AAR-based decomposition method for lower bound limit analysis

Despite recent progress in optimisation techniques, finite element stability analysis of realistic three-dimensional (3D) problems is still hampered by the size of the resulting optimisation problem. Current solvers may take a prohibitive computational time, if they give a solution at all. Possible remedies to this are the design of adaptive deremeshing techniques, decomposition of the system of equations, or the decomposition of the optimisation problem. This paper concentrates on the last approach, and presents an algorithm especially suited for limit analysis. Optimisation problems in limit analysis are in general convex but non-linear. This fact renders the design of decomposition techniques specially challenging. The efficiency of general approaches such as Benders or DantzigWolfe is not always satisfactory, and strongly depends on the structure of the optimisation problem. This work presents a new method that is based on rewriting the feasibility region of the global optimisation problem as the intersection of two subsets. By resorting to the Averaged Alternating Reflections (AAR) method in order to find the distance between the sets, the optimisation problem is successfully solved in a decomposed manner. Some representative examples illustrate the application of the method and its efficiency with respect to other well-known decomposition algorithms.