A level set method for topology optimization of heat conduction problem under multiple load cases

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 4-6, 2007, Pages 1074-1084

  Zhuang, ChunGang ^a   Xiong, ZhenHua ^a   Ding, Han ^a  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

Heat conduction; Level set method; Multiple load cases; Shape derivative; Topological derivative; Topology optimization

Indexed keywords

EQUATIONS OF STATE; OPTIMIZATION; SET THEORY; TOPOLOGY;

LEVEL SET METHOD; MULTIPLE LOAD CASES; SHAPE DERIVATIVE; TOPOLOGICAL DERIVATIVE; TOPOLOGY OPTIMIZATION;

HEAT CONDUCTION;

EQUATIONS OF STATE; HEAT CONDUCTION; OPTIMIZATION; SET THEORY; TOPOLOGY;

EID: 33750448337     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2006.08.005     Document Type: Article

References (41)

1. Xie Y.M., and Steven G.P. Optimal design of multiple load case structures using an evolutionary procedure. Engrg. Comput. 11 (1994) 295-302
2. Xie Y.M., and Steven G.P. A simple evolutionary procedure for structural optimization. Comput. Struct. 49 (1993) 885-896
3. Li Q., Steven G.P., Querin O.M., and Xie Y.M. Shape and topology design for heat conduction by evolutionary structural optimization. Int. J. Heat Mass Transfer 42 (1999) 3361-3371
4. Neagu M., and Bejan A. Constructal-theory tree networks of constant thermal resistance. J. Appl. Phys. 86 2 (1999) 1136-1144
5. Cheng X., Li Z., and Guo Z. Constructs of highly effective heat transport paths by bionic optimization. Sci. China Ser. E - Engrg. Mater. Sci. 46 3 (2003) 296-302
6. Bendsoe M., and Sigmund O. Topology Optimization: Theory Methods and Application (2003), Springer-Verlag, New York
7. Allaire G. Shape Optimization by the Homogenization Method (2002), Springer-Verlag, New York
8. Bendsoe M., and Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Engrg. 71 2 (1988) 197-224
9. Diaz A.R., and Bendsoe M.P. Shape optimization of structures for multiple loading conditions using a homogenization method. Struct. Optim. 4 (1992) 17-22
10. Rozvany G.I.N. Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics. Struct. Multidiscip. Optim. 21 2 (2001) 90-108
11. Donoso A., and Sigmund O. Topology optimization of multiple physics problems modeled by poisson's equation. Latin Am. J. Solids Struct. 1 (2004) 169-189
12. Sigmund O., and Petersson J. Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct. Multidiscip. Optim. 16 1 (1998) 68-75
13. Wang M.Y., and Wang S. Bilateral filtering for structural topology optimization. Int. J. Numer. Methods Engrg. 63 13 (2005) 1911-1938
14. Haber R.B., Jog C.S., and Bendsoe M. A new approach to variable-topology shape design using a constraint on perimeter. Struct. Optim. 11 (1996) 1-12
15. Sethian J.A., and Wiegmann A. Structural boundary design via level set and immersed interface methods. J. Comput. Phys. 163 (2000) 489-528
16. Osher S., and Santosa F. Level set methods for optimization problems involving geometry and constraints, I. Frequencies of a two-density inhomogeneous drum. J. Comput. Phys. 171 (2001) 272-288
17. Allaire G., Jouve F., and Toader A.M. Structural optimization using sensitivity analysis and a level set method. J. Comput. Phys. 194 (2004) 363-393
18. Allaire G., and Jouve F. A level-set method for vibration and multiple loads structural optimization. Comput. Methods Appl. Mech. Engrg. 194 (2005) 3269-3290
19. Wang M.Y., Wang X., and Guo D. A level set method for structural topology optimization. Comput. Methods Appl. Mech. Engrg. 192 (2003) 227-246
20. Wang M.Y., and Wang X. Colro level sets: a multi-phase method for structural topology optimization with multiple materials. Comput. Methods Appl. Mech. Engrg. 193 (2004) 469-496
21. Wang M.Y., and Wang X. A level-set based variational method for design and optimization of heterogeneous objects. Comput.-Aided Des. 37 (2005) 321-337
22. Liu Z., Korvink J.G., and Huang R. Structural topology optimization: Fully coupled level set method via FEMLAB. Struct. Multidiscip. Optim. 29 (2005) 407-417
23. Ha S.H., and Cho S. Topological shape optimization of heat conduction problems using level set approach. Numer. Heat Tranfer B - Fundam. 48 (2005) 67-88
24. Garreau S., Guillaume P., and masmoudi M. The topological asymptotic for PDE systems: the elasticity case. SIAM J. Control Optim. 39 6 (2001) 1756-1778
25. Cea J., Garreau S., Guillaume P., and Masmoudi M. The shape and topological optimizations connection. Comput. Methods Appl. Mech. Engrg. 188 (2000) 713-726
26. Feijoo G.R. A new method in inverse scattering based on the topological derivative. Inverse Probl. 20 (2004) 1819-1840
27. Sokolowski J., and Zochowski A. On the topological derivative in shape optimization. SIAM J. Control Optim. 37 4 (1999) 1251-1272
28. Sokolowski J., and Zochowski A. Topological derivatives for elliptic problems. Inverse Probl. 15 (1999) 123-134
29. Novotny A.A., Feijoo R.A., Taroco E., and Padra C. Topological sensitivity analysis. Comput. Methods Appl. Mech. Engrg. 192 (2003) 803-829
30. Burger M., Hackl B., and Ring W. Incorporating topological derivatives into level set method. J. Comput. Phys. 194 (2004) 344-362
31. G. Allaire, F. de Gournay, F. Jouve, A.-M. Toader, Structural optimization using topological and shape sensitivity via a level set method.Internal report, no. 555, CMAP, Ecole Polytechnique (October 2004).
32. Osher S., and Sethian J.A. Front propagating with curvature dependent speed: algorithms based on Hamilton Jacobi formulations. J. Comput. Phys. 79 (1988) 12-49
33. Sethian J.A. Level Set Methods and Fast Marching Methods (1999), Cambridge University Press
34. Osher S., and Fedkiw R. Level set Method and Dynamic Implicit Surfaces (2003), Springer, New York
35. A. Donoso, Numerical simulations in 3-D heat conduction: minimizing the quadratic mean temperature gradient (Preprint).
36. XinGuang C., Zhi-xin L., and Zeng-Yuan G. Heat conduction optimization based on least dissipation principle of heat transport potential capacity. J. Engrg. Thermophys. 24 1 (2003) 94-96
37. Goodman J., Kohn R.V., and Reyna L. Numerical study of a relaxed variational problem from optimal design. Comput. Methods Appl. Mech. Engrg. 57 1 (1986) 107-127
38. Grabovsky Y. Optimal design problems for two-phase conducting composites with weakly discontinuous objective functionals. Adv. Appl. Math. 27 (2001) 683-704
39. Sokolowski J., and Zolesio J.P. Introduction to Shape Optimization: Shape Sensitivity Analysis (1992), Springer-Verlag, New York
40. Pironneau O. Optimal Shape Design for Elliptic Systems (1983), Springer-Verlag, New York
41. Bendsoe M., and Sigmund O. Material interpolation schemes in topology optimization. Arch. Appl. Mech. 69 (1999) 635-654