Vol. 2, No. 2, 2007

Download this article
Download this article For screen
For printing
Recent Issues

Volume 19
Issue 4, 541–746
Issue 4, 541–572
Issue 3, 303–540
Issue 2, 157–302
Issue 1, 1–156

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 8 issues

Volume 7, 10 issues

Volume 6, 9 issues

Volume 5, 6 issues

Volume 4, 10 issues

Volume 3, 10 issues

Volume 2, 10 issues

Volume 1, 8 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN 1559-3959 (online)
ISSN 1559-3959 (print)
 
Author index
To appear
 
Other MSP journals
Worst case plastic limit analysis of trusses under uncertain loads via mixed 0-1 programming

Yoshihiro Kanno and Izuru Takewaki

Vol. 2 (2007), No. 2, 245–273
Abstract

The paper presents a global optimization method to compute the minimum limit load factor of trusses subjected to unknown but bounded loads. We assume that the external forces consist of a part proportional to a load factor and a part that is uncertain around its nominal value. The worst-case limit load factor is introduced as the smallest limit load factor realized with some uncertain parameters. In order to detect the worst case, we have to find the global optimal solution of a nonconvex optimization problem, which is the major difficulty of the worst-case limit analysis. By reformulating the worst-case determination problem as a mixed 0-1 programming problem, we propose a global optimization algorithm as a combination of a branch-and-bound method based on the linear programming relaxations and a cutting plane method based on the disjunctive or lift-and-project cuts. The worst-case limit loads, as well as the corresponding critical loading patterns, are computed to demonstrate that our method converges to the global optimal solutions successfully.

Keywords
data uncertainty, limit analysis, integer programming, cutting plane, branch-and-bound, global optimization
Milestones
Received: 30 June 2006
Accepted: 23 September 2006
Published: 1 April 2007
Authors
Yoshihiro Kanno
Department of Mathematical Informatics
Graduate School of Information Science and Technology
University of Tokyo
Tokyo 113-8656
Japan
http://www.simplex.t.u-tokyo.ac.jp
Izuru Takewaki
Department of Urban and Environmental Engineering
Graduate School of Engineering
Kyoto University
Kyotodaigaku-Katsura, Nishikyo
Kyoto 615-8540
Japan
http://www.archi.kyoto-u.ac.jp/\%7ebge/tkwk/takewaki-new.html