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A new technique for forming sheet metal makes it possible to construct branched sheet metal products out of one piece of sheet metal. Since the number of potential ways to produce one and the same component increases exponentially with every additional branch, appropriate tools for handling the large number of possibilities are necessary. In this paper we give a Mixed Integer Program that models the different ways of producing branched profiles and show how to incorporate manufacturing constraints into the model.

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.

In order to shorten the design process of a multi-chambered profile, it is important to integrate the Technological Findings of the production and the evaluation of the manufactured product in a structured and systematic way, providing mathematical optimization. The development of profiles exposed to cyclic mechanical loading has to take into consideration their fatigue properties. This paper proposes a classification structure of the existing Technological Findings of Linear Flow Splitting and the continuous manufacturing line. The classification is realized by an ontology, modeling the manufacturing processes, machines, the geometry of the semi-finished product, sub-processes, engaged machine components and specific conditions for the employed material. A profile manufactured by linear flow splitting is subject to severe changes of local material properties. This affects the fatigue properties of the profile. The paper focuses on preparing the integration of these fatigue properties in a simplified approach into the mathematical optimization. The approach is developed by modeling examples of profiles with different material properties by methods of mathematical optimization. The examples are applied to a numerical fatigue evaluation. Results and conclusions drawn of this analysis are incorporated in the ontology as data and rules, serving as an input for the optimization.