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An Improved Density-Based Design Method of Additive Manufacturing Fabricated Inhomogeneous Cellular-Solid Structures

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Abstract

Benefited from the rapid development of additive manufacturing (AM), inhomogeneous cellular structures have attracted many interests for their superior structural and functional performance. Recently proposed density-based design methods have been shown to provide great computational efficiency and obtain structures with excellent performance. To achieve better structural performance while considering AM constraints, an improved density-based design method which introduces solid and void units into the design domain is proposed in this paper. First, based on homogenization theory and solid-body analysis, unit parameters of different preset unit relative densities are determined. And a unit effective property interpolation model is constructed. Then, the macro relative density layout is optimized with density methods. In the optimization process, an efficient density filter is proposed to increase the optimization domain and satisfy minimal feature size constraint. Finally, the structure reconstruction algorithm automatically constructs the optimized cellular structure based on the unit and density information obtained in the first two processes. Numerical examples show that the proposed method efficiently obtains inhomogeneous cellular structures with better performance, compared with existing density-based methods.

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References

  1. Gibson, L. J., & Ashby, M. F. (1999). Cellular solids: Structure and properties. Cambridge: Cambridge University Press.

    MATH  Google Scholar 

  2. Banhart, J. (2001). Manufacture, characterisation and application of cellular metals and metal foams. Progress in Materials Science,46(6), 559–632.

    Google Scholar 

  3. Lim, Y. E., Park, J. H., & Park, K. (2018). Automatic design of 3D conformal lightweight structures based on a tetrahedral mesh. International Journal of Precision Engineering and Manufacturing - Green Technology,5, 499–506.

    Google Scholar 

  4. Chu, J., Engelbrecht, S., Graf, G., & Rosen, D. W. (2010). A comparison of synthesis methods for cellular structures with application to additive manufacturing. Rapid Prototyping Journal,16, 275–283.

    Google Scholar 

  5. Tang, Y., Kurtz, A., & Zhao, Y. F. (2015). Bidirectional Evolutionary Structural Optimization (BESO) based design method for lattice structure to be fabricated by additive manufacturing. Computer-Aided Design,69, 91–101.

    Google Scholar 

  6. Ryan, G., Pandit, A., & Apatsidis, D. P. (2006). Fabrication methods of porous metals for use in orthopaedic applications. Biomaterials,27(13), 2651–2670.

    Google Scholar 

  7. Lee, D., Kim, H., Sim, J., et al. (2019). Trends in 3D printing technology for construction automation using text mining. International Journal of Precision Engineering and Manufacturing.,20, 871–882.

    Google Scholar 

  8. Doubrovski, E. L., Verlinden, J. C., & Geraedts, J. M. P. (2011). Optimal design for additive manufacturing: Opportunities and challenges. In ASME 2011 international design engineering technical conferences and computers and information in engineering conference (pp. 635–646).

  9. Park, J.-H., Goo, B., & Park, K. (2019). Topology optimization and additive manufacturing of customized sports item considering orthotropic anisotropy. International Journal of Precision Engineering and Manufacturing.,20, 1443–1450.

    Google Scholar 

  10. Francois, M. M., Sun, A., King, W. E., Henson, N. J., et al. (2017). Modeling of additive manufacturing processes for metals: Challenges and opportunities. Current Opinion in Solid State and Materials Science 21(LA-UR-16-24513).

  11. Tao, W., & Ming, C. L. (2016). Design of lattice structure for additive manufacturing. In International symposium on flexible automation (pp. 325–332).

  12. Brackett, D. J., Ashcroft, I. A., Wildman, R. D., et al. (2014). An error diffusion based method to generate functionally graded cellular structures. Computers & Structures,138, 102–111.

    Google Scholar 

  13. Dorn, W. S., Gomory, R. E., & Greenberg, H. J. (1964). Automatic design of optimal structures. Journal de Mecanique,3, 25–52.

    Google Scholar 

  14. Savio, G., Meneghello, R., & Concheri, G. (2017). Optimization of lattice structures for Additive Manufacturing Technologies. In B. Eynard, V. Nigrelli, S. Oliveri, G. Peris-Fajarnes, & S. Rizzuti (Eds.), Advances on mechanics, design engineering and manufacturing (pp. 213–222). Cham: Springer.

    Google Scholar 

  15. Chang, P. S., & Rosen, D. W. (2011). An improved size, matching, and scaling method for the design of deterministic mesoscale truss structures. Proceedings of the ASME Design Engineering Technical Conference,2, 697–707.

    Google Scholar 

  16. Nguyen, J., Park, S., & Rosen, D. (2013). Heuristic optimization method for cellular structure design of light weight components. International Journal of Precision Engineering and Manufacturing,14, 1071–1078.

    Google Scholar 

  17. Alzahrani, M., Choi, S. K., & Rosen, D. W. (2015). Design of truss-like cellular structures using relative density mapping method. Materials and Design,85, 349–360.

    Google Scholar 

  18. Alzahrani, M. A. (2014). Design of truss-like cellular structures using density information from topology optimization. European Journal of Operational Research,103(1), 198–208.

    Google Scholar 

  19. Zhang, P., Toman, J., Yu, Y., et al. (2015). Efficient design-optimization of variable-density hexagonal cellular structure by additive manufacturing: Theory and validation. Journal of Manufacturing Science and Engineering,137(2), 021004.

    Google Scholar 

  20. Cheng, L., Zhang, P., Biyikli, E., et al. (2017). Efficient design optimization of variable-density cellular structures for additive manufacturing: Theory and experimental validation. Rapid Prototyping Journal,23, 660–677.

    Google Scholar 

  21. Wu, T., Liu, K., & Tovar, A. (2017). Multiphase topology optimization of lattice injection molds. Computers & Structures,192, 71–82.

    Google Scholar 

  22. Kuo, T. C., Huang, S. H., & Zhang, H. C. (2001). Design for manufacture and design for “X”: Concepts, applications, and perspectives. Computer and Industrial Engineering,41, 241–260.

    Google Scholar 

  23. Gorguluarslan, R. M., Gandhi, U. N., Song, Y., et al. (2017). An improved lattice structure design optimization framework considering additive manufacturing constraints. Rapid Prototyping Journal,23, 305–319.

    Google Scholar 

  24. Hassani, B., & Hinton, E. (1998). A review of homogenization and topology optimization I—Homogenization theory for media with periodic structure. Computers & Structures,69, 707–717.

    MATH  Google Scholar 

  25. Hassani, B., & Hinton, E. (1998). A review of homogenization and topology opimization II—Analytical and numerical solution of homogenization equations. Computers & Structures,69, 719–738.

    Google Scholar 

  26. Gibson, L. J., & Ashby, M. F. (2014). Cellular solids: Structure and properties. Cambridge University Press,33, 487–488.

    Google Scholar 

  27. Zhang, W., Dai, G., Wang, F., et al. (2007). Using strain energy-based prediction of effective elastic properties in topology optimization of material microstructures. Acta Mechanica Sinica,23(1), 77–89.

    MathSciNet  MATH  Google Scholar 

  28. Liu, J., Zheng, Y., Ma, Y., et al. (2019). A topology optimization method for hybrid subtractive–additive remanufacturing. International Journal of Precision Engineering and Manufacturing-Green Technology.

  29. Kim, H., Seong, H., & Yoo, J. (2019). Study on the clear boundary determination from results of the phase field design method. International Journal of Precision Engineering and Manufacturing.,20, 1553–1561.

    Google Scholar 

  30. Bendsøe, M. P., & Sigmund, O. (2003). Topology optimization: theory, methods, and applications. Berlin: Springer.

    MATH  Google Scholar 

  31. Bendsøe, M. P., & Sigmund, O. (1999). Material interpolation schemes in topology optimization. Archive of Applied Mechanics,69, 635–654.

    MATH  Google Scholar 

  32. Bruns, T. E., & Tortorelli, D. A. (2001). Topology optimization of non-linear elastic structures and compliant mechanisms. Computer Methods in Applied Mechanics and Engineering,190, 3443–3459.

    MATH  Google Scholar 

  33. Bourdin, B. (2001). Filters in topology optimization. International Journal for Numerical Methods in Engineering,50, 2143–2158.

    MathSciNet  MATH  Google Scholar 

  34. Andreassen, E., Clausen, A., Schevenels, M., et al. (2011). Efficient topology optimization in MATLAB using 88 lines of code. Structural and Multidisciplinary Optimization,43, 1–16.

    MATH  Google Scholar 

  35. Svanberg, K. (1987). The method of moving asymptotes: A new method for structural optimization. International Journal for Numerical Methods in Engineering,24, 359–373.

    MathSciNet  MATH  Google Scholar 

  36. Liu, J., & Ma, Y. (2016). A survey of manufacturing oriented topology optimization methods. Advances in Engineering Software,100, 161–175.

    Google Scholar 

  37. Brackett, D., Ashcroft, I., & Hagues, R. (2013). Topology optimization for additive manufacturing. Journal of Chemical Information and Modeling,53, 1689–1699.

    Google Scholar 

  38. Liu, J., et al. (2018). Current and future trends in topology optimization for additive manufacturing. Structural and Multidisciplinary Optimization,57, 2457–2483.

    Google Scholar 

  39. Gaynor, A. T., & Guest, J. K. (2016). Topology optimization considering overhang constraints: Eliminating sacrificial support material in additive manufacturing through design. Structural and Multidisciplinary Optimization,54, 1157–1172.

    MathSciNet  Google Scholar 

  40. Langelaar, M. (2017). An additive manufacturing filter for topology optimization of print-ready designs. Structural and Multidisciplinary Optimization,55, 871–883.

    MathSciNet  Google Scholar 

  41. Allaire, G., Dapogny, C., Estevez, R., Faure, A., & Michailidis, G. (2017). Structural optimization under overhang constraints imposed by additive manufacturing technologies. Journal of Computational Physics,351, 295–328.

    MathSciNet  MATH  Google Scholar 

  42. Li, D., Dai, N., Zhou, X., Huang, R., & Liao, W. (2018). Self-supporting interior structures modeling for buoyancy optimization of computational fabrication. International Journal of Advanced Manufacturing Technology,95, 825–834.

    Google Scholar 

  43. Zhao, J., Zhang, M., Zhu, Y., Li, X., Wang, L., & Hu, J. (2019). A novel optimization design method of additive manufacturing oriented porous structures and experimental validation. Materials and Design,163, 107550.

    Google Scholar 

  44. Jiang, J., Xu, X., & Stringer, J. (2018). Support structures for additive manufacturing: A review. Journal of Manufacturing and Materials Processing.,2, 64.

    Google Scholar 

  45. Górski, F., Wichniarek, R., Kuczko, W., Zawadzki, P., & Buń, P. (2015). Strength of abs parts produced by fused deposition modelling technology—A critical orientation problem. Advances in Science and Technology Research Journal,9, 12–19.

    Google Scholar 

Download references

Acknowledgements

The author thanks Prof. Krister Svanberg for use of the MMA optimizer. This work was supported in part by the National Natural Science Foundation of China under Grant 51677104.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Tsinghua University, Haidian District, Beijing, 100-084, China

    Yu Zhu, Jiaqi Zhao, Ming Zhang, Xin Li, Leijie Wang & Chuxiong Hu

  2. State Key Lab of Tribology, Tsinghua University, Haidian District, Beijing, 100-084, China

    Yu Zhu, Jiaqi Zhao, Ming Zhang, Xin Li, Leijie Wang & Chuxiong Hu

  3. Beijing Key Lab of Precision/Ultra-precision Manufacturing Equipments and Control, Tsinghua University, Haidian District, Beijing, 100-084, China

    Yu Zhu, Jiaqi Zhao, Ming Zhang, Xin Li, Leijie Wang & Chuxiong Hu

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  1. Yu Zhu
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  3. Ming Zhang
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Correspondence to Ming Zhang.

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Zhu, Y., Zhao, J., Zhang, M. et al. An Improved Density-Based Design Method of Additive Manufacturing Fabricated Inhomogeneous Cellular-Solid Structures. Int. J. Precis. Eng. Manuf. 21, 103–116 (2020). https://doi.org/10.1007/s12541-019-00230-w

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