Achieving minimum length scale in topology optimization using nodal design variables and projection functions

International Journal for Numerical Methods in Engineering

Volumn 61, Issue 2, 2004, Pages 238-254

  Guest, J K ^a   Prevost J H ^a   Belytschko, T ^b  

^a Princeton University   (United States)

^b Northwestern University   (United States)

Author keywords

Length scale; Topology optimization

Indexed keywords

CHECKERBOARD PATTERNS; ELEMENT VOLUME FRACTIONS; SENSITIVITY FILTERS;

MEASUREMENTS; OPTIMIZATION; PROBLEM SOLVING; PROJECT MANAGEMENT; STIFFNESS;

TOPOLOGY;

MATHEMATICAL METHOD; OPTIMIZATION;

EID: 4444271810     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1064     Document Type: Article

References (27)

1. 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.
2. Diaz AR, Sigmund O. Checkerboard patterns in layout optimization. Structural Optimization 1995; 10: 40-45.
3. 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.
4. Jang G, Jeong JH, Kim YY, Sheen D, Park C, Kim M. Checkerboard-free topology optimization using non-conforming finite elements. International Journal for Numerical Methods in Engineering 2003; 57: 1717-1735.
5. Poulsen TA. A simple scheme to prevent checkerboard patterns and one-node connected hinges in topology optimization. Structural and Multidisciplinary Optimization 2002; 24:396-399.
6. Ambrosio L, Buttazzo G. An optimal design problem with perimeter penalization. Calculus of Variations and Partial Differential Equations 1993; 1:55-69.
7. Petersson J, Sigmund O. Slope constrained topology optimization. International Journal for Numerical Methods in Engineering 1998; 41:1417-1434.
8. Sigmund O. Design of material structures using topology optimization. Ph.D. Thesis, Department of Solid Mechanics, Technical University of Denmark, 1994.
9. Sigmund O. A 99 line topology optimization code written in Matlab. Structural and Multidisciplinary Optimization 2001; 21:120-127.
10. Petersson J, Sigmund O. Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Structural Optimization 1998; 16:68-75.
11. Poulsen TA. A new scheme for imposing minimum length scale in topology optimization. International Journal for Numerical Methods in Engineering 2003; 57:741-760.
12. Belytschko T, Xiao SP, Parimi C. Topology optimization with implicit functions and regularization. International Journal for Numerical Methods in Engineering 2003; 57:1177-1196.
13. Bendsøe MP, Kikuchi N. Generating optimal topologies in structural design using homogenization method. Computer Methods in Applied Mechanics and Engineering 1988; 71:197-224.
14. Bendsøe MP. Optimization of Structural Topology, Shape, and Material. Springer: Berlin, 1995.
15. Rossow MP, Taylor JE. A finite element method for the optimal design of variable thickness sheets. AIAA Journal 1973; 11:1566-1569.
16. Bendsøe MP. Optimal shape design as a material distribution problem. Structural Optimization 1989; 1: 193-202.
17. Zhou M, Rozvany GIN. The COC algorithm, part II: topological, geometry, and generalized shape optimization. Computer Methods in Applied Mechanics and Engineering 1991; 89:197-224.
18. Mlejnek HP. Some aspects of the genesis of structures. Structural Optimization 1992; 5:64-69.
19. Bendsøe MP, Sigmund O. Material interpolations in topology optimization. Archive of Applied Mechanics 1999; 69:635-654.
20. Allaire G, Kohn RV. Topology optimization and optimal shape design using homogenization. In Topology Design of Structures, Bendsøe MP, Mota Soares CA (eds), Kluwer: Dordrecht, 1993; 207-218.
21. Svanberg K. The method of moving asymptotes-a new method for structural optimization. International Journal for Numerical Methods in Engineering 1987; 24:359-373.
22. Svanberg K. A globally convergent version of MMA without linesearch. In Proceedings of the First World Congress of Structural and Multidisciplinary Optimization, Rozvany GIN, Olhoff N (eds), Goslar, Germany, 1995; 9-16.
23. Vanderbei RJ, Shanno DF. An interior-point algorithm for nonconvex nonlinear programming. Computational Optimization and Applications 1999; 13:231-252.
24. Benson HY, Vanderbei RJ, Shanno DF. Interior-point methods for nonconvex nonlinear programming: filter methods and merit functions. Technical Report, Operations Research and Financial Engineering, Princeton University, 2001.
25. Olhoff N, Bendsoe MP, Rasmussen J. On CAD-integrated structural topology and design optimization. Computer Methods in Applied Mechanics and Engineering 1991; 89:259-279.
26. Sigmund O. On the design of compliant mechanisms using topology optimization. Mechanics of Structures and Machines 1997; 25:495-526.
27. Yin L, Ananthasuresh GK. A novel formulation for the design of distributed compliant mechanisms. Proceedings of DETC '02: ASME 2002 Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Montreal, Canada, 2002.