Free Access
Issue
ESAIM: COCV
Volume 16, Number 3, July-September 2010
Page(s) 523 - 544
DOI https://doi.org/10.1051/cocv/2009013
Published online 18 June 2009
  1. R.A. Adams, Sobolev spaces, Pure and Applied Mathematics 65. Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London (1975). [Google Scholar]
  2. G. Allaire, Shape optimization by the homogenization method, Applied Mathematical Sciences 146. Springer-Verlag, New York (2002). [Google Scholar]
  3. G. Allaire, F. Jouve and H. Maillot, Topology optimization for minimum stress design with the homogenization method. Struct. Multidiscip. Optim. 28 (2004) 87–98. [Google Scholar]
  4. G. Allaire, F. Jouve and A.-M. Toader, Structural optimization using sensitivity analysis and a level-set method. J. Comput. Phys. 194 (2004) 363–393. [CrossRef] [Google Scholar]
  5. G. Allaire, F. de Gournay, F. Jouve and A.-M. Toader, Structural optimization using topological and shape sensitivity via a level set method. Control Cybern. 34 (2005) 59–80. [Google Scholar]
  6. S. Amstutz, Sensitivity analysis with respect to a local perturbation of the material property. Asymptot. Anal. 49 (2006) 87–108. [MathSciNet] [Google Scholar]
  7. S. Amstutz and H. Andrä, A new algorithm for topology optimization using a level-set method. J. Comput. Phys. 216 (2006) 573–588. [CrossRef] [MathSciNet] [Google Scholar]
  8. J. Appell and P.P. Zabrejko, Nonlinear superposition operators, Cambridge Tracts in Mathematics 95. Cambridge University Press, Cambridge (1990). [Google Scholar]
  9. M.P. Bendsøe and N. Kikuchi, Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Engrg. 71 (1988) 197–224. [Google Scholar]
  10. M.P. Bendsøe and O. Sigmund, Topology optimization, Theory, methods and applications. Springer-Verlag, Berlin (2003). [Google Scholar]
  11. J.F. Bonnans, J.C. Gilbert, C. Lemaréchal and C.A. Sagastizábal, Numerical optimization, Theoretical and practical aspects. Universitext, Springer-Verlag, Berlin, Second Edition (2006). [Google Scholar]
  12. M. Burger and R. Stainko, Phase-field relaxation of topology optimization with local stress constraints. SIAM J. Control Optim. 45 (2006) 1447–1466 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  13. M. Burger, B. Hackl and W. Ring, Incorporating topological derivatives into level set methods. J. Comput. Phys. 194 (2004) 344–362. [CrossRef] [MathSciNet] [Google Scholar]
  14. P. Duysinx and M.P. Bendsøe, Topology optimization of continuum structures with local stress constraints. Internat. J. Numer. Methods Engrg. 43 (1998) 1453–1478. [Google Scholar]
  15. H. Eschenauer, V.V. Kobolev and A. Schumacher, Bubble method for topology and shape optimization of structures. Struct. Optimization 8 (1994) 42–51. [CrossRef] [Google Scholar]
  16. S. Garreau, P. Guillaume and M. Masmoudi, The topological asymptotic for PDE systems: the elasticity case. SIAM J. Control Optim. 39 (2001) 1756–1778 (electronic). [Google Scholar]
  17. D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, Classics in Mathematics. Springer-Verlag, Berlin (2001). Reprint of the 1998 edition. [Google Scholar]
  18. P. Grisvard, Elliptic problems in nonsmooth domains, Monographs and Studies in Mathematics 24. Pitman (Advanced Publishing Program), Boston, USA (1985). [Google Scholar]
  19. A. Henrot and M. Pierre, Variation et optimisation de formes, Mathématiques et applications 48. Springer-Verlag, Heidelberg (2005). [Google Scholar]
  20. M. Hintermüller and K. Kunisch, Stationary optimal control problems with pointwise state constraints (to appear). [Google Scholar]
  21. M. Hintermüller and W. Ring, A level set approach for the solution of a state-constrained optimal control problem. Numer. Math. 98 (2004) 135–166. [MathSciNet] [Google Scholar]
  22. K. Ito and K. Kunisch, Semi-smooth Newton methods for state-constrained optimal control problems. Systems Control Lett. 50 (2003) 221–228. [CrossRef] [MathSciNet] [Google Scholar]
  23. C. Meyer, A. Rösch and F. Tröltzsch, Optimal control of PDEs with regularized pointwise state constraints. Comput. Optim. Appl. 33 (2006) 209–228. [CrossRef] [MathSciNet] [Google Scholar]
  24. F. Murat and J. Simon, Étude de problèmes d'optimal design, in Lecture Notes in Computer Sciences 41, Springer-Verlag, Berlin (1976) 54–62. [Google Scholar]
  25. S.A. Nazarov and J. Sokołowski, Asymptotic analysis of shape functionals. J. Math. Pures Appl. 82 (2003) 125–196. [MathSciNet] [Google Scholar]
  26. J.A. Norato, M.P. Bendsøe, R.B. Haber and D.A. Tortorelli, A topological derivative method for topology optimization. Struct. Multidiscip. Optim. 33 (2007) 375–386. [CrossRef] [MathSciNet] [Google Scholar]
  27. M. Petzoldt, Regularity results for Laplace interface problems in two dimensions. Z. Anal. Anwendungen 20 (2001) 431–455. [Google Scholar]
  28. J.-J. Rückmann and J.A. Gómez, On generalized semi-infinite programming. Top 14 (2006) 1–59. [CrossRef] [MathSciNet] [Google Scholar]
  29. J.J. Rückmann and A. Shapiro, First-order optimality conditions in generalized semi-infinite programming. J. Optim. Theory Appl. 101 (1999) 677–691. [CrossRef] [MathSciNet] [Google Scholar]
  30. G. Savaré, Regularity results for elliptic equations in Lipschitz domains. J. Funct. Anal. 152 (1998) 176–201. [CrossRef] [MathSciNet] [Google Scholar]
  31. J. Simon, Differentiation with respect to the domain in boundary value problems. Numer. Funct. Anal. Optim. 2 (1980) 649–687. [CrossRef] [MathSciNet] [Google Scholar]
  32. J. Sokołowski and A. Żochowski, On the topological derivative in shape optimization. SIAM J. Control Optim. 37 (1999) 1251–1272 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  33. J. Sokołowski and J.-P. Zolésio, Introduction to shape optimization – Shape sensitivity analysis, Springer Series in Computational Mathematics 16. Springer-Verlag, Berlin (1992). [Google Scholar]
  34. G. Still, Generalized semi-infinite programming: numerical aspects. Optimization 49 (2001) 223–242. [CrossRef] [MathSciNet] [Google Scholar]
  35. M.Y. Wang, X. Wang and D. Guo, A level set method for structural topology optimization. Comput. Methods Appl. Mech. Engrg. 192 (2003) 227–246. [Google Scholar]

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