DOI QR코드

DOI QR Code

A new algorithm for design of support structures in additive manufacturing by using topology optimization

  • 투고 : 2022.10.01
  • 심사 : 2023.03.06
  • 발행 : 2023.04.10

초록

In this paper, a density based topology optimization is proposed for generating of supports required in additive manufacturing to maintain the overhanging regions of main structures during layer by layer fabrication process. For this purpose, isogeometric analysis method is employed to model geometry and structural analysis of main and support structures. In order to model the problem two cases are investigated. In the first case, design domain of supports can easily be separated from the main structure by using distinct isogeometric patches. The second case happens when the main structure itself is optimized by using topology optimization and the supports should be designed in the voids of optimum layout. In this case, in order to avoid boundary identification and re-meshing process for separating design domain of supports from main structure, a parameterization technique is proposed to identify the design domain of supports. To achieve this, two density functions are defined over the entire domain to describe the main structure and supporting areas. On the other hand, since supports are under gravity loads while main structure and its stiffness is not completed during manufacturing process, in the proposed method, stiffness of the main structure is considered to be trivial and the gravity loads are also naturally applied to design support structures. By doing so, the results show reasonable supports are created to protect, continuously, overhanging surfaces of the main structure. Several examples are presented to demonstrate the efficiency of the proposed method and compare the results with literature.

키워드

과제정보

The authors would like to thank Professor Krister Svanberg for providing the MMA optimization code.

참고문헌

  1. Alexander, P., Allen, S. and Dutta, D. (1998), "Part orientation and build cost determination in layered manufacturing", Comput. Aid. Des., 30(5), 343-356. https://doi.org/10.1016/S0010-4485(97)00083-3. 
  2. Allaire, G. and Bogosel, B. (2018), "Optimizing supports for additive manufacturing", Struct. Multidisc. Optim., 58(6), 2493-2515. https://doi.org/10.1007/s00158-018-2125-x. 
  3. Allaire, G., Bihr, M. and Bogosel, B. (2020), "Support optimization in additive manufacturing for geometric and thermo-mechanical constraints", Struct. Multidisc. Optim., 61(6), 2377-2399. https://doi.org/10.1007/s00158-020-02551-1. 
  4. Allen, S. and Dutta, D. (1994), "On the computation of part orientation using support structures in layered manufacturing", Proceedings of the Solid Free-form Fabrication Symposium, Austin. 
  5. Aminzadeh, M. and Tavakkoli, S.M. (2022), "A parameter space approach for isogeometrical level set topology optimization", Int. J. Numer. Meth. Eng., 123(15), 3485-3506. https://doi.org/10.1002/nme.6976. 
  6. Bazilevs, Y., Beirao da Veiga, L., Cottrell, J.A., Hughes, T.J. and Sangalli, G. (2006), "Isogeometric analysis: Approximation, stability and error estimates for h-refined meshes", Math. Model. Meth. Appl. Sci., 16(7), 1031-1090. https://doi.org/10.1142/S0218202506001455. 
  7. Bendsoe, M.P. and Kikuchi, N. (1988), "Generating optimal topologies in structural design using a homogenization method", Comput. Meth. Appl. Mech. Eng., 71(2), 197-224. https://doi.org/10.1016/0045-7825(88)90086-2. 
  8. Bruyneel, M. and Duysinx, P. (2005), "Note on topology optimization of continuum structures including self-weight", Struct. Multidisc. Optim., 29(4), 245-256. https://doi.org/10.1007/s00158-004-0484-y. 
  9. Buchanan, C. and Gardner, L. (2019), "Metal 3D printing in construction: A review of methods, research, applications, opportunities and challenges", Eng. Struct., 180, 332-348. https://doi.org/10.1016/j.engstruct.2018.11.045. 
  10. Carraturo, M., Hennig, P., Alaimo, G., Heindel, L., Auricchio, F., Kastner, M. and Reali, A. (2021), "Additive manufacturing applications of phase-field-based topology optimization using adaptive isogeometric analysis", GAMM Mitteilungen, 44(3), e202100013. https://doi.org/10.1002/gamm.202100013. 
  11. Cheng, L., Liang, X., Bai, J., Chen, Q., Lemon, J. and To, A. (2019), "On utilizing topology optimization to design support structure to prevent residual stress induced build failure in laser powder bed metal additive manufacturing", Addit. Manuf., 27, 290-304. https://doi.org/10.1016/j.addma.2019.03.001. 
  12. Das, P., Chandran, R., Samant, R. and Anand, S. (2015), "Optimum part build orientation in additive manufacturing for minimizing part errors and support structures", Procedia Manuf., 1, 343-354. https://doi.org/10.1016/j.promfg.2015.09.041. 
  13. Dede, L., Borden, M.J. and Hughes, T.J.R. (2012), "Isogeometric analysis for topology optimization with a phase field model", Arch. Comput. Meth. Eng., 19(3), 427-465. https://doi.org/10.1007/s11831-012-9075-z. 
  14. Dumas, J., Hergel, J. and Lefebvre, S. (2014), "Bridging the gap: Automated steady scaffoldings for 3D printing", ACM Trans. Graph., 33(4), 1-10. https://doi.org/10.1145/2601097.2601153. 
  15. Frank, D. and Fadel, G. (1995), "Expert system-based selection of the preferred direction of build for rapid prototyping processes", J. Intel. Manuf., 6(5), 339-345. https://doi.org/10.1007/BF00124677. 
  16. Gan, M.X. and Wong, C.H. (2016), "Practical support structures for selective laser melting", J. Mater. Proc. Technol., 238, 474-484. https://doi.org/10.1016/j.jmatprotec.2016.08.006. 
  17. Garaigordobil, A., Ansola, R., Vegueria, E. and Fernandez, I. (2019), "Overhang constraint for topology optimization of selfsupported compliant mechanisms considering additive manufacturing", Comput. Aid. Des., 109, 33-48. https://doi.org/10.1016/j.cad.2018.12.006. 
  18. Gardner, L. (2023), "Metal additive manufacturing in structural engineering-review, advances, opportunities and outlook", Struct., 47, 2178-2193. https://doi.org/10.1016/j.istruc.2022.12.039. 
  19. Gaynor, A.T. and Guest, J.K. (2016), "Topology optimization considering overhang constraints: Eliminating sacrificial support material in additive manufacturing through design", Struct. Multidisc. Optim., 54(5), 1157-1172. https://doi.org/10.1007/s00158-016-1551-x. 
  20. Ghasemi, H., Park, H.S. and Rabczuk, T. (2017), "A level-set based IGA formulation for topology optimization of flexoelectric materials", Comput. Meth. Appl. Mech. Eng., 313, 239-258. https://doi.org/10.1016/j.cma.2016.09.029. 
  21. Giraldo-Londono, O., Mirabella, L., Dalloro, L. and Paulino, G.H. (2020), "Multi-material thermomechanical topology optimization with applications to additive manufacturing: Design of main composite part and its support structure", Comput. Meth. Appl. Mech. Eng., 363, 112812. https://doi.org/10.1016/j.cma.2019.112812. 
  22. Halaku, A. and Tavakkoli, S.M. (2021), "An isogeometrical level set topology optimization for plate structures", Struct. Eng. Mech., 80(1), 103. https://doi.org/10.12989/sem.2021.80.1.103. 
  23. Hassani, B., Khanzadi, M. and Tavakkoli, S.M. (2012), "An isogeometrical approach to structural topology optimization by optimality criteria", Struct. Multidisc. Optim., 45(2), 223-233. https://doi.org/10.1007/s00158-011-0680-5. 
  24. Hughes, T.J.R., Cottrell, J.A. and Bazilevs, Y. (2005), "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement", Comput. Meth. Appl. Mech. Eng., 194(39-41), 4135-4195. https://doi.org/10.1016/j.cma.2004.10.008. 
  25. Hussein, A., Hao, L., Yan, C., Everson, R. and Young, P. (2013), "Advanced lattice support structures for metal additive manufacturing", J. Mater. Proc. Technol., 213(7), 1019-1026. https://doi.org/10.1016/j.jmatprotec.2013.01.020. 
  26. Hussein, A., Yan, C., Everson, R. and Hao, L. (2011), "Preliminary investigation on cellular support structures using SLM process", Innovative Developments in Virtual and Physical Prototyping; Taylor & Francis Group, London, UK. 
  27. ISO/ASTM 52900 (2015), Additive Manufacturing-General Principles and Terminology, International Standard. 
  28. Jahangiry, H.A. and Tavakkoli, S.M. (2017), "An isogeometrical approach to structural level set topology optimization", Comput. Meth. Appl. Mech. Eng., 319, 240-257. https://doi.org/10.1016/j.cma.2017.02.005. 
  29. Jahangiry, H.A., Gholhaki, M., Naderpour, H. and Tavakkoli, S.M. (2021), "Isogeometric level set topology optimization for elastoplastic plane stress problems", Int. J. Mech. Mater. Des., 17(4), 947-967. https://doi.org/10.1007/s10999-021-09562-w. 
  30. Jahangiry, H.A., Gholhaki, M., Naderpour, H. and Tavakkoli, S.M. (2022), "Isogeometric level set-based topology optimization for geometrically nonlinear plane stress problems", Comput. Aid. Des., 151, 103358. https://doi.org/10.1016/j.cad.2022.103358. 
  31. Jiang, J., Xu, X. and Stringer, J. (2018), "Support structures for additive manufacturing: A review", J. Manuf. Mater. Proc., 2(4), 64. https://doi.org/10.3390/jmmp2040064. 
  32. Kazemi, H.S., Tavakkoli, S.M. and Naderi, R. (2016), "Isogeometric topology optimization of structures considering weight minimization and local stress constraints", Int. J. Optim. Civil Eng., 6(2), 303-317. 
  33. Kuo, Y.H., Cheng, C.C., Lin, Y.S. and San, C.H. (2018), "Support structure design in additive manufacturing based on topology optimization", Struct. Multidisc. Optim., 57(1), 183-195. https://doi.org/10.1007/s00158-017-1743-z. 
  34. Langelaar, M. (2016), "Topology optimization of 3D selfsupporting structures for additive manufacturing", Addit. Manuf., 12, 60-70. https://doi.org/10.1016/j.addma.2016.06.010. 
  35. Langelaar, M. (2018), "Combined optimization of part topology, support structure layout and build orientation for additive manufacturing", Struct. Multidisc. Optim., 57(5), 1985-2004. https://doi.org/10.1007/s00158-017-1877-z. 
  36. Leary, M., Merli, L., Torti, F., Mazur, M. and Brandt, M. (2014), "Optimal topology for additive manufacture: A method for enabling additive manufacture of support-free optimal structures", Mater. Des., 63, 678-690. https://doi.org/10.1016/j.matdes.2014.06.015. 
  37. Les, P. and Tiller, W. (1997), The NURBS Book, Springer-Verlag, New York, USA. 
  38. Liu, J. and To, A.C. (2017), "Deposition path planning-integrated structural topology optimization for 3D additive manufacturing subject to self-support constraint", Comput. Aid. Des., 91, 27-45. https://doi.org/10.1016/j.cad.2017.05.003. 
  39. Liu, Y., Li, Z., Wei, P. and Chen, S. (2019), "Generating support structures for additive manufacturing with continuum topology optimization methods", Rap. Prototyp. J., 25(2), 232-246. https://doi.org/10.1108/RPJ-10-2017-0213. 
  40. Luo, Y., Sigmund, O., Li, Q. and Liu, S. (2020), "Additive manufacturing oriented topology optimization of structures with self-supported enclosed voids", Comput. Meth. Appl. Mech. Eng., 372, 113385. https://doi.org/10.1016/j.cma.2020.113385. 
  41. Mezzadri, F., Bouriakov, V. and Qian, X. (2018), "Topology optimization of self-supporting support structures for additive manufacturing", Addit. Manuf., 21, 666-682. https://doi.org/10.1016/j.addma.2018.04.016. 
  42. Michell, A.G.M. (1904), "The limits of economy of material in frame-structures", London, Edinburgh, Dublin Philos. Mag. J. Sci., 8(47), 589-597. https://doi.org/10.1080/14786440409463229. 
  43. Miki, T. and Nishiwaki, S. (2022), "Topology optimization of the support structure for heat dissipation in additive manufacturing", Finite Elem. Anal. Des., 203, 103708. https://doi.org/10.1016/j.finel.2021.103708. 
  44. Nguyen, C., Zhuang, X., Chamoin, L., Zhao, X., Nguyen-Xuan, H. and Rabczuk, T. (2020), "Three-dimensional topology optimization of auxetic metamaterial using isogeometric analysis and model order reduction", Comput. Meth. Appl. Mech. Eng., 371, 113306. https://doi.org/10.1016/j.cma.2020.113306. 
  45. Pandey, P.M., Thrimurthulu, K. and Reddy, N.V. (2004), "Optimal part deposition orientation in FDM by using a multicriteria genetic algorithm", Int. J. Prod. Res., 42(19), 4069-4089. https://doi.org/10.1080/00207540410001708470. 
  46. Paul, R. and Anand, S. (2015), "Optimization of layered manufacturing process for reducing form errors with minimal support structures", J. Manuf. Syst., 36, 231-243. https://doi.org/10.1016/j.jmsy.2014.06.014. 
  47. Pellens, J., Lombaert, G., Michiels, M., Craeghs, T. and Schevenels, M. (2020), "Topology optimization of support structure layout in metal-based additive manufacturing accounting for thermal deformations", Struct. Multidisc. Optim., 61(6), 2291-2303. https://doi.org/10.1007/s00158-020-02512-8. 
  48. Pham, D.T., Dimov, S.S. and Gault, R.S. (1999), "Part orientation in stereolithography", Int. J. Adv. Manuf. Technol., 15(9), 674-682. https://doi.org/10.1007/s001700050118. 
  49. Rozvany, G.I.N. (1989), "Branching support structures for 3D printing", Structural Design via Optimality Criteria. 
  50. Schmidt, R. and Umetani, N. (2014), SIGGRAPH. https://doi.org/10.1145/2619195.2656293. 
  51. Sethian, J.A. and Wiegmann, A. (2000), "Structural boundary design via level set and immersed interface methods", J. Comput. Phys., 163(2), 489-528. https://doi.org/10.1006/jcph.2000.6581. 
  52. Sha, W., Hu, R., Xiao, M., Chu, S., Zhu, Z., Qiu, C.W. and Gao, L. (2022), "Topology-optimized thermal metamaterials traversing full-parameter anisotropic space", NPJ Comput. Mater., 8(1), 179. https://doi.org/10.1038/s41524-022-00861-0. 
  53. Sha, W., Xiao, M., Zhang, J., Ren, X., Zhu, Z., Zhang, Y., ... & Hu, R. (2021), "Robustly printable freeform thermal metamaterials", Nat. Commun., 12(1), 7228. https://doi.org/10.1038/s41467-021-27543-7. 
  54. Shen, Z.H., Dai, N., Li, D.W. and Wu, C.Y. (2016), "Bridge support structure generation for 3D printing", Materials, Manufacturing Technology, Electronics and Information Science (MMTEI2015) Proceedings for the 2015 International Workshop on Materials, Manufacturing Technology, Electronics and Information Science (MMTEI2015), 141-149. https://doi.org/10.1142/9789813109384_0016. 
  55. Strano, G., Hao, L., Everson, R.M. and Evans, K.E. (2013), "A new approach to the design and optimisation of support structures in additive manufacturing", Int. J. Adv. Manuf. Technol., 66(9-12), 1247-1254. https://doi.org/10.1007/s00170-012-4403-x. 
  56. Svanberg, K. (1987), "The method of moving asymptotes-a new method for structural optimization", Int. J. Numer. Meth. Eng., 24(2), 359-373. https://doi.org/10.1002/nme.1620240207. 
  57. Tavakkoli, S.M. and Hassani, B. (2014), "Isogeometric topology optimization by using optimality criteria and implicit function", Int. J. Optim. Civil Eng., 4(2), 1-26. 
  58. Tavakkoli, S.M., Hassani, B. and Ghasemnejad, H. (2013), "Isogeometric topology optimization of structures by using MMA", Int. J. Optim. Civil Eng., 3(2), 313-326. 
  59. Thore, C.J., Grundstrom, H.A., Torstenfelt, B. and Klarbring, A. (2019), "Penalty regulation of overhang in topology optimization for additive", Struct. Multidisc. Optim., 60, 59-67. https://doi.org/10.1007/s00158-019-02194-x. 
  60. Vaidya, R. and Anand, S. (2016), "Optimum support structure generation for additive manufacturing using unit cell structures and support removal constraint", Procedia Manuf., 5, 1043-1059. https://doi.org/10.1016/j.promfg.2016.08.072. 
  61. Vanek, J., Galicia, J.A.G. and Benes, B. (2014). "Clever support: Efficient support structure generation for digital fabrication", Computer Graphics Forum, 33(5), 117-125.  https://doi.org/10.1111/cgf.12437
  62. Wang, M.Y., Wang, X. and Guo, D. (2003), "A level set method for structural topology optimization", Comput. Meth. Appl. Mech. Eng., 192(1-2). https://doi.org/10.1016/S0045- 7825(02)00559-5. 
  63. Wang, Y., Gao, J. and Kang, Z (2018), "Level set-based topology optimization with overhang constraint: Towards support-free additive manufacturing", Comput. Meth. Appl. Mech. Eng., 339, 591-614. https://doi.org/10.1016/j.cma.2018.04.040. 
  64. Xie, X., Wang, S., Xu, M., Jiang, N. and Wang, Y. (2020), "A hierarchical spline based isogeometric topology optimization using moving morphable components", Comput. Meth. Appl. Mech. Eng., 360, 112696. https://doi.org/10.1016/j.cma.2019.112696. 
  65. Xu, M., Wang, S. and Xie, X. (2019), "Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency", Front. Mech. Eng., 14(2), 222-234. https://doi.org/10.1007/s11465-019-0534-1. 
  66. Yang, Y., Fuh, J.Y., Loh, H.T. and Wong, Y.S. (2003), "Multiorientational deposition to minimize support in the layered manufacturing process", J. Manuf. Syst., 22(2), 116-129. https://doi.org/10.1016/S0278-6125(03)90009-4. 
  67. Ye, J., Kyvelou, P., Gilardi, F., Lu, H., Gilbert, M. and Gardner, L. (2021), "An end-to-end framework for the additive manufacture of optimized tubular structures", IEEE Access, 9, 165476- 165489. https://doi.org/10.1109/ACCESS.2021.3132797. 
  68. Zhang, K. and Cheng, G. (2020), "Three-dimensional high resolution topology optimization considering additive manufacturing constraints", Addit. Manuf., 35, 101224. https://doi.org/10.1016/j.addma.2020.101224. 
  69. Zhang, K., Cheng, G. and Xu, L. (2019), "Topology optimization considering overhang constraint in additive manufacturing", Comput. Struct., 212, 86-100. https://doi.org/10.1016/j.compstruc.2018.10.011. 
  70. Zhang, L., Song, B., Fu, J.J., Wei, S.S., Yang, L., Yan, C.Z., ... & Shi, Y.S. (2020), "Topology-optimized lattice structures with simultaneously high stiffness and light weight fabricated by selective laser melting: Design, manufacturing and characterization", J. Manuf. Proc., 56, 1166-1177. https://doi.org/10.1016/j.jmapro.2020.06.005. 
  71. Zhang, W. and Zhou, L. (2018), "Topology optimization of selfsupporting structures with polygon features for additive manufacturing", Comput. Meth. Appl. Mech. Eng., 334, 56-78. https://doi.org/10.1016/j.cma.2018.01.037. 
  72. Zhao, G., Zhou, C. and Das, S. (2015), "Solid mechanics based design and optimization for support structure generation in stereolithography based additive manufacturing", International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Boston, Massachusetts, USA. 
  73. Zhao, H.M., He, Y., Fu, J.Z. and Qiu, J.J. (2018), "Inclined layer printing for fused deposition modeling without assisted supporting structure", Robot. Comput.-Integr. Manuf., 51, 1-13. https://doi.org/10.1016/j.rcim.2017.11.011. 
  74. Zhao, J. (2005), "Determination of optimal build orientation based on satisfactory degree theory for RPT", 9th International Conference on Computer Aided Design and Computer Graphics, Hong Kong, China. 
  75. Zhou, M., Liu, Y. and Lin, Z. (2019), "Topology optimization of thermal conductive support structures for laser additive manufacturing", Comput. Meth. Appl. Mech. Eng., 353, 24-43. https://doi.org/10.1016/j.cma.2019.03.054. 
  76. Zhou, M., Liu, Y. and Wei, C. (2020), "Topology optimization of easy-removal support structures for additive manufacturing", Struct. Multidisc. Optim., 61(6), F2423-2435. https://doi.org/10.1007/s00158-020-02607-2.