Open Access
Review
Issue
Int. J. Simul. Multidisci. Des. Optim.
Volume 14, 2023
Article Number 12
Number of page(s) 16
DOI https://doi.org/10.1051/smdo/2023015
Published online 25 October 2023
  1. P. Duysinx, Optimization topologique: du milieu continu à la structure élastique, 1996. [Google Scholar]
  2. G.I. Rozvany, A critical review of established methods of structural topology optimization, Struct. Multidiscip. Optim. 37, 217–237 (2009) [CrossRef] [MathSciNet] [Google Scholar]
  3. O. Sigmund, K. Maute, Topology optimization approaches, Struct. Multidiscip. Optim. 48, 1031–1055 (2013) [CrossRef] [MathSciNet] [Google Scholar]
  4. N.P. Van Dijk, K. Maute, M. Langelaar, F. Van Keulen, Level-set methods for structural topology optimization: a review, Struct. Multidiscip. Optim. 48, 437–472 (2013) [CrossRef] [MathSciNet] [Google Scholar]
  5. S. Zargham, T.A. Ward, R. Ramli, I.A. Badruddin, Topology optimization: a review for structural designs under vibration problems, Struct. Multidiscip. Optim. 53, 1157–1177 (2016) [CrossRef] [MathSciNet] [Google Scholar]
  6. J. Wu, O. Sigmund, J.P. Groen, Topology optimization of multi-scale structures: a review, Struct. Multidiscip. Optim. 63, 1455–1480 (2021) [CrossRef] [MathSciNet] [Google Scholar]
  7. M.P. Bendsøe, N. Kikuchi, Generating optimal topologies in structural design using a homogenization method, Comput. Methods Appl. Mech. Eng. 71, 197–224 (1988) [Google Scholar]
  8. G.I. Rozvany, Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics, Struct. Multidiscip. Optim. 21, 90–108 (2001) [CrossRef] [Google Scholar]
  9. A.R. Yıldız, U.A. Kılıçarpa, E. Demirci, M. Doğan, Topography and topology optimization of diesel engine components for light-weight design in the automotive industry, Mater. Test. 61, 27–34 (2019) [CrossRef] [Google Scholar]
  10. P.S.P. SA, G. Balaji, K. Annamalai, Numerical simulation of crashworthiness parameters for design optimization of an automotive crash-box, Int. J. Simul. Multidiscip. Des. Optim. 13, 3 (2022) [CrossRef] [EDP Sciences] [Google Scholar]
  11. M. Calabrese, T. Primo, A. Del Prete, Optimization of machining fixture for aeronautical thin-walled components, Procedia CIRP, 60, 32–37 (2017) [CrossRef] [Google Scholar]
  12. H. Yue, D. Bassir, H. Medromi, H. Ding, K. Abouzaid, Optimal design of vertical-taking-off-and-landing UAV wing using multilevel approach, Int. J. Simul. Multidiscip. Des. Optim. 11, 26 (2020) [CrossRef] [EDP Sciences] [Google Scholar]
  13. M. Osanov, J.K. Guest, Topology optimization for architected materials design, Ann. Rev. Mater. Res. 46, 211–233 (2016) [CrossRef] [Google Scholar]
  14. J. Rokicki, Adjoint lattice Boltzmann for topology optimization on multi-GPU architecture, Comput. Math. Appl. 71, 833–848 (2016) [CrossRef] [MathSciNet] [Google Scholar]
  15. M. Zhou, G.I.N. Rozvany, The COC algorithm, Part II: Topological, geometrical and generalized shape optimization, Comput. Methods Appl. Mech. Eng. 89, 309–336 (1991) [CrossRef] [Google Scholar]
  16. G.I. Rozvany, M. Zhou, T. Birker, Generalized shape optimization without homogenization, Struct. Optim. 4, 250–252 (1992) [CrossRef] [Google Scholar]
  17. P.A. Nana Takougoum, Adaptation et transformation automatiques des résultats d'optimization topologique en modèles CAO de structures de poutres (Doctoral dissertation, Université du Québec à Trois-Rivières, 2018) [Google Scholar]
  18. Y.M. Xie, G.P. Steven, A simple evolutionary procedure for structural optimization, Comput. Struct. 49, 885–896 (1993) [Google Scholar]
  19. Xie, Y.M. and Steven, G.P., 1994. Optimal design of multiple load case structures using an evolutionary procedure. Engineering computations, 11(4), pp.295-302. [Google Scholar]
  20. Y.M. Xie, G.P. Steven, Evolutionary structural optimization for dynamic problems, Comput. Struct. 58, 1067–1073 (1996) [CrossRef] [Google Scholar]
  21. X.Y. Yang, Y.M. Xie, G.P. Steven, O.M. Querin, Bidirectional evolutionary method for stiffness optimization, AIAA J. 37, 1483–1488 (1999) [CrossRef] [Google Scholar]
  22. O.M. Querin, V. Young, G.P. Steven, Y.M. Xie, Computational efficiency and validation of bi-directional evolutionary structural optimization, Comput. Methods Appl. Mech. Eng. 189, 559–573 (2000) [CrossRef] [Google Scholar]
  23. G.I. Rozvany, O.M. Querin, Combining ESO with rigorous optimality criteria, Int. J. Vehicle Des. 28, 294–299 (2002) [CrossRef] [Google Scholar]
  24. M. Yulin, W. Xiaoming, A level set method for structural topology optimization and its applications, Adv. Eng. Softw. 35, 415–441 (2004) [CrossRef] [Google Scholar]
  25. M.Y. Wang, X. Wang, D. Guo, A level set method for structural topology optimization, Comput. Methods Appl. Mech. Eng. 192, 227–246 (2003) [Google Scholar]
  26. G. Allaire, F. Jouve, A level-set method for vibration and multiple loads structural optimization, Comput. Methods Appl. Mech. Eng. 194 (30-33), 3269–3290 (2005) [CrossRef] [Google Scholar]
  27. T.D. Ngo, A. Kashani, G. Imbalzano, K.T. Nguyen, D. Hui, Additive manufacturing (3D printing): a review of materials, methods, applications and challenges, Compos. Part B: Eng. 143, 172–196 (2018) [CrossRef] [Google Scholar]
  28. L. Di Angelo, P. Di Stefano, A. Marzola, Surface quality prediction in FDM additive manufacturing, Int. J. Adv. Manuf. Technol. 93, 3655–3662 (2017) [CrossRef] [Google Scholar]
  29. M. Abouelmajd, A. Bahlaoui, I. Arroub, M. Zemzami, N. Hmina, M. Lagache, S. Belhouideg, Experimental analysis and optimization of mechanical properties of FDM-processed polylactic acid using Taguchi design of experiment, Int. J. Simul. Multidiscip. Des. Optim. 12, 30 (2021) [CrossRef] [EDP Sciences] [Google Scholar]
  30. M. Schmid, A. Amado, K. Wegener, Polymer powders for selective laser sintering (SLS). In: AIP Conference proceedings, AIP Publishing LLC, 2015, May, Vol. 1664, No. 1, p. 160009 [Google Scholar]
  31. T.G. Spears, S.A. Gold, In-process sensing in selective laser melting (SLM) additive manufacturing, Int. Mater. Manuf. Innov. 5, 16–40 (2016) [CrossRef] [Google Scholar]
  32. M. Salmi, K.S. Paloheimo, J. Tuomi, J. Wolff, A. Mäkitie, Accuracy of medical models made by additive manufacturing (rapid manufacturing), J. Cranio-Maxillofac. Surg. 41, 603–609 (2013) [CrossRef] [Google Scholar]
  33. A. Dass, A. Moridi, State of the art in directed energy deposition: from additive manufacturing to materials design, Coatings 9, 418 (2019) [CrossRef] [Google Scholar]
  34. K.V. Wong, A. Hernandez, A review of additive manufacturing, Int. Sch. Res. Notices 2012, (2012). [Google Scholar]
  35. I. Gibson, D. Rosen, B. Stucker, M. Khorasani, Design for additive manufacturing. In: Additive manufacturing technologies, Springer, Cham,xx 2021, pp. 555–607 [Google Scholar]
  36. O. Sigmund, A 99 line topology optimization code written in Matlab, Struct. Multidiscip. Optim. 21, 120–127 (2001) [CrossRef] [Google Scholar]
  37. O. Sigmund, K. Maute, Topology optimization approaches, Struct. Multidiscip. Optim. 48, 1031–1055 (2013) [CrossRef] [MathSciNet] [Google Scholar]
  38. A. Bensoussan, J.L. Lions, G. Papanicolaou, Asymptotic analysis for periodic structures, Am. Math. Soc. 374, (2011) [Google Scholar]
  39. D. Cioranescu, J.S.J. Paulin, Homogenization in open sets with holes, J. Math. Anal. Appl. 71, 590–607 (1979) [CrossRef] [MathSciNet] [Google Scholar]
  40. M.P. Bendsøe, Optimal shape design as a material distribution problem, Struct. Optim. 1, 193–202 (1989) [CrossRef] [Google Scholar]
  41. I. El Khadiri, M. Zemzami, N. Hmina, M. Lagache, S. Belhouideg, Topology optimization of structures obtained by additive manufacturing: case of 3D beam. In: 2021 7th International Conference on Optimization and Applications (ICOA), 2021 May, IEEE, C pp. 1–4 [Google Scholar]
  42. Z. Luo, J. Yang, L. Chen, A new procedure for aerodynamic missile designs using topological optimization approach of continuum structures, Aerosp. Sci. Technol. 10, 364–373 (2006) [CrossRef] [Google Scholar]
  43. N. Sabkhi, D. Frey, S.B. Afia, Optimization topologique des structures autoportantes pour la fabrication additive : application au cas de poutre PMH de la caisse en Blanc, in: 24ème Congrès Français de Mécanique, 2019 [Google Scholar]
  44. L. Xia, Q. Xia, X. Huang, Y.M. Xie, Bi-directional evolutionary structural optimization on advanced structures and materials: a comprehensive review, Arch. Comput. Methods Eng. 25, 437–478 (2018) [CrossRef] [MathSciNet] [Google Scholar]
  45. O.M. Querin, G.P. Steven, Y.M. Xie, Evolutionary structural optimization using an additive algorithm, Finite Elem. Anal. Des. 34, 291–308 (2000) [CrossRef] [Google Scholar]
  46. O.M. Querin, G.P. Steven, Y.M. Xie, Evolutionary structural optimization (ESO) using a bidirectional algorithm, Eng. Comput. 15(8), pp.1031-1048. [Google Scholar]
  47. L. Xia, L. Zhang, Q. Xia, T. Shi, Stress-based topology optimization using bi-directional evolutionary structural optimization method, Comput. Methods Appl. Mech. Eng. 333, 356–370 (2018) [CrossRef] [MathSciNet] [Google Scholar]
  48. J.A. Sethian, Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science (Cambridge university press, 1999), Vol. 3 [Google Scholar]
  49. S. Zargham, T.A. Ward, R. Ramli, I.A. Badruddin, Topology optimization: a review for structural designs under vibration problems, Struct. Multidiscip. Optim. 53, 1157–1177 (2016) [CrossRef] [MathSciNet] [Google Scholar]
  50. X. Gui, M. Xiao, Y. Zhang, L. Gao, Y. Liao, Structural topology optimization based on parametric level set method under the environment of ANSYS secondary development. In: 2nd International Conference on Computer Engineering, Information Science & Application Technology (ICCIA 2017), 2016 July, Atlantis Press, pp. 868–877 [Google Scholar]
  51. M. Mani, P. Witherell, Design rules for additive manufacturing: literature review and research categorization, 2017 [Google Scholar]
  52. A. Diaz, O. Sigmund, Checkerboard patterns in layout optimization, Struct. Optim. 10, 40–45 (1995) [CrossRef] [Google Scholar]
  53. C.S. Jog, R.B. Haber, Stability of finite element models for distributed-parameter optimization and topology design, Comput. Methods Appl. Mech. Eng. 130, 203–226 (1996) [CrossRef] [Google Scholar]
  54. L. Ambrosio, G. Buttazzo, An optimal design problem with perimeter penalization, Calc. Var. Partial Differ. Equ. 1, 55–69 (1993) [CrossRef] [Google Scholar]
  55. J.K. Guest, J.H. Prévost, T. Belytschko, Achieving minimum length scale in topology optimization using nodal design variables and projection functions, Int. J. Numer. Methods Eng. 61, 238–254 (2004) [Google Scholar]
  56. O. Sigmund, Morphology-based black and white filters for topology optimization, Struct. Multidiscip. Optim. 33, 401–424 (2007) [CrossRef] [Google Scholar]
  57. F. Wang, B.S. Lazarov, O. Sigmund, On projection methods, convergence and robust formulations in topology optimization, Struct. Multidiscip. Optim. 43, 767–784 (2011) [CrossRef] [Google Scholar]
  58. W. Zhang, W. Zhong, X. Guo, An explicit length scale control approach in SIMP-based topology optimization, Comput. Methods Appl. Mech. Eng. 282, 71–86 (2014) [CrossRef] [Google Scholar]
  59. L. Hägg, E. Wadbro, On minimum length scale control in density based topology optimization, Struct. Multidiscip. Optim. 58, 1015–1032 (2018) [CrossRef] [MathSciNet] [Google Scholar]
  60. K. Yang, E. Fernandez, C. Niu, P. Duysinx, J. Zhu, W. Zhang, Note on spatial gradient operators and gradient-based minimum length constraints in SIMP topology optimization, Struct. Multidiscip. Optim. 60, 393–400 (2019) [CrossRef] [MathSciNet] [Google Scholar]
  61. G. Costa, M. Montemurro, J. Pailhès, Minimum length scale control in a NURBS-based SIMP method, Comput. Methods Appl. Mech. Eng. 354, 963–989 (2019) [CrossRef] [Google Scholar]
  62. X. Rong, J. Rong, S. Zhao, F. Li, J. Yi, L. Peng, New method for controlling minimum length scales of real and void phase materials in topology optimization, Acta Mech. Sin. 36, 805–826 (2020) [CrossRef] [MathSciNet] [Google Scholar]
  63. X. Guo, W. Zhang, W. Zhong, Explicit feature control in structural topology optimization via level set method, Comput. Methods Appl. Mech. Eng. 272, 354–378 (2014) [CrossRef] [Google Scholar]
  64. Q. Xia, T. Shi, Constraints of distance from boundary to skeleton: for the control of length scale in level set based structural topology optimization, Comput. Methods Appl. Mech. Eng. 295, 525–542 (2015) [CrossRef] [Google Scholar]
  65. W. Zhang, D. Li, J. Zhang, X. Guo, Minimum length scale control in structural topology optimization based on the Moving Morphable Components (MMC) approach, Comput. Methods Appl. Mech. Eng. 311, 327–355 (2016) [CrossRef] [Google Scholar]
  66. R. Wang, X. Zhang, B. Zhu, Imposing minimum length scale in moving morphable component (MMC)-based topology optimization using an effective connection status (ECS) control method, Comput. Methods Appl. Mech. Eng. 351, 667–693 (2019) [CrossRef] [Google Scholar]
  67. J. Liu, Piecewise length scale control for topology optimization with an irregular design domain, Comput. Methods Appl. Mech. Eng. 351, 744–765 (2019) [CrossRef] [Google Scholar]
  68. C.S. Andreasen, M.O. Elingaard, N. Aage, Level set topology and shape optimization by density methods using cut elements with length scale control, Struct. Multidiscip. Optim. 62, 685–707 (2020) [CrossRef] [MathSciNet] [Google Scholar]
  69. P.D. Dunning, Minimum length-scale constraints for parameterized implicit function based topology optimization, Struct. Multidiscip. Optim. 58, 155–169 (2018) [CrossRef] [MathSciNet] [Google Scholar]
  70. S. Liu, Q. Li, W. Chen, L. Tong, G. Cheng, An identification method for enclosed voids restriction in manufacturability design for additive manufacturing structures, Front. Mech. Eng. 10, 126–137 (2015) [CrossRef] [Google Scholar]
  71. Q. Li, W. Chen, S. Liu, L. Tong, Structural topology optimization considering connectivity constraint, Struct. Multidiscip. Optim. 54, 971–984 (2016) [CrossRef] [MathSciNet] [Google Scholar]
  72. L. Zhou, W. Zhang, Topology optimization method with elimination of enclosed voids, Struct. Multidiscip. Optim. 60, 117–136 (2019) [CrossRef] [Google Scholar]
  73. Y. Xiong, S. Yao, Z.L. Zhao, Y.M. Xie, A new approach to eliminating enclosed voids in topology optimization for additive manufacturing, Addit. Manuf. 32, 101006 (2020) [Google Scholar]
  74. C. Wang, B. Xu, Q. Meng, J. Rong, Y. Zhao, Numerical performance of Poisson method for restricting enclosed voids in topology optimization, Comput. Struct. 239, 106337 (2020) [CrossRef] [Google Scholar]
  75. K. Hu, S. Jin, C.C. Wang, Support slimming for single material based additive manufacturing, Computer-Aided Des. 65, 1–10 (2015) [CrossRef] [Google Scholar]
  76. H.D. Morgan, J.A. Cherry, S. Jonnalagadda, D. Ewing, J. Sienz, Part orientation optimization for the additive layer manufacture of metal components, Int. J. Adv. Manuf. Technol. 86, 1679–1687 (2016) [CrossRef] [Google Scholar]
  77. A.T. Gaynor, J.K. Guest, Topology optimization considering overhang constraints: Eliminating sacrificial support material in additive manufacturing through design, Struct. Multidiscip. Optim. 54, 1157–1172 (2016) [CrossRef] [Google Scholar]
  78. T.E. Johnson, A.T. Gaynor, Three-dimensional projection-based topology optimization for prescribed-angle self-supporting additively manufactured structures, Addit. Manuf. 24, 667–686 (2018) [Google Scholar]
  79. Y.F. Fu, B. Rolfe, L.N. Chiu, Y. Wang, X. Huang, K. Ghabraie, Design and experimental validation of self-supporting topologies for additive manufacturing, Virtual Phys. Prototyp. 14, 382–394 (2019) [CrossRef] [Google Scholar]
  80. J. Zou, Y. Zhang, Z. Feng, Topology optimization for additive manufacturing with self-supporting constraint, Struct. Multidiscip. Optim. 63, 2341–2353 (2021) [CrossRef] [MathSciNet] [Google Scholar]
  81. M. Bi, P. Tran, Y.M. Xie, Topology optimization of 3D continuum structures under geometric self-supporting constraint, Addit. Manuf. 36, 101422 (2020) [Google Scholar]
  82. Y. Zhou, H. Lu, Q. Ren, Y. Li, Generation of a tree-like support structure for fused deposition modelling based on the L-system and an octree, Graph. Models 101, 8–16 (2019) [CrossRef] [Google Scholar]
  83. J. Liu, Q. Chen, X. Liang, A.C. To, Manufacturing cost constrained topology optimization for additive manufacturing, Front. Mech. Eng. 14, 213–221 (2019) [CrossRef] [Google Scholar]
  84. K. Zhang, G. Cheng, Three-dimensional high resolution topology optimization considering additive manufacturing constraints, Addit. Manuf. 35, 101224 (2020) [Google Scholar]
  85. S. Guessasma, W. Zhang, J. Zhu, S. Belhabib, H. Nouri, Challenges of additive manufacturing technologies from an optimization perspective, Int. J. Simul. Multidiscip. Des. Optim. 6, A9 (2015) [CrossRef] [EDP Sciences] [Google Scholar]
  86. C.Y. Chen, L. Freißmuth, S.M. Altug, D. Colin, M. Feuchtgruber, K. Drechsler, Non-planar slicing method for maximizing the anisotropic behavior of continuous fiber-reinforced fused filament fabricated parts, In: International Manufacturing Science and Engineering Conference, 2022 June, American Society of Mechanical Engineers, Vol. 85802, p. V001T01A002 [Google Scholar]
  87. J. Liu, J. Yan, H. Yu, Stress-constrained topology optimization for material extrusion polymer additive manufacturing, J. Comput. Des. Eng. 8, 979–993 (2021) [Google Scholar]
  88. M. Nirish, R. Rajendra, Suitability of metal additive manufacturing processes for part topology optimization-a comparative study, Mater. Today: Proc. 27, 1601–1607 (2020) [CrossRef] [Google Scholar]
  89. R. Ranjan, R. Samant, S. Anand, Integration of design for manufacturing methods with topology optimization in additive manufacturing, J. Manuf. Sci. Eng. 139, 061007 (2017) [CrossRef] [Google Scholar]
  90. L. Meng, W. Zhang, D. Quan, G. Shi, L. Tang, Y. Hou, P. Breitkopf, J. Zhu, T. Gao, From topology optimization design to additive manufacturing: today's success and tomorrow's roadmap, Arch. Comput. Methods Eng. 27, 805–830 (2020) [CrossRef] [Google Scholar]
  91. R.M. Gorguluarslan, U.N. Gandhi, R. Mandapati, S.K. Choi, Design and fabrication of periodic lattice-based cellular structures. Comput. Aided Des. Appl. 13, 50–62 (2016) [CrossRef] [Google Scholar]
  92. F.W. Zok, R.M. Latture, M.R. Begley, Periodic truss structures, J. Mech. Phys. Solids 96, 184–203 (2016) [CrossRef] [Google Scholar]
  93. P.J. Gandy, S. Bardhan, A.L. Mackay, J. Klinowski, Nodal surface approximations to the P, G, D and I-WP triply periodic minimal surfaces, Chem. Phys. Lett. 336, 187–195 (2001) [CrossRef] [Google Scholar]
  94. V.S. Deshpande, N.A. Fleck, M.F. Ashby, Effective properties of the octet-truss lattice material, J. Mech. Phys. Solids 49, 1747–1769 (2001) [CrossRef] [Google Scholar]
  95. P. Qiao, M. Yang, F. Bobaru, Impact mechanics and high-energy absorbing materials, J. Aerosp. Eng. 21, 235–248 (2008) [Google Scholar]
  96. T. Tancogne-Dejean, A.B. Spierings, D. Mohr, Additively-manufactured metallic micro-lattice materials for high specific energy absorption under static and dynamic loading, Acta Mater. 116, 14–28 (2016) [CrossRef] [Google Scholar]
  97. M. Helou, S. Vongbunyong, S. Kara, Finite element analysis and validation of cellular structures, Proc. CIRP 50, 94–99 (2016) [CrossRef] [Google Scholar]
  98. D.W. Lee, Z.D. Ma, N. Kikuchi, An innovative I-bumper concept for improved crashworthiness of military and commercial vehicles (No. 2008 −01-0512), SAE Technical Paper, 2008 [Google Scholar]
  99. L.E. Murr, S.M. Gaytan, F. Medina, H. Lopez, E. Martinez, B.I. Machado, D.H. Hernandez, L. Martinez, M.I. Lopez, R.B. Wicker, J. Bracke, Next-generation biomedical implants using additive manufacturing of complex, cellular and functional mesh arrays, Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. 368 (1917) 1999–2032 (2010) [Google Scholar]
  100. L.E. Murr, K.N. Amato, S.J. Li, Y.X. Tian, X.Y. Cheng, S.M. Gaytan, E. Martinez, P.W. Shindo, F. Medina, R.B. Wicker, Microstructure and mechanical properties of open-cellular biomaterials prototypes for total knee replacement implants fabricated by electron beam melting, J. Mech. Behav. Biomed. Mater. 4, 1396–1411 (2011) [CrossRef] [Google Scholar]
  101. M. Helou, S. Kara, Design, analysis and manufacturing of lattice structures: an overview. Int. J. Comput. Integr. Manuf. 31, 243–261 (2018) [CrossRef] [Google Scholar]
  102. J. Robbins, S.J. Owen, B.W. Clark, T.E. Voth, An efficient and scalable approach for generating topologically optimized cellular structures for additive manufacturing, Addit. Manuf. 12, 296–304 (2016) [Google Scholar]
  103. C. Wang, J.H. Zhu, W.H. Zhang, S.Y. Li, J. Kong, Concurrent topology optimization design of structures and non-uniform parameterized lattice microstructures, Struct. Multidiscip. Optim. 58, 35–50 (2018) [CrossRef] [MathSciNet] [Google Scholar]
  104. C.R. Thomsen, F. Wang, O. Sigmund, Buckling strength topology optimization of 2D periodic materials based on linearized bifurcation analysis, Comput. Meth. Appl. Mech. Eng. 339, 115–136 (2018) [CrossRef] [Google Scholar]
  105. Z. Fan, J. Yan, M. Wallin, M. Ristinmaa, B. Niu, G. Zhao, Multiscale eigenfrequency optimization of multimaterial lattice structures based on the asymptotic homogenization method, Struct. Multidiscip. Optim. 61, 983–998 (2020) [CrossRef] [Google Scholar]
  106. J. Wu, W. Wang, X. Gao, Design and optimization of conforming lattice structures, IEEE Trans. Vis. Comput. Graph. 27, 43–56 (2019) [Google Scholar]
  107. M. Jansen, O. Pierard, A hybrid density/level set formulation for topology optimization of functionally graded lattice structures, Comput. Struct. 231, 106205 (2020) [CrossRef] [Google Scholar]
  108. L. Cheng, J. Liu, X. Liang, A.C. To, Coupling lattice structure topology optimization with design-dependent feature evolution for additive manufactured heat conduction design, Comput. Methods Appl. Mech. Eng. 332, 408–439 (2018) [CrossRef] [Google Scholar]
  109. Y. Tang, A. Kurtz, Y.F. Zhao, Bidirectional Evolutionary Structural Optimization (BESO) based design method for lattice structure to be fabricated by additive manufacturing, Comput. Aided Des. 69, 91–101 (2015) [CrossRef] [Google Scholar]
  110. Y. Tang, G. Dong, Q. Zhou, Y.F. Zhao, Lattice structure design and optimization with additive manufacturing constraints, IEEE Trans. Autom. Sci. Eng. 15, 1546–1562 (2017) [Google Scholar]
  111. A.M. Vilardell, A. Takezawa, A. Du Plessis, N. Takata, P. Krakhmalev, M. Kobashi, I. Yadroitsava, I. Yadroitsev, Topology optimization and characterization of Ti6Al4V ELI cellular lattice structures by laser powder bed fusion for biomedical applications, Mater. Sci. Eng.: A 766, 138330 (2019) [CrossRef] [Google Scholar]
  112. S. Mantovani, G.A. Campo, M. Giacalone, Steering column support topology optimization including lattice structure for metal additive manufacturing, Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci. 21(4), pp. 235-248. [Google Scholar]
  113. A.J. Kulangara, C.S.P. Rao, J. Cherian, Topology optimization of lattice structure on a brake pedal, Mater. Today: Proc. 47, 5334–5337 (2021) [CrossRef] [Google Scholar]
  114. A. Panesar, M. Abdi, D. Hickman, I. Ashcroft, Strategies for functionally graded lattice structures derived using topology optimization for additive manufacturing, Addit. Manuf. 19, 81–94 (2018) [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.