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Topology optimization of multi-phase shell-infill composite structure for additive manufacturing

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Abstract

This paper presents a topology optimization method for a multi-phase shell-infill composite, accounting for the coated shell and graded multi-phase microstructural infill. The method builds upon extended multi-phase density-based topology optimization approaches, and it consists of two major steps: (1) general structural configuration design of the shell-base composite structure and (2) detailed design of the graded multi-phase infill architecture. An erosion-based interface identification method is adopted to evolve the general structural configuration with a coated shell. Then the maximum and minimum length scale control constraints are simultaneously imposed on each phase material to generate graded multi-phase porous structures in the base region. The whole design process is performed on a full-size finite element analysis and only involves standard filtering operations. It avoids the separation of scales and guarantees the connectivity of microstructures. Several numerical examples for minimum compliance are presented, and a post-processing method is proposed to smooth the design boundaries when extracting CAD models for additive manufacturing. Eventually, the manufacturability of the post-processed prototype is verified with a multi-material 3D printer, which further illustrates the applicability of the proposed method.

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References

  1. Gibson LJ, Ashby MF (1999) Cellular solids: structure and properties. Cambridge University Press, Cambridge

    Google Scholar 

  2. Ha CS, Lakes RS, Plesha ME (2018) Design, fabrication, and analysis of lattice exhibiting energy absorption via snap-through behavior. Mater Des 141:426–437

    Google Scholar 

  3. Clausen A, Aage N, Sigmund O (2016) Exploiting additive manufacturing infill in topology optimization for improved buckling load. Engineering 2:250–257

    Google Scholar 

  4. Wu J, Aage N, Westermann R, Sigmund O (2017) Infill optimization for additive manufacturing—approaching bone-like porous structures. IEEE Trans Visual Comput Graphics 24:1127–1140

    Google Scholar 

  5. Bendsoe MP, Sigmund O (2013) Topology optimization: theory, methods, and applications. Springer, Berlin

    Google Scholar 

  6. Zheng Y, Wang Y, Lu X, Liao Z, Qu J (2020) Evolutionary topology optimization for mechanical metamaterials with auxetic property. Int J Mech Sci 179:105638

    Google Scholar 

  7. Li H, Li H, Xiao M, Zhang Y, Fu J, Gao L (2020) Robust topology optimization of thermoelastic metamaterials considering hybrid uncertainties of material property. Compos Struct 248:112477

    Google Scholar 

  8. Xu S, Liu J, Zou B, Li Q, Ma Y (2021) Stress constrained multi-material topology optimization with the ordered SIMP method. Comput Methods Appl Mech Eng 373:113453

    MathSciNet  Google Scholar 

  9. Zheng Y, Wang Y, Lu X, Zheng J, Qu J (2021) Topology optimisation for isotropic mechanical metamaterials considering material uncertainties. Mech Mater 155:103742

    Google Scholar 

  10. Ye M, Li H, Cai X, Gao L, Zhang A, Zhao Z (2021) Progressive design of gradually stiffer metamaterial using surrogate model. Compos Struct 264:113715

    Google Scholar 

  11. Pham Q-H, Phan D-H (2020) Polygonal topology optimization for Reissner–Mindlin plates. Eng Comput 38:141–154

  12. Cui M, Luo C, Li G, Pan M (2021) The parameterized level set method for structural topology optimization with shape sensitivity constraint factor. Eng Comput 37:855–872

    Google Scholar 

  13. Yu H, Huang J, Zou B, Shao W, Liu J (2020) Stress-constrained shell-lattice infill structural optimisation for additive manufacturing. Virtual Phys Prototyping 15:35–48

    Google Scholar 

  14. Das S, Sutradhar A (2020) Multi-physics topology optimization of functionally graded controllable porous structures: application to heat dissipating problems. Mater Des 193:108775

    Google Scholar 

  15. Xu S, Liu J, Huang J, Zou B, Ma Y (2021) Multi-scale topology optimization with shell and interface layers for additive manufacturing. Addit Manuf 37:101698

    Google Scholar 

  16. Sigmund O (1994) Materials with prescribed constitutive parameters: an inverse homogenization problem. Int J Solids Struct 31:2313–2329

    MathSciNet  Google Scholar 

  17. Vicente W, Zuo Z, Pavanello R, Calixto T, Picelli R, Xie Y (2016) Concurrent topology optimization for minimizing frequency responses of two-level hierarchical structures. Comput Methods Appl Mech Eng 301:116–136

    MathSciNet  Google Scholar 

  18. Wang F, Sigmund O (2020) Numerical investigation of stiffness and buckling response of simple and optimized infill structures. Struct Multidiscip Optim 61:2629–2639

  19. Wang Y, Wang MY, Chen F (2016) Structure-material integrated design by level sets. Struct Multidiscip Optim 54:1145–1156

    MathSciNet  Google Scholar 

  20. Fu J, Li H, Gao L, Xiao M (2019) Design of shell-infill structures by a multiscale level set topology optimization method. Comput Struct 212:162–172

    Google Scholar 

  21. Li H, Luo Z, Gao L, Walker P (2018) Topology optimization for functionally graded cellular composites with metamaterials by level sets. Comput Methods Appl Mech Eng 328:340–364

    MathSciNet  Google Scholar 

  22. Yan X, Xu Q, Huang D, Zhong Y, Huang X (2019) Concurrent topology design of structures and materials with optimal material orientation. Compos Struct 220:473–480

    Google Scholar 

  23. Lee J, Kim D, Nomura T, Dede EM, Yoo J (2018) Topology optimization for continuous and discrete orientation design of functionally graded fiber-reinforced composite structures. Compos Struct 201:217–233

    Google Scholar 

  24. Li H, Luo Z, Gao L, Qin Q (2018) Topology optimization for concurrent design of structures with multi-patch microstructures by level sets. Comput Methods Appl Mech Eng 331:536–561

    MathSciNet  Google Scholar 

  25. Gao J, Luo Z, Li H, Gao L (2019) Topology optimization for multiscale design of porous composites with multi-domain microstructures. Comput Methods Appl Mech Eng 344:451–476

    MathSciNet  Google Scholar 

  26. Zhang Y, Xiao M, Gao L, Gao J, Li H (2020) Multiscale topology optimization for minimizing frequency responses of cellular composites with connectable graded microstructures. Mech Syst Signal Process 135:106369

    Google Scholar 

  27. Groen JP, Wu J, Sigmund O (2019) Homogenization-based stiffness optimization and projection of 2D coated structures with orthotropic infill. Comput Methods Appl Mech Eng 349:722–742

    MathSciNet  Google Scholar 

  28. Groen JP, Sigmund O (2018) Homogenization-based topology optimization for high-resolution manufacturable microstructures. Int J Numer Methods Eng 113:1148–1163

    MathSciNet  Google Scholar 

  29. Kim D, Lee J, Nomura T, Dede EM, Yoo J, Min S (2020) Topology optimization of functionally graded anisotropic composite structures using homogenization design method. Comput Methods Appl Mech Eng 369:113220

    MathSciNet  Google Scholar 

  30. Liu P, Kang Z, Luo Y (2020) Two-scale concurrent topology optimization of lattice structures with connectable microstructures. Addit Manuf 36:101427

    Google Scholar 

  31. Wang Y, Zhang L, Daynes S, Zhang H, Feih S, Wang MY (2018) Design of graded lattice structure with optimized mesostructures for additive manufacturing. Mater Des 142:114–123

    Google Scholar 

  32. Garner E, Kolken HM, Wang CC, Zadpoor AA, Wu J (2019) Compatibility in microstructural optimization for additive manufacturing. Addit Manuf 26:65–75

    Google Scholar 

  33. Luo Y, Hu J, Liu S (2021) Self-connected multi-domain topology optimization of structures with multiple dissimilar microstructures. Struct Multidiscip Optim 64:125–140

  34. Alexandersen J, Lazarov BS (2015) Topology optimisation of manufacturable microstructural details without length scale separation using a spectral coarse basis preconditioner. Comput Methods Appl Mech Eng 290:156–182

    MathSciNet  Google Scholar 

  35. Dou S (2020) A projection approach for topology optimization of porous structures through implicit local volume control. Struct Multidiscip Optim 62:835–850

  36. Li H, Gao L, Li H, Tong H (2020) Spatial-varying multi-phase infill design using density-based topology optimization. Comput Methods Appl Mech Eng 372:113354

    MathSciNet  Google Scholar 

  37. Clausen A, Aage N, Sigmund O (2015) Topology optimization of coated structures and material interface problems. Comput Methods Appl Mech Eng 290:524–541

    MathSciNet  Google Scholar 

  38. Clausen A, Andreassen E, Sigmund O (2017) Topology optimization of 3D shell structures with porous infill. Acta Mech Sin 33:778–791

    MathSciNet  Google Scholar 

  39. Luo Y, Li Q, Liu S (2019) Topology optimization of shell–infill structures using an erosion-based interface identification method. Comput Methods Appl Mech Eng 355:94–112

    MathSciNet  Google Scholar 

  40. Wang Y, Kang Z (2018) A level set method for shape and topology optimization of coated structures. Comput Methods Appl Mech Eng 329:553–574

    MathSciNet  Google Scholar 

  41. Fu J, Li H, Xiao M, Gao L, Chu S (2019) Topology optimization of shell-infill structures using a distance regularized parametric level-set method. Struct Multidiscip Optim 59:249–262

    MathSciNet  Google Scholar 

  42. Hoang V-N, Nguyen N-L, Nguyen-Xuan H (2020) Topology optimization of coated structure using moving morphable sandwich bars. Struct Multidiscip Optim 61:491–506

    Google Scholar 

  43. Wadbro E, Niu B (2019) Multiscale design for additive manufactured structures with solid coating and periodic infill pattern. Comput Methods Appl Mech Eng 357:112605

    MathSciNet  Google Scholar 

  44. Wu J, Clausen A, Sigmund O (2017) Minimum compliance topology optimization of shell–infill composites for additive manufacturing. Comput Methods Appl Mech Eng 326:358–375

    MathSciNet  Google Scholar 

  45. Qiu W, Jin P, Jin S, Wang C, Xia L, Zhu J et al (2020) An evolutionary design approach to shell-infill structures. Addit Manuf 34:101382

  46. Bandyopadhyay A, Heer B (2018) Additive manufacturing of multi-material structures. Mater Sci Eng R Rep 129:1–16

    Google Scholar 

  47. Wang F, Lazarov BS, Sigmund O (2011) On projection methods, convergence and robust formulations in topology optimization. Struct Multidiscip Optim 43:767–784

    Google Scholar 

  48. Diaz A, Sigmund O (1995) Checkerboard patterns in layout optimization. Struct Optim 10:40–45

    Google Scholar 

  49. Lazarov BS, Sigmund O (2011) Filters in topology optimization based on Helmholtz-type differential equations. Int J Numer Methods Eng 86:765–781

    MathSciNet  Google Scholar 

  50. Svanberg K (1987) The method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng 24:359–373

    MathSciNet  Google Scholar 

  51. Li H, Gao L, Li H, Li X, Tong H (2021) Full-scale topology optimization for fiber-reinforced structures with continuous fiber paths. Comput Methods Appl Mech Eng 377:113668

    MathSciNet  Google Scholar 

  52. Fernández E, Yang K-K, Koppen S, Alarcón P, Bauduin S, Duysinx P (2020) Imposing minimum and maximum member size, minimum cavity size, and minimum separation distance between solid members in topology optimization. Comput Methods Appl Mech Eng 368:113157

    MathSciNet  Google Scholar 

  53. Da D, Xia L, Li G, Huang X (2018) Evolutionary topology optimization of continuum structures with smooth boundary representation. Struct Multidiscip Optim 57:2143–2159

    MathSciNet  Google Scholar 

Download references

Acknowledgements

This research is partially supported by the National Natural Science Foundation of China (52075195), the Fundamental Research Funds for the Central Universities through Program no. 2172019kfyXJJS078 and 2019kfyXKJC042, and the Program for HUST Academic Frontier Youth Team (No. 2017QYTD04).

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Correspondence to Liang Gao.

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Li, H., Li, H., Gao, L. et al. Topology optimization of multi-phase shell-infill composite structure for additive manufacturing. Engineering with Computers 40, 1049–1064 (2024). https://doi.org/10.1007/s00366-023-01837-4

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