Integer linear programming models for topology optimization in sheet metal design

Mathematical Methods of Operations Research

Volumn 68, Issue 2, 2008, Pages 313-331

  Fügenschuh, Armin ^a   Fügenschuh, Marzena ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Discretization; Integer programming; Multicommodity flow; Separation; Sheet metal products; Topology optimization

Indexed keywords

COMPUTER AIDED ENGINEERING; DESIGN; DYNAMIC PROGRAMMING; INTEGER PROGRAMMING; LINEAR PROGRAMMING; LINEARIZATION; MATHEMATICAL MODELS; METALS; OPTIMIZATION; PARTICLE SIZE ANALYSIS; PROCESS DESIGN; PROCESS ENGINEERING; STRUCTURAL OPTIMIZATION; THREE DIMENSIONAL; TOPOLOGY;

DISCRETIZATION; MULTICOMMODITY FLOW; SEPARATION; SHEET METAL PRODUCTS; TOPOLOGY OPTIMIZATION;

SHEET METAL;

EID: 53149086289     PISSN: 14322994     EISSN: 14325217     Source Type: Journal    
DOI: 10.1007/s00186-008-0223-z     Document Type: Article

References (25)

1. Achterberg T (2004) SCIP-a framework to constraint and mixed integer programming. ZIB Report 04-19, Berlin
2. Applegate DL, Bixby RE, Chvatal V, Cook WJ (2006) The traveling salesman problem: a computational study. Princeton University Press, 606 pp
3. MP Bendsøe N Kikuchi 1988 Generating optimal topologies in structural design using a homogenization method Comput Methods Appl Mech Eng 71 2 197 224
4. Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods and applications. Springer, Berlin, p 370
5. Birkhofer H, Fügenschuh A, Günther U, Junglas D, Martin A, Sauer T, Ulbrich S, Wäldele M, Walter S (2006) Topology- and shape-optimization of branched sheet metal products. In: Haasis H, Kopfer H, Schönberger J(eds) Operations research proceedings 2005. Springer, Berlin, pp 327-336
6. W Dobbs LP Felton 1969 Optimization of truss geometry Proc ASCE 95 2105 2119
7. W Dorn R Gomory H Greenberg 1964 Automatic design of optimal structures Journal de Mechanique 3 25 52
8. Ehrgott M (2000) Multicriteria optimization. Springer, Berlin
9. Groche P, Breitenbach Gv, Jöckel M, Zettler A (2003) New tooling concepts for the future roll forming applications. ICIT Conference. Bled, Yugoslavia
10. Gross D, Hauger W, Schnell W (2005) Technische Mechanik, Bd. 2: Elastostatik. Springer, Berlin (In German)
11. Hochbaum D (2008) The pseudoflow algorithm: a new algorithm for the maximum flow problem. Oper Res (to appear)
12. Kang Z, Zhang C, Cheng G (2005) Structural topology optimization considering mass moment of inertia. In: Proc. of the 6th world congresses of structural and multidisciplinary optimization, Rio de Janeiro, Paper No. 4611
13. Kessel S, Fröng D (1998) Technische Mechanik-technical mechanics. Teubner Verlag, Stuttgart
14. RV Kohn G Strang 1986 Optimal design in elasticity and plasticity Numer Methods Eng 22 183 188
15. Kohn RV, Strang G (1986b) Optimal design and relaxation of variational problems. In: Communications in pure and applied mathematics, vol 39, pp 1-25 (Part I)
16. Kohn RV, Strang G (1986b) Optimal design and relaxation of variational problems. In: Communications in pure and applied mathematics, vol 39, pp 139-182 (Part II)
17. Kohn RV, Strang G (1986b) Optimal design and relaxation of variational problems. In: Communications in pure and applied mathematics, vol 39, pp 353-357 (Part III)
18. Kühhorn A, Silber G (2000) Technische Mechanik für Ingenieure. Hüthig Verlag, Heidelberg (In German)
19. Meyberg K, Vachenauer P (1997) Höhere Mathematik 1. Springer, Berlin, Heidelberg (In German)
20. AGM Michell 1904 The limits of economy of material in frame structures Philos Mag 8 6 589 597
21. Nemhauser G, Wolsey L (1998) Integer programming and combinatorial optimization. Wiley, Philadelphia
22. GIN Rozvany 2001 Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics Struct Multidiscip Optim 21 2 90 108
23. M Stolpe 2007 On the reformulation of topology optimization problems as linear or convex quadratic mixed 0-1 programs Optim Eng 8 2 163 192
24. M Stolpe K Svanberg 2003 Modeling topology optimization problems as linear mixed 0-1 programs Int J Numer Methods Eng 57 5 723 739
25. Wunderling R (1996) Paralleler und Objektorientierter Simplex-Algorithmus. ZIB Report TR 96-09, Berlin