Continuous approximation of material distribution for topology optimization

International Journal for Numerical Methods in Engineering

Volumn 59, Issue 14, 2004, Pages 1925-1944

  Matsui, K ^a   Terada, K ^b  

^a YOKOHAMA NATIONAL UNIVERSITY   (Japan)

^b TOHOKU UNIVERSITY   (Japan)

Author keywords

Homogenization design method; Homogenization theory; Structural design; Topology optimization

Indexed keywords

APPROXIMATION THEORY; CONSTRAINT THEORY; FINITE ELEMENT METHOD; INTERPOLATION; OPTIMIZATION; PARAMETER ESTIMATION; TOPOLOGY;

CHECKERBOARD PATTERNS; FIXED DESIGN DOMAINS; TOPOLOGY OPTIMIZATION;

MATERIALS HANDLING;

MATHEMATICAL METHOD;

EID: 1842783308     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.945     Document Type: Article

References (27)

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. Suzuki K, Kikuchi N. A homogenization method for shape and topology optimization. Computer Methods in Applied Mechanics and Engineering 1991; 93:291-318.
3. Ma ZD, Kukuchi N, Cheng HC. Topological design for vibrating structures. Computer Methods in Applied Mechanics and Engineering 1995; 121:259-280.
4. Nishiwaki S, Frecker MI, Min S, Kikuchi N. Topology optimization of compliant mechanisms using the homogenization method. International Journal for Numerical Methods in Engineering 1998; 42:535-559.
5. Bendsøe MP. Optimal shape design as a material distribution problem. Structural Optimization 1989; 1: 193-202.
6. Rozvany GIN. Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics. Structural and Multidisciplinary Optimization 2001; 21:90-108.
7. Yang RJ, Chuang CH. Optimal topology design using linear programming. Computers and Structures 1994; 52:265-275.
8. Bendsøe MP, Sigmund O. Material interpolation schemes in topology optimization. Archive of Applied Mechanics 1999; 69:635-654.
9. Mayer RR, Kikuchi N, Scott RA. Application of topological optimization techniques to structural crashworthiness. International Journal for Numerical Methods in Engineering 1996; 39(8):1383-1403.
10. Swan CC, Kosaka I. Voigt-Rcuss topology optimization for structures with nonlinear material behaviours. International Journal for Numerical Methods in Engineering 1997; 40:3785-3814.
11. Maute K, Schwarz S, Ramm E. Adaptive topology optimization of elastoplastic structures. Structural Optimization 1998; 15:81-91.
12. Burns TE, Tortorrelli DA. Topology optimization of non-linear elastic structures and compliant mechanisms. Computer Methods in Applied Mechanics and Engineering 2001; 190:3443-3459.
13. Buhl T, Pedersen CBW, Sigmund O. Stiffness design of geometrically nonlinear structures using topology optimization. Structural and Multidisciplinary Optimization 2001; 19:93-104.
14. Gea HC, Luo J. Topology optimization of structures with geometrical nonlinearities. Computers and Structures 2001; 79:1977-1985.
15. Kemmler R, Schwarz S, Ramm E. Topology optimization including geometrically nonlinear response. Proceedings of the 3rd World Congress of Structural and Multidisciplinary Optimization, New York, 1999: 17-21.
16. Sigmund O, Petersson J. Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Structural Optimization 1998; 16:68-75.
17. Bourdin B. Filters in topology optimization. International Journal for Numerical Methods in Engineering 2001; 50:2143-2158.
18. Diaz J, Sigmund O. Checkerboard patterns in layout optimization. Structural Optimization 1995; 10:40-45.
19. Fujii D, Kikuchi N. Improvement of numerical instabilities in topology optimization using the SLP method. Structural Optimization 2000: 19:113-121.
20. Haber RB, Jog CS, Bendsøe MP. A new approach to variable-topology shape design using a constraint on perimeter. Structural Optimization 1996; 11:1-12.
21. Petersson J, Sigmund O. Slope constrained topology optimization. International Journal for Numerical Methods in Engineering 1998; 41;1417-1434.
22. Kohn RV, Strang G. Optimal design and relaxation of variational problems. Communications on Pure and Applied Mathematics 1986; 39:1-25 (Part I), 139-182 (Part II), 353-377 (Part III).
23. Allaire G. Shape Optimization by the Homogenization Method. Springer: New York, 2001.
24. Benssousan A, Lions JL, Papanicoulau G. Asymptotic Analysis for Periodic Structures. North-Holland: Amsterdam, 1978.
25. Terada K, Kikuchi N. A class of general algorithms for multi-scale analyses of heterogeneous media. Computer Methods in Applied Mechanics and Engineering 2001; 190:5427-5464.
26. 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.
27. Michel JC, Moulinec H, Squet P. Effective properties of composite material with periodic microstructure: a computational approach. Computer Methods in Applied Mechanics and Engineering 1999: 172:109-143.