AA, UK

The combined axial shearing, extension, and straightening of an annular cylindrical sector is a deformation that, following Truesdell & Noll (1965, The Non-Linear Field Theories of Mechanics, Encyclopedia of Physics III/3) and Hill (1973, Z. Angew. Math. Phys., 24, 609–618), we describe in terms of two prescribed constants and two unknown functions that depend only on the radial material coordinate. Under the assumption that the material is elastic, compressible, and isotropic we show that for equilibrium in the absence of body forces the unknown functions must satisfy a system of first-order nonlinear ordinary differential equations. The system of differential equations can be decoupled for certain material classes, one of which is the class of Hadamard–Green materials. Thus, several new exact solutions are obtained and, under the assumption that the annular cylindrical sector is composed of a Hadamard–Green material that is strongly elliptic, the existence and uniqueness of solutions for two types of boundary conditions is established.

Keywords: finite elastic deformations; nonlinear elastostatics.

* Dedicated to Ray W. Ogden on the occasion of his 60th birthday


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.