Worst case plastic limit analysis of trusses under uncertain loads via mixed 0-1 programming

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.