Multidimensional max-flow method and its application for plastic analysis

This paper expands the use of network flows to the multidimensional case, in which network flows are associated with vectors, instead of the conventionally used scalar values. A method for solving a multidimensional max-flow problem is systematically developed, on the basis of the primal-dual algorithm. It is demonstrated that upon reduction to a one-dimensional case, the method is transformed to the known Ford and Fulkerson algorithm. This multidimensional flow network can be applied to a variety of engineering applications, as the variables underlying engineering systems frequently possess a vector form. In this paper, the multidimensional max-flow problem is shown to correspond to the problem of plastic analysis of trusses. q 2005 Published by Elsevier Ltd.