An alternative interpolation scheme for minimum compliance topology optimization

Structural and Multidisciplinary Optimization

Volumn 22, Issue 2, 2001, Pages 116-124

  Stolpe, M ^a   Svanberg, K ^a  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Topology optimization

Indexed keywords

EID: 0006234362     PISSN: 1615147X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s001580100129     Document Type: Article

References (29)

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 Soares 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. Calculus of variations and partial differential equations 1, 55-69
4. Bendsøe, M.P. 1989: Optimal shape design as a material distribution problem. Struct. Optim. 1, 193-202
5. Bendsøe, M.P. 1995: Optimization of structural topology, shape, and material. Berlin, Heidelberg, New York: Springer
6. Bendsøe, M.P.; Sigmund, O. 1999: Material interpolation schemes in topology optimization. Arch. Appl. Mech. 69, 635-654
7. Borrvall, T.; Petersson, J. 2001: Topology optimization using regularized intermediate density control. Comp. Meth. Appl. Mech. Engrg. 190, 4911-4928
8. Bourdin, B. 1999: Filters in topology optimization. Technical Report 627, DCAMM Department of Mathematics, Technical University of Denmark
9. Golub, G.H.; van Loan, C.F. 1996: Matrix computations. The Johns Hopkins University Press
10. Haber, R.B.; Jog, C.S.; Bendsøe, M.P. 1996: A new approach to variable-topology shape design using a constraint on perimeter. Struct. Optim. 11, 1-12
11. Hashin, Z.; Shtrikman, S. 1963: A variational approach to the theory of the elastic behaviour of multiphase materials. J. Mech. Phys. Solids 11, 127-140
12. Luenberger, D.G. 1989: Linear and nonlinear programming. Addison-Wesley
13. Petersson, J. 1999: Some convergence results in perimeter-controlled topology optimization. Comp. Meth. Appl. Mech. Engrg. 171, 123-140
14. Petersson, J. 2001: On continuity of the design-to-state mappings for trusses with variable topology. Int. J. Eng. Sci. 39, 1119-1141
15. Petersson, J.; Sigmund, O. 1998: Slope constrained topology optimization. International Journal for Numerical Methods in Engineering 41, 1417-1434
16. Rietz, A. 2001: Sufficiency of a finite exponent in the SIMP (power law) method. Struct. Multidisc. Optim. 21, 159-163
17. Rozvany, G.I.N.; Bendsøe, M.P.; Kirsch, U. 1995: Layout optimization of structures. Appl. Mech. Rev. 48, 41-119
18. Rozvany, G.I.N; Zhou, M.; Birker, T. 1992: Generalized shape optimization without homogenization. Struct. Optim. 4,250-252
19. Sigmund, O. 1994: Design of material structures using topology optimization. Ph.D. Thesis, Department of Solid Mechanics, Technical University of Denmark
20. Sigmund, O.; Petersson, J. 1998: Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Optim. 16, 68-75
21. 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
22. Stolpe, M.; Svanberg, K. 2001: On the trajectories of penalization methods for topology optimization. Struct. Multidisc. Optim. 21, 140-151
23. Svanberg, K. 1984: On local and global minima in structural optimization. In: Atrek, E.; Gallagher, R.H.; Ragsdell, K.M.; Zienkiewicz, O.C. (eds.) New directions in optimum structural design, pp. 327-341. John Wiley and Sons
24. Svanberg, K. 1987: The method of moving asymptotes - a new method for structural optimization. Int. J. Numer. Meth. Eng. 24, 359-373
25. Svanberg, K. 1994a: Global convergence of the stress ratio method for truss sizing. Struct. Optim. 8, 60-68
26. Svanberg, K. 1994b: On the convexity and concavity of compliances. Struct. Optim. 7, 42-46
27. Svanberg, K. 1999: The MMA for modeling and solving optimization problems. Proc. 3rd World Cong. of Structural and Multidisciplinary Optimization (held in Buffalo, NY) On CDROM
28. Wolkowicz, H.; Saigal, R.; Vandenberghe, L. 2000: Handbook of semidefinite programming. Dordrecht: Kluwer
29. Zhou, M.; Shyy, Y.K. Thomas, H.L. 1999: Checkerboard and minimum member size control in topology optimization. Proc. 3rd World Congress of Structural and Multidisciplinary Optimization (held in Buffalo, NY), pp. 440-442