Structural shape and topology optimization in a level-set-based framework of region representation

Structural and Multidisciplinary Optimization

Volumn 27, Issue 1-2, 2004, Pages 1-19

  Wang, X ^a   Wang, M Y ^b   Guo, D ^a  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Boundary optimization; Level set methods; Region representation; Shape optimization; Structural optimization; Topology optimization

Indexed keywords

COMPUTATIONAL METHODS; ELASTICITY; FINITE ELEMENT METHOD; ITERATIVE METHODS; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; STRESSES; STRUCTURAL OPTIMIZATION; TOPOLOGY; VARIATIONAL TECHNIQUES;

BOUNDARY OPTIMIZATION; LEVEL-SET METHODS; REGION REPRESENTATION; SHAPE OPTIMIZATION; TOPOLOGY OPTIMIZATION;

STRUCTURAL DESIGN;

EID: 2642524473     PISSN: 1615147X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00158-003-0363-y     Document Type: Article

References (37)

1. Allaire, G. 1997: The homogenization method for topology and shape optimization. In: Rozvany, G. (ed.) Topology Optimization in Structural Mechanics, pp. 101-133
2. Allaire, G.; Jouve, F.; Taoder, A.-M. 2002: A level-set method for shape optimization. C. R. Acad. Sci. Paris, Ser. 1334, 1-6
3. Bendsoe, M.P. 1989: Optimal shape design as a material distribution problem. Struct. Optim. 1, 193-202
4. Bendsoe, M.P. 1997: Optimization of Structural Topology, Shape and Material. Berlin: Springer
5. Bendsoe, M.P. 1999: Variable-topology optimization: Status and challenges. In: Wunderlich, W. (ed.) Proceedings of the European Conference on Computational Mechanics (held in Munich, Germany)
6. Bendsoe, M.P.; Haber, R. 1993: The Michell layout problem as a low volume fraction limit of the homogenization method for topology design: an asymptotic study. Struct. Optim. 6, 63-267
7. Bendsoe, M.P.; Kikuchi, N. 1988: Generating optimal topologies in structural design using a homogenisation method. Comput. Methods Appl. Mech. Eng. 71, 197-224
8. Bendsoe, M.P.; Sigmund, O. 1999: Material interpolations in topology optimization. Arch. Appl. Mech. 69, 635-654
9. Breen, D.; Whitaker, R. 2001: A level set approach for the metamorphosis of solid models. IEEE Trans. Visual. Comput. Graphics 7(2), 173-192
10. Bulman, S.; Sienz, J.; Hinton, E. 2001: Comparisons between algorithms for structural topology optimization using a series of benchmark studies. Comput. Struct. 79, 1203-1218
11. Diaz, A.R.; Bendsoe, M.P. 1992: Shape optimization of structures for multiple loading conditions using a homogenization method. Struct. Optim. 4, 17-22
12. Eschenauer, H.A.; Kobelev, H.A.; Schumacher, A. 1994: Bubble method for topology and shape optimization of structures. Struct. Optim. 8, 142-151
13. Eschenauer, H.A.; Schumacher, A. 1997: Topology and shape optimization procedures using hole positioning criteria. In: Rozvany, G. (ed.) Topology Optimization in Structural Mechanics, pp. 135-196. Wien: Springer
14. Lewinski, T.; Sokolowski, J.; Zochowski, A. 1999: Justification of the bubble method for the compliance minimization problems of plates and spherical shells. Proc. 3rd World Congress of Structural and Multidisciplinary Optimization (WCSMO-3) (held in Buffalo, NY)
15. Lin, C.Y.; Chao, L.-S. 2000: Automated image interpretation for integrated topology and shape optimization. Struct. Multidisc. Optim. 20, 125-137
16. Mlejnek, H.P. 1992: Some aspects of the genesis of structures. Struct. Optim. 5, 64-69
17. Osher, S.; Sethian, J.A. 1988: Front propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79, 12-49
18. Osher, S.; Fedkiw, R. Level set methods: an overview and some recent results. J. Comput. Phys. 169, 475-502
19. Peng, D.; Merriman, B.; Osher, S.; Zhao, H.-K.; Kang, M. 1999: A PED-based fast local level set method. J. Comput. Phys. 155, 410-438
20. Reynolds, D.; McConnachie, J.P.; Bettess, W.; Christie, C.; J. Bull, W. 1999: Reverse Adaptivity - a new evolutionary tool for structural optimization. Int. J. Numer. Methods Eng. 45, 529-552
21. Rozvany, G. 1989: Structural Design via Optimality Criteria. Dordrecht: Kluwer
22. Rozvany, G.; Zhou, M. 1991: The COG algorithm, Part II: topological, geometrical and generalized shape optimization. Comput. Methods Appl. Mech. Eng. 89, 309-336
23. Rozvany, G.; Zhou, M.; Birker, T. 1992: Generalized shape optimization without homogenization. Struct. Optim. 4, 250-252
24. Rozvany, G. 2001: Aims, scope, methods, history and unified terminology of computer aided topology optimization in structural mechanics. Struct. Multidisc. Optim. 21, 90-108
25. Sapiro, G. 2001: Geometric Partial Differential Equations and Image Analysis. Cambridge: Cambridge University Press
26. Sethian, J.A.; Wiegmann, A. 2000: Structural boundary design via level set and immersed interface methods. J. Comput. Phys. 163(2), 489-528
27. Sethian, J.A. 1999: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge: Cambridge University Press
28. Shu, C.-W. 1988: Total-variation-diminishing time discretization. SIAM J. Sci. Stat. Comput. 9, 1073-1084
29. Shu, C.-W.; Osher, S. 1988: Efficient implementation of essentially non-oscillatory shock capture schemes. J. Comput. Phys. 77, 439-471
30. Sigmund, O. 2000: Topology optimization: A tool for the tailoring of structures and materials. Philos. Trans.: Math. Phys. Eng. Sci. 358, 211-228
31. Sigmund, O. 2001: A 99 topology optimization code written in Matlab. Struct. Multidisc. Optim. 21, 120-718
32. Sokolowski, J.; Zochowski, A. 1999: On the topological derivative in shape optimization. SIAM J. Control Optim. 37(4), 1251-1272
33. Sokolowski, J.; Zolesio, J.P. 1992: Introduction to Shape Optimization: Shape Sensitivity Analysis. New York: Springer-Verlag
34. Suzuki, K.; Kikuchi, N. 1991: A homogenization method for shape and topology optimization. Comput. Methods Appl. Mech. Eng. 93, 291-381
35. Wang, M.Y.; Wang, X.M.; Guo, D.M. 2003: A level set method for structural topology optimization. Comput. Methods Appl. Mech. Eng. 192(1-2), 227-246
36. Wang, M.Y.; Wang, X.M. 2003: A multi-phase level set model for multi-material structural optimization. Proc. 5th World Congress of Structural and Multidisciplinary Optimization (WCSMO5) (held in Lido di Jesolo, Italy)
37. Xie, Y.M.; Steven, G.P. 1997: Evolutionary Structural Optimization. New York: Springer