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Adaptive Concurrent Topology Optimization of Cellular Composites for Additive Manufacturing

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Abstract

This paper introduces a new concurrent topology optimization approach based on adaptive geometric components for designing and fabricating cellular composites using 3D printing. The key idea behind this approach is to model adaptive geometric components by projecting them onto macro- and microelement density fields, combining them to calculate the effective densities of grid elements. The cellular structure at the macro- and microstructural levels are optimized at the same time by finding optimal geometric parameters for adaptive geometric components. The proposed method enables designing high-porosity composites on a coarse finite element mesh without material homogenization. As a result, it provides a cost-effective way to obtain optimal designs of cellular composites and simultaneously control the length scales of both the macro- and microstructures. The effectiveness of this method is demonstrated through several numerical examples. This work also explores the ability to realize concurrent optimized structures using additive manufacturing.

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References

  1. L.J. Gibson and M.F. Ashby, Cellular Solids: Structure and Properties, 2nd ed. (Cambridge: Cambridge University Press, 1997).

    Book  MATH  Google Scholar 

  2. R.M. Christensen, Int. J. Solids Struct. 37, 93 (2000).

    Article  Google Scholar 

  3. J. Wang, T.J. Lu, J. Woodhouse, R.S. Langley, and J. Evans, J. Sound Vib. 286, 817 (2005).

    Article  Google Scholar 

  4. X. Sun and W. Liang, Compos. Part B Eng. 87, 21 (2016).

    Article  Google Scholar 

  5. I. Elnasri, S. Pattofatto, H. Zhao, H. Tsitsiris, F. Hild, and Y. Girard, J. Mech. Phys. Solids 55, 2652 (2007).

    Article  Google Scholar 

  6. A. Ajdari, H. Nayeb-Hashemi, and A. Vaziri, Int. J. Solids Struct. 48, 506 (2011).

    Article  Google Scholar 

  7. C.Y. Zhao, W. Lu, and Y. Tian, Sol. Energy 84, 1402 (2010).

    Article  Google Scholar 

  8. H.L. Fan, F.N. **, and D.N. Fang, Compos. Sci. Technol. 68, 3380 (2008).

    Article  Google Scholar 

  9. J. Huang, Q. Zhang, F. Scarpa, Y. Liu, and J. Leng, Compos. Part B Eng. 140, 35 (2018).

    Article  Google Scholar 

  10. T. Nomura, A. Kawamoto, T. Kondoh, E.M. Dede, J. Lee, Y. Song, and N. Kikuchi, Compos. Part B Eng. 176, 107187 (2019).

    Article  Google Scholar 

  11. J. Song, Y. Wang, W. Zhou, R. Fan, B. Yu, Y. Lu, and L. Li, Compos. Part B Eng. 160, 402 (2019).

    Article  Google Scholar 

  12. O.L.E. Sigmund, Int. J. Solids Struct. 31, 2313 (1994).

    Article  Google Scholar 

  13. O. Sigmund and S. Torquato, Appl. Phys. Lett. 69, 3203 (1996).

    Article  Google Scholar 

  14. E.C.N. Silva, J.S.O. Fonseca, and N. Kikuchi, Comput. Mech. 19, 397 (1997).

    Article  Google Scholar 

  15. J.K. Guest and J.H. Prévost, Int. J. Solids Struct. 43, 7028 (2006).

    Article  Google Scholar 

  16. A. Radman, X. Huang, and Y.M. **e, J. Mater. Sci. 48, 1503 (2013).

    Article  Google Scholar 

  17. A. Faure, G. Michailidis, G. Parry, N. Vermaak, and R. Estevez, Struct. Multidiscip. Optim. 56, 823 (2017).

    Article  MathSciNet  Google Scholar 

  18. L. **a and P. Breitkopf, Comput. Methods Appl. Mech. Eng. 278, 524 (2014).

    Article  Google Scholar 

  19. L. **a and P. Breitkopf, Arch. Comput. Methods Eng. 24, 227 (2016).

    Article  Google Scholar 

  20. H. Li, Z. Luo, L. Gao, and Q. Qin, Comput. Methods Appl. Mech. Eng. 331, 536 (2018).

    Article  Google Scholar 

  21. R. Sivapuram, P.D. Dunning, and H.A. Kim, Struct. Multidiscip. Optim. 54, 1267 (2016).

    Article  MathSciNet  Google Scholar 

  22. J. Deng, C.B.W. Pedersen, and W. Chen, Front. Mech. Eng. 14, 129 (2019).

    Google Scholar 

  23. J. Deng, J. Yan, and G. Cheng, Struct. Multidiscip. Optim. 47, 583 (2013).

    Article  MathSciNet  Google Scholar 

  24. J. Yan, X. Guo, and G. Cheng, Comput. Mech. 57, 437 (2016).

    Article  MathSciNet  Google Scholar 

  25. J. Deng and W. Chen, Struct. Multidiscip. Optim. 56, 1 (2017).

    Article  MathSciNet  Google Scholar 

  26. W.M. Vicente, Z.H. Zuo, R. Pavanello, T.K.L. Calixto, R. Picelli, and Y.M. **e, Comput. Methods Appl. Mech. Eng. 301, 116 (2016).

    Article  Google Scholar 

  27. M.P. Bendsoe and N. Kikuchi, Comput. Methods Appl. Mech. Eng. 71, 197 (1988).

    Article  Google Scholar 

  28. M.P. Bendsøe, Struct. Optim. 1, 193 (1989).

    Article  Google Scholar 

  29. J.P. Groen and O. Sigmund, Int. J. Numer. Methods Eng. 113, 1148 (2018).

    Article  Google Scholar 

  30. B. Lozanovski, M. Leary, P. Tran, D. Shidid, M. Qian, P. Choong, and M. Brandt, Mater. Des. 171, 107671 (2019).

    Article  Google Scholar 

  31. X. Ren, J. Shen, P. Tran, T.D. Ngo, and Y.M. **e, Compos. Struct. 184, 288 (2018).

    Article  Google Scholar 

  32. X. Ren, J. Shen, P. Tran, T.D. Ngo, and Y.M. **e, Mater. Des. 139, 336 (2018).

    Article  Google Scholar 

  33. P. Tran, T.D. Ngo, A. Ghazlan, and D. Hui, Compos. Part B Eng. 108, 210 (2017).

    Article  Google Scholar 

  34. K.C. Nguyen, P. Tran, and H.X. Nguyen, Autom. Constr. 99, 79 (2019).

    Article  Google Scholar 

  35. D. Brackett, I. Ashcroft, and R. Hagues, in Solid Freeform Fabrication Symposium (2011), p. 348.

  36. L. Cheng, P. Zhang, E. Biyikli, J. Bai, P. Steve, and A. C. To, in Solid Freeform Fabrication Symposium (2015), p. 1370.

  37. X. Wang, P. Zhang, S. Ludwick, E. Belski, and A.C. To, Addit. Manuf. 20, 189 (2018).

    Article  Google Scholar 

  38. P. Zhang, J. Toman, Y. Yu, E. Biyikli, M. Kirca, M. Chmielus, and A.C. To, J. Manuf. Sci. Eng. Trans. ASME. 137, 41 (2015).

    Google Scholar 

  39. L. Cheng, J. Bai, and A.C. To, Comput. Methods Appl. Mech. Eng. 344, 334 (2019).

    Article  Google Scholar 

  40. L. Cheng, X. Liang, E. Belski, X. Wang, J.M. Sietins, S. Ludwick, and A. To, J. Manuf. Sci. Eng. Trans. ASME 140, 105002 (2018).

    Article  Google Scholar 

  41. J. Wu, C.C.L. Wang, X. Zhang, R. Westermann, and C.A.D. Comput, Aided Des. 80, 32 (2016).

    Article  Google Scholar 

  42. J. Wu, N. Aage, R. Westermann, O. Sigmund, and I.E.E.E. Trans, Vis. Comput. Graph. 24, 1127 (2018).

    Article  Google Scholar 

  43. X. Guo, W. Zhang, and W. Zhong, J. Appl. Mech. 81, 081009 (2014).

    Article  Google Scholar 

  44. J.A. Norato, B.K. Bell, and D.A. Tortorelli, Comput. Methods Appl. Mech. Eng. 293, 306 (2015).

    Article  Google Scholar 

  45. V.N. Hoang and G.W. Jang, Comput. Methods Appl. Mech. Eng. 317, 153 (2017).

    Article  Google Scholar 

  46. W. Zhang, D. Li, J. Zhang, and X. Guo, Comput. Methods Appl. Mech. Eng. 311, 327 (2016).

    Article  Google Scholar 

  47. H. Kazemi, A. Vaziri, and J.A. Norato, J. Mech. Des. 140, 111401 (2018).

    Article  Google Scholar 

  48. W. Zhang, J. Song, J. Zhou, Z. Du, Y. Zhu, Z. Sun, and X. Guo, Int. J. Numer. Methods Eng. 113, 1653 (2018).

    Article  Google Scholar 

  49. X. Wang, K. Long, V.N. Hoang, and P. Hu, Comput. Methods Appl. Mech. Eng. 342, 46 (2018).

    Article  Google Scholar 

  50. W. Zhang, Y. Liu, Z. Du, Y. Zhu, and X. Guo, J. Mech. Des. 140, 111404 (2018).

    Article  Google Scholar 

  51. X. Guo, W. Zhang, J. Zhang, and J. Yuan, Comput. Methods Appl. Mech. Eng. 310, 711 (2016).

    Article  Google Scholar 

  52. S. Zhang, J.A. Norato, A.L. Gain, and N. Lyu, Struct. Multidiscip. Optim. 54, 1173 (2016).

    Article  MathSciNet  Google Scholar 

  53. S. Zhang, A.L. Gain, and J.A. Norato, Int. J. Numer. Methods Eng. 114, 128 (2018).

    Article  Google Scholar 

  54. S. Zhang, A.L. Gain, and J.A. Norato, Comput. Methods Appl. Mech. Eng. 325, 1 (2017).

    Article  Google Scholar 

  55. J. Deng and W. Chen, Sci. China Technol. Sci. 59, 839 (2016).

    Article  Google Scholar 

  56. V.N. Hoang, N.L. Nguyen, and H. Nguyen-Xuan, Struct. Multidiscip. Optim. 61, 491 (2020).

    Article  Google Scholar 

  57. M. Zhou and G.I.N. Rozvany, Comput. Methods Appl. Mech. Eng. 89, 309 (1991).

    Article  Google Scholar 

  58. H.P. Mlejnek, Struct. Optim. 5, 64 (1992).

    Article  Google Scholar 

  59. A. Saxena, Struct. Multidiscip. Optim. 44, 629 (2011).

    Article  Google Scholar 

  60. K. Svanberg, Int. J. Numer. Methods Eng. 24, 359 (1987).

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

Research is supported by Vingroup Innovation Foundation (VINIF) in project code VINIF.2019.DA04. The authors acknowledge the facilities and technical assistance of the RMIT Advanced Manufacturing Precinct and Vietnam Maritime University.

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Authors and Affiliations

  1. Mechanical Engineering Institute, Vietnam Maritime University, Hai Phong City, Vietnam

    Van-Nam Hoang

  2. Faculty of Mechanical and Aerospace Engineering, Sejong University, Seoul, Republic of Korea

    Ngoc-Linh Nguyen

  3. Department of Civil and Infrastructure Engineering, RMIT University, Melbourne, Australia

    Phuong Tran

  4. Centre for Additive Manufacturing, School of Engineering, RMIT University, Melbourne, VIC, 3000, Australia

    Phuong Tran & Ma Qian

  5. CIRTECH Institute, Ho Chi Minh City University of Technology (HUTECH), Ho Chi Minh City, Vietnam

    H. Nguyen-Xuan

  6. Department of Architectural Engineering, Sejong University, Seoul, Republic of Korea

    H. Nguyen-Xuan

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  1. Van-Nam Hoang
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  2. Ngoc-Linh Nguyen
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  3. Phuong Tran
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  4. Ma Qian
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  5. H. Nguyen-Xuan
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Correspondence to Phuong Tran or H. Nguyen-Xuan.

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Hoang, VN., Nguyen, NL., Tran, P. et al. Adaptive Concurrent Topology Optimization of Cellular Composites for Additive Manufacturing. JOM 72, 2378–2390 (2020). https://doi.org/10.1007/s11837-020-04158-9

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  • DOI: https://doi.org/10.1007/s11837-020-04158-9

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