Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima

Structural Optimization

Volumn 16, Issue 1, 1998, Pages 68-75

  Sigmund, O ^a   Petersson, J ^b  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^b LINKÖPING UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; NUMERICAL ANALYSIS; OPTIMIZATION; PARAMETER ESTIMATION; STABILITY;

CHECKERBOARDS;

TOPOLOGY;

EID: 0032137868     PISSN: 09344373     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01214002     Document Type: Article

References (32)

1. Allaire, G.; Francfort, G.A. 1993: A numerical algorithm for topology and shape optimization. In: Bendsøe, M.P.; Mota Soares, C.A. (eds.) Topology design of structures, pp. 239-248. Dordrecht: Kluwer
2. Allaire, G.; Kohn, R.V. 1993: Topology optimization and optimal shape design using homogenization. In: Bendsøe, M.P.; Mota Soates, C.A. (eds) Topology design of structures, pp. 207-218. Dordrecht: Kluwer
3. Ambrosio, L.; Buttazzo, G. 1993: An optimal design problem with perimeter penalization. Calc. Var. 1, 55-69
4. Deckers, M. 1996: Optimisation topologique de structures continues en variable discretes. Technical Report OF-38, LTAS, University of Liège
5. Beckers, M. 1997a: Methodes du perimetre et des filtres pour l'optimisation topologique en variable discretes. Technical Report OF-45, LTAS, University of Liège
6. Beckers, M. 1997b: Optimisation topologique de structures tridimensionelles en variable discretes. Technical Report OF-44, LTAS, University of Liège
7. Bendsøe, M.P. 1989: Optimal shape design as a material distribution problem. Struct. Optim. 1, 193-202
8. Bendsøe, M.P. 1995: Optimization of structural topology, shape and material. Berlin, Heidelberg, New York: Springer
9. Bendsøe, M.P.; Guedes, J.M.; Haber, R.B.; Pedersen, P.; Taylor, J.E. 1994: An analytical model to predict optimal material properties in the context of optimal structural design. Trans. ASME, J. Appl. Mech. 61, 930-937
10. Bendsøe, M.P.; Kikuchi, N. 1988: Generating optimal topologies in optimal design using a homogenization method. Comp. Meth. Appl. Mech. Engng. 71, 197-224
11. Bendsøe, M.P.; Kikuchi, N.; Diaz, A.R. 1993: Topology and generalized layout optimization of elastic structures. In: Bendsøe, M.P.; Mota Scares, C.A. (eds.) Topology design of structures, pp. 159-205. Dordrecht: Kluwer
12. Chambolle, A. 1995: Image segmentation by variational methods: Mumford and shah functional and the discrete approximations. SIAM J. Appl Math. 55, 827-863
13. Díaz, A.R.; Sigmund, O. 1995: Checkerboard patterns in layout optimization. Struct. Optim. 10, 40-45
14. Duysinx, P. 1997: Layout optimization: A mathematical programming approach. (Submitted). Also: DCAMM Report No. 540, Technical University of Denmark
15. Duysinx, P. 1997: Layout optimization: A mathematical programming approach. (Submitted). Also: DCAMM Report No. 540, Technical University of Denmark
16. Guedes, J.M.; Taylor, J.E. 1997: On the prediction of material properties and topology for optimal continuum structures. Struct. Optim. 14, 183-192
17. Haber, R.B.; Bendsøe, M.P.; Jog, C. 1996: A new approach to variable-topology shape design using a constraint on the perimeter. Struct. Optim. 11, 1-12
18. Jog, C.S.; Haber, R.B. 1996: Stability of finite element models for distributed-parameter optimization and topology design. Comp. Meth. Appl. Mech. Engng. 130, 203-226
19. Johnson, C.; Pitkäranta, J. 1982: Analysis of some mixed finite element methods related to reduced integration. Mathematics of Computations 38, 375-400
20. Leblond, J.B.; Perrin, G.; Deveaux, J. 1994: Bifurcation effects in ductile metals with damage delocalization. J. Appl. Mech. 61, 236-242
21. Mullender, M.G.; Huiskes, R.; Weihnans, H. 1994: A physiological approach to the simulation of bone remodelling as a self-organizational controll process. J. Biomech. 11, 1389-1394
22. Niordson, F.I. 1983: Optimal design of plates with a constraint on the slope of the thickness function. Int. J. Solids & Struct. 19, 141-151
23. Petersson, J. 1997a: A finite element analysis of optimal variable thickness sheets. (Submitted). Also: Mat. Report No. 1996-4, December 1996, Technical University of Denmark
24. Petersson, J. 1997a: A finite element analysis of optimal variable thickness sheets. (Submitted). Also: Mat. Report No. 1996-4, December 1996, Technical University of Denmark
25. Petersson, J. 1997b: Some convergence results in perimeter-controlled topology optimization. (Submitted). Also: Report LiTH-IKP-R-995, Linköping University, Sweden
26. Petersson, J. 1997b: Some convergence results in perimeter-controlled topology optimization. (Submitted). Also: Report LiTH-IKP-R-995, Linköping University, Sweden
27. Petersson, J.; Sigmund, O. 1998: Slope constrained topology optimization. Int. J. Numer. Meth. Engng. 41, 1417-1434
28. Sigmund, O. 1994: Design of material structures using topology optimization. Ph.D. Thesis, Department of Solid Mechanics, Technical University of Denmark
29. Sigmund, O. 1997: On the design of compliant mechanisms using topology optimization. Mech. Struct. Mach. 25, 495-526
30. Sigmund, O.; Torquato, S. 1997: Design of materials with extreme thermal expansion using a three-phase topology optimization method. J. Mech. Phys. Solids 45, 1037-1067
31. Sigmund, O.; Torquato, S.; Aksay, I.A. 1998: On the design of 1-3 piezocomposites using topology optimization. J. Mat. Res. 13 (4)
32. Zhou, M.; Rozvany, G.I.N. 1991: The COC algorithm, Part II: Topological, geometry and generalized shape optimization. Comp. Meth. Appl. Mech. Engng. 89, 197-224