Piecewise constant level set method for structural topology optimization

International Journal for Numerical Methods in Engineering

Volumn 78, Issue 4, 2009, Pages 379-402

  Wei, Peng ^a   Wang, Michael Yu ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Level set method; Piecewise constant level set method; Topology optimization

Indexed keywords

ADDITIVE OPERATOR SPLITTING; HAMILTON-JACOBI EQUATIONS; ITERATIVE PROCEDURES; LEVEL SET FUNCTIONS; LEVEL SET METHOD; MINIMIZATION PROBLEMS; MINIMUM COMPLIANCE DESIGNS; NUMERICAL SCHEMES; PHASE-FIELD METHODS; PIECEWISE CONSTANT LEVEL SET METHOD; RE INITIALIZATIONS; SIGNED DISTANCE FUNCTIONS; STRUCTURAL SHAPES; STRUCTURAL TOPOLOGY OPTIMIZATIONS; TOPOLOGY OPTIMIZATION; ZERO LEVEL SETS;

DROP BREAKUP; LEVEL MEASUREMENT; MATHEMATICAL OPERATORS; NUMBER THEORY; SET THEORY; STRUCTURAL OPTIMIZATION; TOPOLOGY;

SHAPE OPTIMIZATION;

EID: 64049088299     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2478     Document Type: Article

References (32)

1. Bendsøe MP, Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering 1988; 71:197-224.
2. Osher SJ, Sethian JA. Front propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics 1988; 79:12-49.
3. Wang MY, Wang XM, Guo DM. A level set method for structural topology optimization. Computer Methods in Applied Mechanics and Engineering 2003; 192:227-246.
4. Allaire G, Jouve F, Toader AM. Structural optimization using sensitivity analysis and a level-set method. Journal of Computational Physics 2004; 194:363-393.
5. Belytschko T, Parimi C, Moes N, Sukumar N, Usui S. Structured extended finite element methods for solids defined by implicit surfaces. International Journal for Numerical Methods in Engineering 2003; 56:609-635.
6. Belytschko T, Xiao SP, Parimi C. Topology optimization with implicit functions and regularization. International Journal for Numerical Methods in Engineering 2003; 57:1177-1196.
7. Norato J, Haber R, Tortorelli D, Bendsoe MP. A geometry projection method for shape optimization. International Journal for Numerical Methods in Engineering 2004; 60:2289-2312.
8. Peng D, Merriman B, Osher S, Zhao H, Kang M. A pde-based local level set method. Journal of Computational Physics 1999; 155:410-438.
9. Sethian JA. Level Set Methods and Fast Marching Methods (2nd edn). Cambridge University Press: Cambridge, 1999.
10. Wang SY, Wang MY. Structural shape and topology optimization using an implicit free boundary parameterization method. CMES: Computer Modeling in Engineering and Sciences 2006; 13(2):119-147.
11. Lie J, Lysaker M, Tai XC. A variant of the level set method and applications to image segmentation. Mathematics of Computation 2006; 75:1155-1174.
12. Wang MY, Zhou SW. Phase field: a variational method for structural topology optimization. CMES: Computer Modeling in Engineering and Sciences 2004; 6(6):547-566.
13. Zhou SW, Wang MY. 3d multi-material structural topology optimization with the generalized Cahn-Hilliard equations. CMES: Computer Modeling in Engineering and Sciences 2006; 16(2):83-102.
14. Rockafellar RT. The multiplier method of Hestenes and Powell applied to convex programming. Journal of Optimization Theory and Applications 1973; 12:555-562.
15. Tai XC, Yao CH. Image segmentation by piecewise constant Mumford-Shah model without estimating the constants. Technical Report 06-18, Group in Computational and Applied Mathematics, Department of Mathematics, University of California, April 2006.
16. Wei P, Wang MY. A piecewise constant level set method for structural topology optimization. Proceedings of WCSMO-7, COEX, Seoul, Korea, May 2007.
17. Wei P. Level set methods for shape and topology optimization of structures. Ph.D. Thesis, The Chinese University of Hong Kong, 2007.
18. Sigmund O. A 99 line topology optimization code written in MATLAB. Structural and Multidisciplinary Optimization 2001; 31(6):419-429.
19. Bendsøe MP. Optimization of Structural Topology, Shape and Material. Springer: Berlin, 1997.
20. Bendsøe MP. Optimal shape design as a material distribution problem. Structural Optimization 1989; 1:193-202.
21. Zhou M, Rozvany G. The COC algorithm. Part II: topological, geometry and generalized shape optimization. Computer Methods in Applied Mechanics and Engineering 1991; 89:197-224.
22. Bendsøe MP, Sigmund O. Material interpolations in topology optimization. Archive of Applied Mechanics 1999; 69:635-654.
23. Lu T, Neittaanmaki P, Tai XC. A parallel splitting up method and its application to Navier-Stokes equations. Applied Mathematics Letters 1991; 4:25-29.
24. Weickert J, Romeny BH, Viergever MA. Efficient and reliable schemes for nonlinear diffusion filtering. IEEE Transactions on Image Processing 1998; 7:398-409.
25. Kühne G, Weickert J, Beier M, Effelsberg W. Fast implicit active contour models. Pattern Recognition: 24th DAGM Symposium, vol. 2449/2002, Zurich, Switzerland. Springer: Berlin, Heidelberg, 2002; 133-140.
26. Wang MY, Wei P. Topology optimization with level set method incorporating topological derivative. 6th World Congress on Structural and Multidisciplinary Optimization, Rio de Janeiro, Brazil, 2005; 761-769.
27. Li HW, Tai XC. Piecewise constant level set methods for multiphase motion. Technical Report 06-17, Group in Computational and Applied Mathematics, Department of Mathematics, University of California, April 2006.
28. Rozvany G. Aim, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanisms. Structural and Multidisciplinary Optimization 2001; 21(2):90-108.
29. Wang SY, Wang MY. Radial basis functions and level set method for structural topology optimization. International Journal for Numerical Methods in Engineering 2006; 65(12):2060-2090.
30. Osher SJ, Fedkiw RP. Level Set Methods and Dynamic Implicit Surfaces. Springer: New York, 2002.
31. Burger M, Haclk B, Ring W. Incorporating topological derivatives into level set methods. Journal of Computational Physics 2004; 194:344-362.
32. Allaire G, Gournay FD, Jouve F, Toader AM. Structural optimization using topological and shape sensitivity via a level set method. Control and Cybernetics 2005; 34:59-80.