Vol. 2, No. 2, 2007

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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

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.

data uncertainty, limit analysis, integer programming, cutting plane, branch-and-bound, global optimization
Received: 30 June 2006
Accepted: 23 September 2006
Published: 1 April 2007
Yoshihiro Kanno
Department of Mathematical Informatics
Graduate School of Information Science and Technology
University of Tokyo
Tokyo 113-8656
Izuru Takewaki
Department of Urban and Environmental Engineering
Graduate School of Engineering
Kyoto University
Kyotodaigaku-Katsura, Nishikyo
Kyoto 615-8540