Free Access
Issue
ESAIM: COCV
Volume 18, Number 1, January-March 2012
Page(s) 229 - 258
DOI https://doi.org/10.1051/cocv/2010045
Published online 23 December 2010
  1. G. Allaire, Shape optimization by the homogenization method, Applied Mathematical Sciences 146. Springer-Verlag, New York (2002). [Google Scholar]
  2. G. Allaire, Topology Optimization with the Homogenization and the Level-Set Method, in Nonlinear Homogenization and its Applications to Composites, Polycrystals and Smart Materials, NATO Science Series II : Mathematics, Physics and Chemistry 170, Springer (2004) 1–13. [Google Scholar]
  3. G. Allaire, E. Bonnetier, G. Francfort and F. Jouve, Shape optimization by the homogenization method. Numer. Math. 76 (1997) 27–68. [CrossRef] [MathSciNet] [Google Scholar]
  4. G. Allaire, F. Jouve and A.-M. Toader, A level-set method for shape optimization. C. R. Acad. Sci. Paris, Sér. I 334 (2002) 1125–1130. [CrossRef] [MathSciNet] [Google Scholar]
  5. G. Allaire, F. Jouve and H. Maillot, Topology optimization for minimum stress design with the homogenization method. Struct. Multidisc. Optim. 28 (2004) 87–98. [Google Scholar]
  6. 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. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed] [Google Scholar]
  7. 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]
  8. S.M. Allen and J.W. Cahn, A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Metall. 27 (1979) 1085–1095. [CrossRef] [Google Scholar]
  9. L. Ambrosio and G. Buttazzo, An optimal design problem with perimeter penalization. Calc. Var. 1 (1993) 55–69. [CrossRef] [MathSciNet] [Google Scholar]
  10. R. Ansola, E. Veguería, J. Canales and J.A. Tárrago, A simple evolutionary topology optimization procedure for compliant mechanism design. Finite Elements Anal. Des. 44 (2007) 53–62. [CrossRef] [Google Scholar]
  11. J.M. Ball, Convexity conditions and existence theorems in nonlinear elasiticity. Arch. Ration. Mech. Anal. 63 (1977) 337–403. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed] [Google Scholar]
  12. J.M. Ball, Global invertibility of Sobolev functions and the interpenetration of matter. Proc. R. Soc. Edinb. A 88 (1981) 315–328. [CrossRef] [MathSciNet] [Google Scholar]
  13. B. Bourdin and A. Chambolle, Design-dependent loads in topology optimization. ESAIM : COCV 9 (2003) 19–48. [CrossRef] [EDP Sciences] [Google Scholar]
  14. A. Braides, Γ-convergence for beginners, Oxford Lecture Series in Mathematics and its Applications 2. Oxford University Press, Oxford (2002). [Google Scholar]
  15. M. Burger and R. Stainko, Phase-field relaxation of topology optimization with local stress constraints. SIAM J. Control Optim. 45 (2006) 1447–1466. [CrossRef] [MathSciNet] [Google Scholar]
  16. A. Chambolle, A density result in two-dimensional linearized elasticity, and applications. Arch. Ration. Mech. Anal. 167 (2003) 211–233. [CrossRef] [MathSciNet] [Google Scholar]
  17. Y. Chen, T.A. Davis, W.W. Hager and S. Rajamanickam, Algorithm 887 : CHOLMOD, supernodal sparse Cholesky factorization and update/downdate. ACM Trans. Math. Softw. 35 (2009) 22 :1–22 :14. [Google Scholar]
  18. P.G. Ciarlet, Three-dimensional elasticity. Elsevier Science Publishers B. V. (1988). [Google Scholar]
  19. A.R. Conn, N.I.M Gould and P.L. Toint, Trust-Region Methods. SIAM (2000). [Google Scholar]
  20. S. Conti, H. Held, M. Pach, M. Rumpf and R. Schultz, Risk averse shape optimization. SIAM J. Control Optim. (to appear). [Google Scholar]
  21. B. Dacorogna, Direct methods in the calculus of variations. Springer-Verlag, New York (1989). [Google Scholar]
  22. T.A. Davis and W.W. Hager, Dynamic supernodes in sparse Cholesky update/downdate and triangular solves. ACM Trans. Math. Softw. 35 (2009) 27 :1–27 :23. [CrossRef] [Google Scholar]
  23. G.P. Dias, J. Herskovits and F.A. Rochinha, Simultaneous shape optimization and nonlinear analysis of elastic solids, in Computational Mechanics – New Trends and Applications, E. Onate, I. Idelsohn and E. Dvorkin Eds., CIMNE, Barcelona (1998) 1–13. [Google Scholar]
  24. X. Guo, K. Zhao and M.Y. Wang, Simultaneous shape and topology optimization with implicit topology description functions. Control Cybern. 34 (2005) 255–282. [Google Scholar]
  25. Z. Liu, J.G. Korvink and R. Huang, Structure topology optimization : Fully coupled level set method via femlab. Struct. Multidisc. Optim. 29 (2005) 407–417. [CrossRef] [Google Scholar]
  26. J.E. Marsden and T.J.R. Hughes, Mathematical Foundations of Elasticity. Prentice-Hall, Englewood Cliffs (1983). [Google Scholar]
  27. L. Modica and S. Mortola, Un esempio di Γ-convergenza. Boll. Un. Mat. Ital. B (5) 14 (1977) 285–299. [MathSciNet] [Google Scholar]
  28. P. Pedregal, Variational Methods in Nonlinear Elasticity. SIAM (2000). [Google Scholar]
  29. J.A. Sethian and A. Wiegmann, Structural boundary design via level set and immersed interface methods. J. Comput. Phys. 163 (2000) 489–528. [CrossRef] [MathSciNet] [Google Scholar]
  30. O. Sigmund and P.M. Clausen, Topology optimization using a mixed formulation : An alternative way to solve pressure load problems. Comput. Methods Appl. Mech. Eng. 196 (2007) 1874–1889. [CrossRef] [Google Scholar]
  31. J. Sikolowski and J.-P. Zolésio, Introduction to shape optimization, in Shape sensitivity analysis, Springer (1992). [Google Scholar]
  32. M.Y. Wang and S. Zhou, Synthesis of shape and topology of multi-material structures with a phase-field method. J. Computer-Aided Mater. Des. 11 (2004) 117–138. [CrossRef] [Google Scholar]
  33. M.Y. Wang, X. Wang and D. Guo, A level set method for structural topology optimization. Comput. Methods Appl. Mech. Eng. 192 (2003) 227–246. [CrossRef] [MathSciNet] [Google Scholar]
  34. M.Y. Wang, S. Zhou and H. Ding, Nonlinear diffusions in topology optimization. Struct. Multidisc. Optim. 28 (2004) 262–276. [CrossRef] [Google Scholar]
  35. P. Wei and M.Y. Wang, Piecewise constant level set method for structural topology optimization. Int. J. Numer. Methods Eng. 78 (2009) 379–402. [CrossRef] [Google Scholar]
  36. Q. Xia and M.Y. Wang, Simultaneous optimization of the material properties and the topology of functionally graded structures. Comput. Aided Des. 40 (2008) 660–675. [CrossRef] [Google Scholar]
  37. S. Zhou and M.Y. Wang, Multimaterial structural topology optimization with a generalized Cahn–Hilliard model of multiphase transition. Struct. Multidisc. Optim. 33 (2007) 89–111. [CrossRef] [Google Scholar]

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