Material cloud method for topology optimization

International Journal for Numerical Methods in Engineering

Volumn 65, Issue 10, 2006, Pages 1585-1607

  Chang, Su Young ^a   Youn, Sung Kie ^a  

^a Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

Author keywords

Convergence; Design domain; Efficiency; Material cloud method; Topology optimization

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; OPTIMIZATION;

DESIGN DOMAIN; MATERIAL CLOUD METHOD; TOPOLOGY OPTIMIZATION;

TOPOLOGY;

CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; OPTIMIZATION; TOPOLOGY;

EID: 33244459121     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1508     Document Type: Article

References (42)

1. Bendsoe 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. Bendsoe MP. Optimal shape design as a material distribution problem. Structural Optimization 1989; 1: 193-202.
3. Suzuki K, Kikuchi N. A homogenization method for shape and topology optimization. Computer Methods in Applied Mechanics and Engineering 1991; 93:291-318.
4. Bendsoe MP, Diaz A, Kikuchi N. Topology and generalized layout optimization of elastic structures. In Topology Optimization of Structures, Bendsoe MP, Mota Soares CA (eds). Kluwer Academic Publishers: Amsterdam, 1993; 159-205.
5. Rozvany GIN, Zhou M, Sigmund O. Topology optimization in structural design. Advances in Design Optimization. Chapman and Hall: London, 1994; 340-399 (Chapter 10).
6. Yang RJ, Chuang CH. Optimal topology design using linear programming. Computers and Structures 1994; 52(2):265-276.
7. Bendsoe MP, Sigmund O. Material interpolation schemes in topology optimization. Archive of Applied Mechanics 1999; 69:635-654.
8. Olhoff L. Optimal design of vibrating circular plates. International Journal of Solids and Structures 1970; 6:139-156.
9. Taylor JE, Rossow MP. Optimal truss design based on an algorithm using optimality criteria. International Journal of Solids and Structures 1977; 13:913-923.
10. Cheng GD, Olhoff N. An investigation concerning optimal design of solid elastic plates. International Journal of Solids and Structures 1981; 17:305-323.
11. Rozvany GIN, Zhou M. The COC algorithm, part I: cross-section optimization of sizing. Computer Methods in Applied Mechanics and Engineering 1991; 89:281-308.
12. Diaz AR, Kikuchi N. Solutions to shape and topology eigenvalue optimization problems using a homogenization method. International Journal for Numerical Methods in Engineering 1992; 35:1487-1502.
13. Ma ZD, Kikuchi N, Cheng HC, Hagiwara I. Topology optimization technique for free vibration problems. Journal of Applied Mechanics (ASME) 1995; 62:200-207.
14. Svanberg K. The method of moving asymptotes - a new method for structural optimization. International Journal for Numerical Methods in Engineering 1987; 24:359-373.
15. Svanberg K. A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM Journal on Optimization 2002; 12(2):555-573.
16. Bendsoe MP, Sigmund O. Topology Optimization - Theory, Methods and Applications. Springer: Berlin, 2003.
17. Jog CS, Haber RB, Bendsoe MP. A displacement based topology design with self-adaptive materials. In Topology Optimization of Structures, Bendsoe MP, Mota Soares CA (eds). Kluwer Academic Publishers: Amsterdam, 1993; 219-238.
18. Rodrigues HC, Fernandes P. Topology optimization of linear elastic structures subjected to thermal loads. In Topology Optimization of Structures, Bendsoe MP, Mota Soares CA (eds). Kluwer Academic Publishers: Amsterdam, 1993; 437-450.
19. Diaz AR, Sigmund O. Checkerboard patterns in layout optimization. Structural Optimization 1995; 10(1): 40-45.
20. Jog CS. Haber RB. Stability of finite element models for distributed-parameter optimization and topology design. Computer Methods in Applied Mechanics and Engineering 1996; 130:203-226.
21. Youn SK, Park SH. A study on the shape extraction process in the structural topology optimization using homogenized material. Computers and Structures 1997; 62(3):527-538.
22. Haber RB, Jog CS, Bendsoe MP. A new approach to variable-topology shape design using a constraint on perimeter. Structural Optimization 1996; 11:1-12.
23. Ambrosio L, Buttazzo G. An optimal design problem with perimeter penalization. Calculus and Variation 1993; 1:55-69.
24. Borrvall T. Topology optimization of elastic continua using restriction. Archives of Computational Methods in Engineering 2001; 8(4):351-385.
25. Petersson J, Sigmund O. Slope constrained topology optimization. International Journal for Numerical Methods in Engineering 1998; 41(8):1417-1434.
26. Zhou M, Shyy YK, Thomas HL. Checkerboard and minimum member size control in topology optimization. Structural and Multidisciplinary Optimization 2001; 21:152-158.
27. Bruns TE, Tortorelli DA. Topology optimization of non-linear elastic structures and compliant mechanisms. Computer Methods in Applied Mechanics and Engineering 2001; 190:3443-3459.
28. Bourdin B. Filters in topology optimization. International Journal for Numerical Methods in Engineering 2001; 50(9):2143-2158.
29. Sigmund O. Design of material structures using topology optimization. Ph.D. Thesis, Department of Solid Mechanics, Technical University of Denmark, 1994.
30. Sigmund O. On the design of compliant mechanisms using topology optimization. Mechanics of Structures and Machines 1997; 25(4):495-526.
31. Sigmund O, Petersson J. Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Structural Optimization 1998; 16(1):68-75.
32. Kumar AV, Gossard DC. Synthesis of optimal shape and topology of structures. Journal of Mechanical Design (ASME) 1996; 118(1):68-74.
33. Sethian JA, Wiegmann A. Structural boundary design via level set and immersed interface methods. Journal of Computational Physics 2000; 163(2):489-528.
34. Belytschko T, Xiao SP, Parimi C. Topology optimization with implicit functions and regularization. International Journal for Numerical Methods in Engineering 2003; 57:1177-1196.
35. Xie YM, Steven GP. A simple evolutionary procedure for structural optimization. Computers and Structures 1993; 49:885-896.
36. Querin OM, Xie YM, Steven GP. Evolutionary structural optimization (ESO) using a bi-directional algorithm. Engineering Computations 1998; 15:1031-1048.
37. Kim H, Querin OM, Steven GP, Xie YM. Improving efficiency of evolutionary structural optimization by implementing fixed grid mesh. Structural and Multidisciplinary Optimization 2003; 24:441-448.
38. Liu JS, Parks GT, Clarkson PJ. Metamorphic development: a new topology optimization method for continuum structures. Structural and Multidisciplinary Optimization 2000; 20:288-300.
39. Kim IY, Kwak BM. Design space optimization using a numerical design continuation method. International Journal for Numerical Methods in Engineering 2002; 53:1979-2002.
40. Swan CC, Kosaka I. Voigt-Reuss topology optimization for structures with linear elastic material behaviours. International Journal for Numerical Methods in Engineering 1997; 40:3033-3057.
41. Park KS, Chang SY, Youn SK. Topology optimization of the primary mirror of a multi-spectral camera. Structural and Multidisciplinary Optimization 2003; 25:46-53.
42. Chang SY, Cho JH, Youn SK, Kim CS, Oh DH. Topology optimization of a HDD actuator arm. Computational and Structural Engineering 2001; 1(2):89-96.