Evolutionary topology optimization using design space adjustment based on fixed grid

International Journal for Numerical Methods in Engineering

Volumn 66, Issue 11, 2006, Pages 1817-1840

  Jang, In Gwun ^a   Kwak, Byung Man ^a  

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

Author keywords

Design space optimization; Fixed grid; Large scale optimization; Sensitivity analysis; Topology optimization

Indexed keywords

DESIGN; EVOLUTIONARY ALGORITHMS; OPTIMIZATION; SENSITIVITY ANALYSIS;

DESIGN SPACE OPTIMIZATION; FIXED GRID; LARGE-SCALE OPTIMIZAITION; TOPOLOGY OPTIMIZATION;

TOPOLOGY;

DESIGN; EVOLUTIONARY ALGORITHMS; OPTIMIZATION; SENSITIVITY ANALYSIS; TOPOLOGY;

EID: 33745563534     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1607     Document Type: Article

References (29)

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. Suzuki K, Kikuchi N. A homogenization method for shape and topology optimization. Computer Methods in Applied Mechanics and Engineering 1991; 93:291-318.
3. 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.
4. Ma ZD, Kikuchi N, Cheng HC. Topological design for vibrating structures. Computer Methods in Applied Mechanics and Engineering 1995; 232:259-280.
5. Hassani B, Hinton E. A review of homogenization and topology optimization I - homogenization theory for media with periodic structure. Computers and Structures 1998; 69:707-717.
6. Hassani B, Hinton E. A review of homogenization and topology optimization II - analytical and numerical solution of homogenization equations. Computers and Structures 1998; 69:719-738.
7. Hassani B, Hinton E. A review of homogenization and topology optimization III - topology optimization using optimality criteria. Computers and Structures 1998; 69:739-756.
8. Bendsoe MP. Optimal shape design as a material distribution problem. Structural Optimization 1989; 1:193-303.
9. Zhou M, Rozvany GIN. The COC algorithm. Part II: topology geometrical and generalized shape optimization. Computer Methods in Applied Mechanics and Engineering 1991; 89:309-336.
10. Mlejnik HP, Schirrmacher R. An engineering approach to optimal material distribution and shape finding. Computer Methods in Applied Mechanics and Engineering 1993; 106:1-26.
11. Yang RJ, Chuang CH. Optimal topology design using linear programming. Computers and Structures 1994; 52:265-275.
12. Bendsoe MP, Sigmund O. Material interpolation schemes in topology optimization. Archive of Applied Mechanics 1999; 69:635-654.
13. Xie YM, Steven GP. A simple evolutionary procedure for structural optimization. Computers and Structures 1993; 49:885-896.
14. Querin OM, Steven GP. Evolutionary structural optimization (ESO) using a bidirectional algorithm. Engineering Computations 1998; 15:1031-1048.
15. Bruns TE, Tortorelli DA. An element removal and reintroduction strategy for the topology optimization of structures and compliant mechanisms. International Journal for Numerical Methods in Engineering 2003; 57:1413-1430.
16. Kim IY, Kwak BM. Design space optimization using a numerical design continuation method. International Journal for Numerical Methods in Engineering 2002; 53:1979-2002.
17. Voller VR, Swaninathan CR, Thomas BG. Fixed grid techniques for phase change problems: a review. International Journal for Numerical Methods in Engineering 1990; 30:875-898.
18. Udaykumar HS, Kan HC, Shyy W, Tran-Son-Tay R. Multiphase dynamics in arbitrary geometries on fixed Cartesian grids. Journal of Computational Physics 1997; 137:366-405.
19. Dantzig JA. Modelling liquid-solid phase changes with melt convection. International Journal for Numerical Methods in Engineering 1989; 28:1769-1785.
20. Kim H, Garcia MJ, Querin OM, Steven GP, Xie YM. Introduction of fixed grid in evolutionary structural optimization. Engineering Computations 2000; 17:427-439.
21. Sigmund O. A 99 line topology optimization code written in Matlab. Journal of the International Society for Structural and Multidisciplinary Optimization 2001; 21:120-127.
22. Wang L, Basu PK, Leiva JP. Automobile body reinforcement by finite element optimization. Finite Elements in Analysis and Design 2004; 40:879-893.
23. Krog L, Tucker A, Kemp M, Boyd R. Topology optimization of aircraft wing box ribs. Proceedings of the 10th AIAA/ISSMO MAO Conference, Albany, 2004.
24. Borrvall T, Petersson J. Large-scale topology optimization in 3D using parallel computing. Computer Methods in Applied Mechanics and Engineering 2001; 190:6201-6229.
25. Kim TS, Kim JE, Kim YY. Parallelized structural topology optimization for eigenvalue problems. International Journal of Solids and Structures 2004; 41:2623-2641.
26. Haug EJ, Choi KK, Komkov V. Design Sensitivity Analysis of Structural Systems. Academic Press: New York, 1986; 104-108.
27. Bendsoe MP, Sigmund O. Topology Optimization, Theory, Methods and Applications. Springer: Berlin, 2003; 4-7.
28. Sigmund O, Petersson J. Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-independencies and local minima. Structural Optimization 1998; 16:68-75.
29. Kim IY. Design space optimization using a numerical design continuation method. Ph.D. Thesis, Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 2002; 50-69.