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Topology and alignment optimization of additively manufactured, fiber-reinforced composites

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Abstract

A design algorithm is presented for finding optimal topologies and alignment profiles of additively manufactured, fiber-reinforced composite structures. A SIMP-like scheme is used to determine where a constrained amount of material is to be located in the design space, while an additional local design variable determines print speed. The local print speed affects fiber alignment based on an experimentally determined relationship, allowing for graded control over effective orthotropy. Material properties are selected from experimental results for additive printed, chopped fiber composites. Two different load cases and three different global print directions are selected for a total of six minimum compliance optimization cases. Results show the design is sensitive to both local fiber control and global print angle selection. A post-processing and manufacturing technique is also introduced for fabricating the optimized structures.

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References

  • Alizadeh F (1995) Interior point methods in semidefinite programming with applications to combinatorial optimization. SIAM journal on Optimization 5(1):13–51

    Article  MathSciNet  Google Scholar 

  • Bendsøe MP (2009) Topology optimization. Springer, Berlin

    MATH  Google Scholar 

  • Blasques JP, Stolpe M (2012) Multi-material topology optimization of laminated composite beam cross sections. Compos Struct 94(11):3278–3289

    Article  Google Scholar 

  • Boggs PT, Tolle JW (1995) Sequential quadratic programming. Acta numerica 4:1–51

    Article  MathSciNet  Google Scholar 

  • Boudaoud A, Burian A, Borowska-Wykret D, Uyttewaal M, Wrzalik R, Kwiatkowska D, Hamant O (2014) Fibriltool, an imagej plug-in to quantify fibrillar structures in raw microscopy images. Nature protocols 9(2):457

    Article  Google Scholar 

  • Compton BG, Lewis JA (2014) 3d-printing of lightweight cellular composites. Advanced materials 26(34):5930–5935

    Article  Google Scholar 

  • Dunning PD, Brampton CJ, Kim HA (2015) Simultaneous optimisation of structural topology and material grading using level set method. Mater Sci Technol 31(8):884–894

    Article  Google Scholar 

  • Esposito L, Cutolo A, Barile M, Lecce L, Mensitieri G, Sacco E, Fraldi M (2019) Topology optimization-guided stiffening of composites realized through automated fiber placement. Composites Part B: Engineering 164:309–323

    Article  Google Scholar 

  • Fernandez F, Compel WS, Lewicki JP, Tortorelli DA (2019) Optimal design of fiber reinforced composite structures and their direct ink write fabrication. Comput Methods Appl Mech Eng 353:277–307

    Article  MathSciNet  Google Scholar 

  • 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(6):061015

    Article  Google Scholar 

  • Hoglund R, Smith DE (2016) Continuous fiber angle topology optimization for polymer fused filament fabrication. In: Proceedings of the 27th annual international solid freeform fabrication symposium, Austin, TX, USA, pp 8–10

  • Kato J, Lipka A, Ramm E (2009) Multiphase material optimization for fiber reinforced composites with strain softening. Structural and multidisciplinary optimization 39(1):63

    Article  Google Scholar 

  • Kattan PI (2007) MATLAB guide to finite elements: an interactive approach, 2nd ed. Springer, Berlin

    MATH  Google Scholar 

  • Knn search: finding k-nearest neighbors using input data (2020) https://www.mathworks.com/help/stats/knnsearch.html. Accessed: 2020-02-20

  • Lewicki JP, Rodriguez JN, Zhu C, Worsley MA, Wu AS, Kanarska Y, Horn JD, Duoss EB, Ortega JM, Elmer W, et al. (2017) 3d-printing of meso-structurally ordered carbon fiber/polymer composites with unprecedented orthotropic physical properties. Scientific reports 7:43401

    Article  Google Scholar 

  • Liu C, Du Z, Zhang W, Zhu Y, Guo X (2017) Additive manufacturing-oriented design of graded lattice structures through explicit topology optimization. J Appl Mech 84(8):081008

    Article  Google Scholar 

  • Liu J, Gaynor AT, Chen S, Kang Z, Suresh K, Takezawa A, Li L, Kato J, Tang J, Wang CCL, et al. (2018) Current and future trends in topology optimization for additive manufacturing. Struct Multidiscip Optim 57(6):2457–2483

    Article  Google Scholar 

  • Melenka GW, et al. (2015) Evaluation of dimensional accuracy and material properties of the MakerBot 3D desktop printer. Rapid Prototyp J 21(5):618

    Article  Google Scholar 

  • Pierson HA, Celik E, Abbott A, De Jarnette H, Gutierrez LS, Johnson K, Koerner H, Baur JW (2019) Mechanical properties of printed epoxy-carbon fiber composites. Exp Mech 59(6):843–857

    Article  Google Scholar 

  • Raney JR, Compton BG, Mueller J, Ober TJ, Shea K, Lewis JA (2018) Rotational 3d printing of damage-tolerant composites with programmable mechanics. Proceedings of the National Academy of Sciences 115(6):1198–1203

    Article  Google Scholar 

  • Rosen D W (2016) A review of synthesis methods for additive manufacturing. Virtual and Physical Prototyping 11(4):305–317

    Article  Google Scholar 

  • Roylance D (2001) Transformation of stresses and strains. Lecture Notes for Mechanics of Materials

  • Saito Y, Fernandez F, Tortorelli DA, Compel WS, Lewicki JP, Lambros J (2019) Experimental validation of an additively manufactured stiffness-optimized short-fiber reinforced composite clevis joint. Exp Mech 59(6):859–869

    Article  Google Scholar 

  • Setoodeh S, Abdalla MM, Gurdal Z (2005) Combined topology and fiber path design of composite layers using cellular automata. Struct Multidiscip Optim 30(6):413–421

    Article  Google Scholar 

  • Sigmund O (2001) A 99 line topology optimization code written in matlab. Structural and multidisciplinary optimization 21(2):120–127

    Article  Google Scholar 

  • Svanberg K (1993) The method of moving asymptotes (mma) with some extensions. In: Optimization of large structural systems, pp 555–566. Springer

  • Svanberg K, Svärd H (2013) Density filters for topology optimization based on the pythagorean means. Struct Multidiscip Optim 48(5):859–875

    Article  MathSciNet  Google Scholar 

  • Taheri AH, Suresh K (2017) An isogeometric approach to topology optimization of multi-material and functionally graded structures. Int J Numer Methods Eng 109(5):668–696

    Article  MathSciNet  Google Scholar 

  • Vermaak N, Michailidis G, Parry G, Estevez R, Allaire G, Bréchet Y (2014) Material interface effects on the topology optimizationof multi-phase structures using a level set method. Struct Multidiscip Optim 50(4):623–644

    Article  MathSciNet  Google Scholar 

  • Wahba G (1975) Smoothing noisy data with spline functions. Numer Math 24(5):383–393

    Article  MathSciNet  Google Scholar 

  • Wang MY, Chen S, Wang X, Mei Y (2005) Design of multimaterial compliant mechanisms using level-set methods. Journal of mechanical design 127(5):941–956

    Article  Google Scholar 

  • Zhou K-M, Li X (2006) Topology optimization of structures under multiple load cases using a fiber-reinforced composite material model. Comput Mech 38(2):163–170

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to acknowledge Dr. Emrah Celik for their work in developing the experimental fiber alignment measurement technique used in this research. They would also like to thank Dr. Jon Cherry for providing microscopy expertise, and Mr. Arthur Safriet for his aid in milling and processing the printed samples.

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Authors and Affiliations

  1. Air Force Research Laboratory, Dayton, USA

    David Ryan Seifert, Andrew Abbott & Jeffery Baur

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  1. David Ryan Seifert
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  2. Andrew Abbott
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  3. Jeffery Baur
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Correspondence to David Ryan Seifert.

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The authors declare that they have no conflict of interest.

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Responsible Editor: Juliá n Andrés Norato

Replication of results

All presented results were obtained using a set of Matlab codes that are available upon request.

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Seifert, D.R., Abbott, A. & Baur, J. Topology and alignment optimization of additively manufactured, fiber-reinforced composites. Struct Multidisc Optim 63, 2673–2683 (2021). https://doi.org/10.1007/s00158-020-02826-7

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  • DOI: https://doi.org/10.1007/s00158-020-02826-7

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