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All issues Volume 25 (2024) Mechanics & Industry, 25 (2024) 7 References
Open Access
Issue
Mechanics & Industry
Volume 25, 2024
Article Number 7
Number of page(s) 19
DOI https://doi.org/10.1051/meca/2024004
Published online 01 March 2024
  1. W. Prager, G. Rozvany, Optimization of structural geometry, in: A. Bednarek, L. Cesari (Eds.), Dynamical Systems. Academic Press, 1977, pp. 265–293 [CrossRef] [Google Scholar]
  2. M.P. Bendsøe, N. Kikuchi, Generating optimal topologies in structural design using a homogenization method, Appl. Mech. Eng. 71, 197–224 (1988) [CrossRef] [Google Scholar]
  3. M.P. Bendsøe, Optimal shape design as a material distribution problem, Struct. Optim. 1, 193–202 (1989) [CrossRef] [Google Scholar]
  4. O. Sigmund, Materials with prescribed constitutive parameters: an inverse homogenization problem, Int. J. Solids Struct. 31, 2313–2329 (1994) [CrossRef] [Google Scholar]
  5. Y. Xie, G. Steven, A simple evolutionary procedure for structural optimization, Comput. Struct. 49, 885–896 (1993) [CrossRef] [Google Scholar]
  6. G. Allaire, F. Jouve, A.-M. Toader, A level-set method for shape optimization, C.R. Acad. Sci. Paris, Série I, 334, 1125–1130 (2002) [CrossRef] [Google Scholar]
  7. M. Zhou, G. Rozvany, The coc algorithm, part ii: Topological, geometrical and generalized shape optimization, Comput. Methods Applied Mech. Eng. 89, 309–336 (1991) [CrossRef] [Google Scholar]
  8. M.P. Bendsøe, O. Sigmund, Material interpolation schemes in topology optimization, Archive of Applied Mechanics 69, 635–654 (1999) [CrossRef] [Google Scholar]
  9. V. Challis, A. Roberts, A. Wilkins, Design of three dimensional isotropic microstructures for maximized stiffness and conductivity, Int. J. Solids Struct. 45, 4130–4146 (2008) [CrossRef] [Google Scholar]
  10. X. Huang, A. Radman, Y. Xie, Topological design of microstructures of cellular materials for maximum bulk or shear modulus, Comput. Mater. Sci. 50, 1861–1870 (2011) [CrossRef] [Google Scholar]
  11. Y.M. Xie, X. Yang, J. Shen, X. Yan, A. Ghaedizadeh, J. Rong, X. Huang, S. Zhou, Designing orthotropic materials for negative or zero compressibility, Int. J. Solids Struct. 51, 4038–4051 (2014) [CrossRef] [Google Scholar]
  12. O. Sigmund, S. Torquato, Design of materials with extreme thermal expansion using a three-phase topology optimization method, J. Mech. Phys. Solids 45, 1037–1067 (1997) [CrossRef] [MathSciNet] [Google Scholar]
  13. J. Wu, O. Sigmund, J.P. Groen, Topology optimization of multi-scale structures: a review, Struct. Multidiscipl. Optim. 63, 1455–1480 (2021) [CrossRef] [Google Scholar]
  14. Y. Wang, H. Xu, D. Pasini, Multiscale isogeometric topology optimization for lattice materials, Comput. Methods Appl. Mech. Eng. 316, 568–585 (2017) [CrossRef] [Google Scholar]
  15. S. Watts, W. Arrighi, J. Kudo, D. Tortorelli, D. White, Simple, accurate surrogate models of the elastic response of three-dimensional open truss micro-architectures with applications to multiscale topology design, Struct. Multidiscipl. Optim. 60, 1887–1920 (2019) [CrossRef] [Google Scholar]
  16. S. Zhou, Q. Li, Microstructural design of connective base cells for functionally graded materials, Mater. Lett. 62, 4022–4024 (2008) [CrossRef] [Google Scholar]
  17. E. Garner, H.M. Kolken, C.C. Wang, A.A. Zadpoor, J. Wu, Compatibility in microstructural optimization for additive manufacturing, Addit. Manuf. 26, 65–75 (2019) [Google Scholar]
  18. L. Xia, P. Breitkopf, Concurrent topology optimization design of material and structure within fe2 nonlinear multiscale analysis framework, Comput. Methods Appl. Mech. Eng. 278, 524–542 (2014) [CrossRef] [Google Scholar]
  19. L. Xia, P. Breitkopf, Multiscale structural topology optimization with an approximate constitutive model for local material microstructure, Comput. Methods Appl. Mech. Eng. 286, 147–167 (2015b) [CrossRef] [Google Scholar]
  20. C. Wang, J. Zhu, W. Zhang, S. Li, J. Kong, Concurrent topology optimization design of structures and non-uniform parameterized lattice microstructures, Struct. Multidiscipl. Optim. 58, 35–50 (2018) [CrossRef] [Google Scholar]
  21. C. Imediegwu, R. Murphy, R. Hewson, M. Santer, Multiscale structural optimization towards three-dimensional printable structures, Struct. Multidiscipl. Optim. 60, 513–525 (2019) [CrossRef] [Google Scholar]
  22. C. Wang, X. Gu, J. Zhu, H. Zhou, S. Li, W. Zhang, Concurrent design of hierarchical structures with three-dimensional parameterized lattice microstructures for additive manufacturing, Struct. Multidiscipl. Optim. 61, 869–894 (2020) [CrossRef] [Google Scholar]
  23. N. Ferro, S. Perotto, D. Bianchi, R. Ferrante, M. Mannisi, Design of cellular materials for multiscale topology optimization: application to patient-specific orthopedic devices, Struct. Multidiscipl. Optim. 65, 79 (2022) [CrossRef] [Google Scholar]
  24. O. Pantz, K. Trabelsi, A post-treatment of the homogenization method for shape optimization, SIAM J. Control Optim. 47, 1380–1398 (2008) [CrossRef] [MathSciNet] [Google Scholar]
  25. G. Allaire, P. Geoffroy-Donders, O. Pantz, Topology optimization of modulated and oriented periodic microstruc-tures by the homogenization method, Comput. Math. Appl. 78, 2197–2229 (2019) [MathSciNet] [Google Scholar]
  26. P. Geoffroy-Donders, G. Allaire, O. Pantz, 3-d topology optimization of modulated and oriented periodic micro-structures by the homogenization method, J. Comput. Phys. 108994 (2019) [Google Scholar]
  27. J.P. Groen, O. Sigmund, Homogenization-based topology optimization for high-resolution manufacturable mi-crostructures, Int. J. Numer. Methods Eng. 113, 1148–1163 (2018) [CrossRef] [Google Scholar]
  28. E. Duriez, J. Morlier, M. Charlotte, C. Azzaro-Pantel, A well connected, locally-oriented and efficient multi-scale to-pology optimization (emto) strategy, Struct. Multidiscipl. Optim. 64, 3705–3728 (2021) [CrossRef] [Google Scholar]
  29. L. Xia, P. Breitkopf, Design of materials using topology optimization and energy-based homogenization approach in matlab, Struct. Multidiscipl. Optim. 52, 1229–1241 (2015a) [CrossRef] [Google Scholar]
  30. Z. Xia, Y. Zhang, F. Ellyin, A unified periodical boundary conditions for representative volume elements of compo-sites and applications, Int. J. Solids Struct. 40, 1907–1921 (2003) [CrossRef] [Google Scholar]
  31. Z. Wu, L. Xia, S. Wang, T. Shi, Topology optimization of hierarchical lattice structures with substructuring, Comput. Methods Appl. Mech. Eng. 345, 602–617 (2019) [CrossRef] [Google Scholar]
  32. C. Zhang, S. Xu, J. Liu, Y. Ma, Comprehensive clustering-based topology optimization for connectable multi-scale additive manufacturing structures, Addit. Manuf. 54, 102786 (2022) [Google Scholar]
  33. E. Andreassen, A. Clausen, M. Schevenels, B.S. Lazarov, O. Sigmund, Efficient topology optimization in matlab us-ing 88 lines of code, Struct. Multidiscipl. Optim. 43, 1–16 (2011) [CrossRef] [Google Scholar]
  34. O. Sigmund, A 99 line topology optimization code written in matlab, Struct. Multidiscipl. Optim. 21, 120–127 (2001) [Google Scholar]
  35. E.A. Nadaraya, On estimating regression, Theory Probab. Appl. 9, 141–142 (1964) [CrossRef] [Google Scholar]
  36. K. Svanberg, The method of moving asymptotes — a new method for structural optimization, Int. J. Numer. Methods Eng. 24, 359–373 (1987) [CrossRef] [Google Scholar]
  37. J. Wallach, L. Gibson, Mechanical behavior of a three-dimensional truss material, Int. J. Solids Struct. 38, 7181–7196 (2001) [CrossRef] [Google Scholar]
  38. L. Liu, J. Yan, G. Cheng, Optimum structure with homogeneous optimum truss-like material, Comput. Struct. 86, 1417–1425 (2008) [CrossRef] [Google Scholar]
  39. M.P. Schmidt, C.B.W. Pedersen, C. Gout, On structural topology optimization using graded porosity control, Struct. Multidiscipl. Optim. 60, 1437–1453 (2019) [CrossRef] [Google Scholar]
  40. Open-source available on GitHub for reproducible research purpose (https://github.com/mid2SUPAERO/Ex-EMTO) [Google Scholar]

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