Mathematical Models and Polyhedral Studies for Integral Sheet Metal Design

Abstract

Using the new manufacturing technique linear flow splitting it is possible to produce branched sheet metal products containing several chambers out of one piece of sheet metal. This yields a wide variety of possible products. Even if the geometry of a profile is given, it is open how to produce it, that is how to unroll it. With every additional branch the number of possible ways to produce a profile increases exponentially. In this paper we present how the problem of finding a valid unrolling that approximates a given geometry as close as possible can be modelled as a discrete optimization problem. In order to be able to solve the model in reasonable time, further modifications are necessary. In this context we give the complete convex hull description of some substructures of the underlying polyhedron. Moreover, we introduce a new class of facet-defining inequalities that represent connectivity constraints for the profile. Finally, we will show how these inequalities can be separated in polynomial time.