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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.
Department of Mathematical
Informatics
Graduate School of Information Science and Technology
University of Tokyo
Hongo 7-3-1, Bunkyo-ku
Tokyo 113-8656
Japan
