Summary
Linear flow splitting enables the forming of branched sheet metal products in integral style. To optimize those products design parameters have to be based on market requirements. We show that methods that are also used in Operations Research can, in principle, be applied to solve these optimization problems. For this, engineers provide constructive parameters that describe the demands of customers in a mathematical way. Based on these descriptions, we develop a two-stage model. First, a topology and shape optimization of branched sheet metal products is carried out, where the best-possible product is automatically designed by solving some OR models. Then, in stage two, we deal with the problem of how to incorporate manufacturing constraints for sheet metal products. The solution to this model corresponds to a construction plan. The entire approach is demonstrated in the design and construction of a cable conduit.
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R. Fletcher, N.I.M. Gould, S. Leyffer, Ph.L. Toint, A. Wächter. Global convergence of a trust-region SQP-filter algorithm for general nonlinear programming. SIAM J. Optim. 13: 635–659, 2002.
M.R. Garey, D.S. Johnson. Computers and Intractability: A Guide to the Theory of NP-completeness. W.H. Freeman, San Francisco, 1979.
P. Groche, G. v. Breitenbach, M. Jöckel, A. Zettler. New tooling concepts for the future roll forming applications. ICIT Conference. Bled, Yugoslvia, 2003.
D. Gross, W. Hauger, W. Schnell. Technische Mechanik, Bd. 2: Elastostatik. Springer, Berlin, 2005.
O.S. Hakimi. Optimal Locations of Switching Centers and Medians of a Graph. Operations Research 12:450–459, 1964.
M. Hintermüller, K. Ito, K. Kunisch. The primal-dual active set strategy as a semismooth Newton method. SIAM J. Optim. 13: 865–888, 2002.
J.-M. Ho, D.T. Lee, C.-H. Chang, C.K. Wong. Minimum diameter spanning trees and related problems. SIAM J. Computing 20: 987–997, 1991.
V. Hubka, E. W. Eder. Theorie technischer Systeme-Grundlagen einer wissenschaftlichen Konstruktionslehre. Springer-Verlag, Hamburg, 1984.
ILOG CPLEX Division. Suite 279, 930 Tahoe Blvd., Bldg 802, Incline Village, NV 89451, USA. Information available via WWW at URL http://www.cplex.com.
T. Sauer, M. Wäldele, H. Birkhofer. Providing Examples for Students and Designers. Proceedings of the NordDesign 2004 Conference, 340–349. Tampere, Finnland.
A. Schrijver. Theory of Linear and Integer Programming. Wiley, Chichester, 1986.
G. Specht, C. Beckmann. F&E Management, Schäffer Poeschel Verlag. Stuttgart, 1996.
N.P. Suh. Axiomatic Design-Advances and Applications. Oxford University Press, New York, 2001.
M. Ulbrich. Semismooth Newton methods for operator equations in function spaces. SIAM J. Optim. 13: 805–842, 2003.
S. Ulbrich. On the Superlinear Local Convergence of a Filter-SQP Method. Mathematical Programming 100:217–245, 2004.
S. Ulbrich, M. Ulbrich, L.N. Vincente. A Globally Convergent Primal-Dual Interior Point Filter Method for Nonconvex Nonlinear Programming. Mathematical Programming 100:379–410, 2004.
A. Wächter, L.T. Biegler. On the Implementation of an Interior-Point Filter Line-Search Algorithm for Large-Scale Nonlinear Programming. To appear in Mathematical Programming, 2005.
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© 2006 Springer-Verlag Berlin Heidelberg
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Birkhofer, H. et al. (2006). Optimization of Sheet Metal Products. In: Haasis, HD., Kopfer, H., Schönberger, J. (eds) Operations Research Proceedings 2005. Operations Research Proceedings, vol 2005. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-32539-5_52
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DOI: https://doi.org/10.1007/3-540-32539-5_52
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