Vol. 8, No. 8-10, 2013

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ISSN: 1559-3959
Worst-case load in plastic limit analysis of frame structures

Yoshihiro Kanno

Vol. 8 (2013), No. 8-10, 415–439
Abstract
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This paper addresses the plastic limit analysis of a frame structure under uncertainty in the external load. Given a bounded set in which an external load can vary, we attempt to find the worst load that minimizes the limit load factor. It is shown that this problem can be formulated as a mixed-integer linear programming problem. The global optimal solution of this optimization problem can be found by using an existing algorithm, e.g., a branch-and-cut method. Guaranteed convergence to a global optimal solution is important because it implies that the proposed method yields neither overestimation nor underestimation in this uncertainty analysis problem. Two numerical examples illustrate that the worst scenario problem can be solved with modest computational effort. They also show that not only does the limit load factor depend on the level of uncertainty in the external load, but the collapse mode as well.

Keywords
robustness, uncertainty, worst scenario detection, plastic limit analysis, global optimization, mixed-integer programming
Milestones
Received: 10 March 2013
Revised: 19 July 2013
Accepted: 19 August 2013
Published: 30 December 2013
Authors
Yoshihiro Kanno
Department of Mathematical Informatics
Graduate School of Information Science and Technology
University of Tokyo
Hongo 7-3-1, Bunkyo-ku
Tokyo 113-8656
Japan