Skip Navigation


IMA Journal of Applied Mathematics Advance Access originally published online on August 24, 2006
IMA Journal of Applied Mathematics 2006 71(5):635-657; doi:10.1093/imamat/hxl014
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
71/5/635    most recent
hxl014v1
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 arrow Search for citing articles in:
ISI Web of Science (1)
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Kovtunenko, V. A.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Primal–dual methods of shape sensitivity analysis for curvilinear cracks with nonpenetration

V. A. Kovtunenko**

Lavrent'ev Institute of Hydrodynamics, 630090 Novosibirsk, Russia and Institute for Mathematics, University of Graz, 8010 Graz, Austria

** Email: kovtunen{at}kfunigraz.ac.at

Based on a level-set description of a crack moving with a given velocity, the problem of shape perturb-ation of the crack is considered. Nonpenetration conditions are imposed between opposite crack surfaces which result in a constrained minimization problem describing equilibrium of a solid with the crack. We suggest a minimax formulation of the state problem thus allowing curvilinear (nonplanar) cracks for the consideration. Utilizing primal–dual methods of shape sensitivity analysis we obtain the general formula for a shape derivative of the potential energy, which describes an energy-release rate for the curvilinear cracks. The conditions sufficient to rewrite it in the form of a path-independent integral (J-integral) are derived.

Keywords: curvilinear crack; nonpenetration; energy release; constrained minimization; shape sensitivity analysis; primal–dual methods.

Received on 12 August 2004. accepted on 20 July 2005.


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.