MATHEMATICAL ENGINEERING TECHNICAL REPORTS Worst-Case Plastic Limit Analysis of Trusses under Uncertain Loads via Mixed 0-1 Programming

The paper presents a global optimization method to compute the minimum limit load factor of trusses under the unknown-but-bounded load uncertainty. 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. By reformulating the worstcase determination problem as a mixed 0-1 programming problem, we propose a global optimization algorithm as a combination of a branch-and-boud 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.