AAR-based decomposition method for lower bound limit analysis

Abstract

Despite recent progress in the 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 de-remeshing techniques, decomposition of the system of equations, or the decomposition of the optimisation problem. In this paper we concentrate on the last approach, and present an algorithm especially suited for limit analysis.The optimisation problems in limit analysis are convex but non-linear. This fact renders the design of decomposition techniques specially challenging. The efficiency of general approaches such as Benders or Dantzig-Wolfe is not always satisfactory, and strongly depends on the structure of the optimisation problem. We here present 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 Alternate Reflections (AAR) in order to find the distance between the sets, we achieve to solve the optimisation problem in a decomposed manner. We illustrate the method with some representative problems, and comment its efficiency with respect to other well-known decomposition algorithms.

Editorial

“…In their paper, Muñoz and Rabiei (2015) present a decomposition method for lower bound limit analysis. Decomposition methods allow a large problem to be split into a series of smaller sub-problems that are solved separately, with a view to achieving savings in run times and/or required memory usage.…”