Light-weight shape and topology optimization with hybrid deposition path planning for FDM parts

  • Jikai Liu
  • Yongsheng Ma
  • A. J. Qureshi
  • Rafiq AhmadEmail author


FDM (fused deposition modeling) parts demonstrate anisotropic properties between the in-layer raster and transverse directions. However, structural optimization of FDM parts has rarely taken the deposition path and thus the anisotropic material properties into consideration. This work proposes a methodology that integrates optimal hybrid deposition paths with the shape and topology optimization and brings all aspects under a unified level set framework. A dedicated sensitivity analysis is performed on both the shape and path variables, which ensures the optimality of the derived design solutions. Effectiveness of the proposed method is demonstrated through a number of 2D and 3D numerical examples.


Hybrid deposition paths Shape and topology optimization Level set 3D printing Fused deposition modeling 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The authors would like to acknowledge the support from China Scholarship Council (CSC) and Department of Mechanical Engineering at University of Alberta.


  1. 1.
    Rosen DW (2007) Computer-aided design for additive manufacturing of cellular structures. Comput-Aided Des Applic 4:585–594. CrossRefGoogle Scholar
  2. 2.
    Gorguluarslan RM, Park S-I, Rosen DW, Choi S-K (2015) A multilevel upscaling method for material characterization of additively manufactured part under uncertainties. J Mech Des 137:111408. CrossRefGoogle Scholar
  3. 3.
    Ponche R, Kerbrat O, Mognol P, Hascoet J-Y (2014) A novel methodology of design for additive manufacturing applied to additive laser manufacturing process. Rob Comput Integr Manuf 30:389–398. CrossRefGoogle Scholar
  4. 4.
    Meisel N, Williams C (2015) An investigation of key design for additive manufacturing constraints in multimaterial three-dimensional printing. J Mech Des 137:111406. CrossRefGoogle Scholar
  5. 5.
    Gao W, Zhang Y, Ramanujan D, Ramani K, Chen Y, Williams CB, Wang CCL, Shin YC, Zhang S, Zavattieri PD (2015) The status, challenges, and future of additive manufacturing in engineering. Comput Aided Des 69:65–89. CrossRefGoogle Scholar
  6. 6.
    Brackett D, Ashcroft I, Hague R (2011) Topology optimization for additive manufacturing. AustinGoogle Scholar
  7. 7.
    Bendsøe MP, Sigmund O (2004) Topology optimization. Springer Berlin Heidelberg, BerlinCrossRefzbMATHGoogle Scholar
  8. 8.
    Gaynor AT, Meisel NA, Williams CB, Guest JK (2014) Multiple-material topology optimization of compliant mechanisms created via PolyJet three-dimensional printing. J Manuf Sci Eng 136:061015. CrossRefGoogle Scholar
  9. 9.
    Zhang P, Toman J, Yu Y, Biyikli E, Kirca M, Chmielus M, To AC (2015) Efficient design-optimization of variable-density hexagonal cellular structure by additive manufacturing: theory and validation. J Manuf Sci Eng 137:021004. CrossRefGoogle Scholar
  10. 10.
    Maute K, Tkachuk A, Wu J, Jerry Qi H, Ding Z, Dunn ML (2015) Level set topology optimization of printed active composites. J Mech Des 137:111402. CrossRefGoogle Scholar
  11. 11.
    Liu J, To AC (2017) Topology optimization for hybrid additive-subtractive manufacturing. Struct Multidiscip Optim 55:1281–1299. MathSciNetCrossRefGoogle Scholar
  12. 12.
    Liu J, To AC (2017) Deposition path planning-integrated structural topology optimization for 3D additive manufacturing subject to self-support constraint. Comput Aided Des 91:27–45. CrossRefGoogle Scholar
  13. 13.
    Zhang P, Liu J, To AC (2017) Role of anisotropic properties on topology optimization of additive manufactured load bearing structures. Scr Mater 135:148–152. CrossRefGoogle Scholar
  14. 14.
    Liu J, Ma Y (2016) A survey of manufacturing oriented topology optimization methods. Adv Eng Softw 100:161–175. CrossRefGoogle Scholar
  15. 15.
    Qureshi AJ, Shahrain M, Wong WLE, Didier T (2015) Design for scalability and strength optimisation for components created through FDM process. In: 20th International Conference on Engineering Design (ICED 15)Google Scholar
  16. 16.
    Shahrain M, Didier T, Lim GK, Qureshi AJ (2016) Fast deviation simulation for ‘fused deposition modeling’ process. Proc CIRP 43:327–332. CrossRefGoogle Scholar
  17. 17.
    Ahn SH, Montero M, Odell D, Roundy S, Wright PK (2002) Anisotropic material properties of fused deposition modeling ABS. Rapid Prototyp J 8:248–257. CrossRefGoogle Scholar
  18. 18.
    Bellini A, Güçeri S (2003) Mechanical characterization of parts fabricated using fused deposition modeling. Rapid Prototyp J 9:252–264. CrossRefGoogle Scholar
  19. 19.
    Hill N, Haghi M (2014) Deposition direction-dependent failure criteria for fused deposition modeling polycarbonate. Rapid Prototyp J 20:221–227. CrossRefGoogle Scholar
  20. 20.
    Zhou Q, Panetta J, Zorin D (2013) Worst-case structural analysis. ACM Trans Graph 32:137:1–137:12 . doi:
  21. 21.
    Ulu E, Korkmaz E, Yay K, Burak Ozdoganlar O, Burak Kara L (2015) Enhancing the structural performance of additively manufactured objects through build orientation optimization. J Mech Des 137:111410. CrossRefGoogle Scholar
  22. 22.
    Zhang P, To AC (2016) Transversely isotropic hyperelastic-viscoplastic model for glassy polymers with application to additive manufactured photopolymers. Int J Plast 80:56–74. CrossRefGoogle Scholar
  23. 23.
    Umetani N, Schmidt R (2013) Cross-sectional structural analysis for 3D printing optimization. In: SIGGRAPH Asia 2013 Technical Briefs. ACM, New York, NY, USA, p 5:1–5:4Google Scholar
  24. 24.
    Liu J (2016) Guidelines for AM part consolidation. Virtual Phys Prototyp 11:133–141. CrossRefGoogle Scholar
  25. 25.
    Liu J, Yu H (2017) Concurrent deposition path planning and structural topology optimization for additive manufacturing. Rapid Prototyp J 23:930–942. CrossRefGoogle Scholar
  26. 26.
    Shen H, Fu J, Chen Z, Fan Y (2010) Generation of offset surface for tool path in NC machining through level set methods. Int J Adv Manuf Technol 46:1043–1047. CrossRefGoogle Scholar
  27. 27.
    Zhuang C, Xiong Z, Ding H (2010) High speed machining tool path generation for pockets using level sets. Int J Prod Res 48:5749–5766. CrossRefzbMATHGoogle Scholar
  28. 28.
    Wang MY, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192:227–246. MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Allaire G, Jouve F, Toader A-M (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194:363–393. MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Liu J, Cheng L, To AC (2017) Arbitrary void feature control in level set topology optimization. Comput Methods Appl Mech Eng 324:595–618. MathSciNetCrossRefGoogle Scholar
  31. 31.
    Liu J, Cheng Z, Ma Y (2016) Product design-optimization integration via associative optimization feature modeling. Adv Eng Inform 30:713–727. CrossRefGoogle Scholar
  32. 32.
    van Dijk NP, Maute K, Langelaar M, van Keulen F (2013) Level-set methods for structural topology optimization: a review. Struct Multidiscip Optim 48:437–472. MathSciNetCrossRefGoogle Scholar
  33. 33.
    Osher S, Sethian JA (1988) Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J Comput Phys 79:12–49. MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Osher S, Fedkiw R (2003) Level set methods and dynamic implicit surfaces. Springer New York, New YorkCrossRefzbMATHGoogle Scholar
  35. 35.
    Ding D, Pan Z, Cuiuri D, Li H (2015) A practical path planning methodology for wire and arc additive manufacturing of thin-walled structures. Robot Comput Integr Manuf 34:8–19. CrossRefGoogle Scholar
  36. 36.
    Brampton CJ, Wu KC, Kim HA (2015) New optimization method for steered fiber composites using the level set method. Struct Multidiscip Optim 52:493–505. MathSciNetCrossRefGoogle Scholar
  37. 37.
    Guo X, Zhang W, Zhong W (2014) Explicit feature control in structural topology optimization via level set method. Comput Methods Appl Mech Eng 272:354–378. MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Kwok T-H, Li Y, Chen Y (2016) A structural topology design method based on principal stress line. Comput Aided Des 80:19–31. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  • Jikai Liu
    • 1
  • Yongsheng Ma
    • 1
  • A. J. Qureshi
    • 1
  • Rafiq Ahmad
    • 1
    Email author
  1. 1.Department of Mechanical EngineeringUniversity of AlbertaEdmontonCanada

Personalised recommendations