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Integer linear programming models for topology optimization in sheet metal design

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  • Armin Fügenschuh
  • Marzena Fügenschuh

Abstract

The process of designing new industrial products is in many cases solely based on the intuition and experience of the responsible design engineer. The aid of computers is restricted to visualization and manual manipulation tools. We demonstrate that the design process for conduits, which are made out of sheet metal plates, can be supported by mathematical optimization models and solution techniques, leading to challenging optimization problems. The design goal is to find a topology that consists of several channels with a given cross section area using a minimum amount of sheet metal and, at the same time, maximizing its stiffness. We consider a mixed integer linear programming model to describe the topology of two dimensional slices of a three dimensional sheet metal product. We give different model formulations, based on cuts and on multicommodity flows. Numerical results for various test instances are presented. Copyright Springer-Verlag 2008

Suggested Citation

  • Armin Fügenschuh & Marzena Fügenschuh, 2008. "Integer linear programming models for topology optimization in sheet metal design," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(2), pages 313-331, October.
    • Handle: RePEc:spr:mathme:v:68:y:2008:i:2:p:313-331
    DOI: 10.1007/s00186-008-0223-z
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    References listed on IDEAS

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    1. Dorit S. Hochbaum, 2008. "The Pseudoflow Algorithm: A New Algorithm for the Maximum-Flow Problem," Operations Research, INFORMS, vol. 56(4), pages 992-1009, August.
    2. Herbert Birkhofer & Armin Fügenschuh & Ute Günther & Daniel Junglas & Alexander Martin & Thorsten Sauer & Stefan Ulbrich & Martin Wäldele & Stephan Walter, 2006. "Optimization of Sheet Metal Products," Operations Research Proceedings, in: Hans-Dietrich Haasis & Herbert Kopfer & Jörn Schönberger (ed.), Operations Research Proceedings 2005, pages 327-336, Springer.
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