Worst-case load in plastic limit analysis of frame structures

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.