Skip Navigation

The Quarterly Journal of Mechanics and Applied Mathematics 2001 54(2):329-339; doi:10.1093/qjmam/54.2.329
© 2001 by Oxford University Press
This Article
Right arrow Full Text (PDF)
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 Knops, R. J.
Right arrow Articles by Villaggio, P.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

The High Cantilevered Beam of Minimal Compliance

Robin J. Knops1 and Piero Villaggio2

( 1 Department of Mathematics, Heriot–Watt University, Riccarton, Edinburgh EH14 4AS, Scotland 2 Dipartimento di Ingegneria Strutturale, Università di Pisa, Via Diotisalvi 2, 56126, Pisa, Italy )

The state of stress in a high (that is, blunt, tapering) trapezoidal cantilevered elastic beam loaded by a transverse force applied at the free end is determined by extending an approximate method proposed by Galerkin (Sbornik Len. Inst. 99 (1929)). The solution is used to solve the problem of finding, among the trapezoidal profiles of given area and width, that one which minimizes the compliance, or equivalently the displacement of the point of application of the load. The optimum profile is an isosceles trapezium, but certain additional conditions, for example those found in the bird kingdom, cause the optimum profile to become a non-symmetric trapezium two of whose adjacent sides contain a right angle.


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.