Abstract
Recent advances in additive manufacturing have enabled the manufacture of hollow shapes with complex external geometry and multiple materials using networks of small periodic cells known as lattice structures. The porosity and high number of elements in these structures generate lightweight designs with improved performance and functionality. This paper proposes a design approach for lattice structures considering both multi-material design and uncertainty in material properties. A density-based multi-material topology optimization method is proposed to find the optimal geometry and material layout. In addition, a new interpolation scheme for using multiple and arbitrary materials is presented. For robustness of structural compliance against uncertainty in material properties, a weighted sum of the mean and standard deviation is chosen as an objective function. To estimate statistical moments by the material uncertainty, the univariate dimension-reduction (UDR) method combined with Gauss-type quadrature sampling is employed. Two numerical examples demonstrate the efficiency of the proposed approach and the effect of material uncertainty on the robust design results.
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References
Murr, L.E., et al.: Next-generation biomedical implants using additive manufacturing of complex, cellular. Philos. Trans. R. Soc. A 368, 1999–2032 (2010)
Parthasarathy, J., Starly, B., Raman, S.: A design for the additive manufacture of functionally graded porous structures with tailored mechanical properties for biomedical applications. J. Manuf. Process. 13(2), 160–170 (2011)
Maloney, K.J., Fink, K.D., Schaedler, T.A., Kolodziejska, J.A., Jacobsen, A.J., Roper, C.S.: Multifunctional heat exchangers derived from three-dimensional micro-lattice structures. Int. J. Heat Mass Transf. 55(9–10), 2486–2493 (2012)
Moon, S.K., Tan, Y.E., Hwang, J., Yoon, Y.J.: Application of 3D printing technology for designing light-weight unmanned aerial vehicle wing structures. Int. J. Precis. Eng. Manuf. Green Technol. 1(3), 223–228 (2014)
Stankovic, T., Mueller, J., Egan, P., Shea, K.: A generalized optimality criteria method for optimization of additively manufactured multimaterial lattice structures. J. Mech. Des. 137(11), 111405 (2015)
Brennan-Craddock, J., Brackett, D., Wildman, R., Hague, R.: The design of impact absorbing structures for additive manufacture. Mod. Pract. Stress Vib. Anal. 382(1), 12042 (2012)
Hussein, A., Hao, L., Yan, C., Everson, R., Young, P.: Advanced lattice support structures for metal additive manufacturing. J. Mater. Process. Technol. 213(7), 1019–1026 (2013)
Wang, M.Y., Wang, X.: ‘Color’ level sets: a multi-phase method for structural topology optimization with multiple materials. Comput. Meth. Appl. Mech. Eng. 193(6–8), 469–496 (2004)
Zhou, S., Wang, M.Y.: Multimaterial structural topology optimization with a generalized Cahn-Hilliard model of multiphase transition. Struct. Multidiscip. Optim. 33(2), 89–111 (2007)
Hiller, J.D., Lipson, H.: Multi material topological optimization of structures and mechanisms. In: 11th Annual Conference on Genetic and Evolutionary Computation, pp. 1521–1528 (2009)
Ramani, A.: Multi-material topology optimization with strength constraints. Struct. Multidiscip. Optim. 43(5), 597–615 (2011)
Bendsoe, M.P., Sigmund, O.: Topology Optimization: Theory, Methods, and Applications. Springer, Heidelberg (2004)
Sigmund, O.: Morphology-based black and white filters for topology optimization. Struct. Multidiscip. Optim. 33(4–5), 401–424 (2007)
Stegmann, J., Lund, E.: Discrete material optimization of general composite shell structures. Int. J. Numer. Meth. Eng. 62(14), 2009–2027 (2005)
Gaynor, A., Meisel, N.A., Williams, C.B., Guest, J.K.: Multiple-material topology optimization of compliant mechanisms created via PolyJet 3D printing. J. Manuf. Sci. Eng. 136(6), 1–10 (2014)
Yin, L., Ananthasuresh, G.K.: Topology optimization of compliant mechanisms with multiple materials using a peak function material interpolation scheme. Struct. Multidiscip. Optim. 23(1), 49–62 (2001)
Zuo, W., Saitou, K.: Multi-material topology optimization using ordered SIMP interpolation. Struct. Multidiscip. Optim. 55(2), 1–15 (2016)
Chen, S., Chen, W.: A new level-set based approach to shape and topology optimization under geometric uncertainty. Struct. Multidiscip. Optim. 44(1), 1–18 (2011)
Jansen, M., Lombaert, G., Diehl, M., Lazarov, B.S., Sigmund, O., Schevenels, M.: Robust topology optimization accounting for misplacement of material. Struct. Multidiscip. Optim. 47(3), 317–333 (2013)
Rahman, S., Xu, H.: A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics. Probab. Eng. Mech. 19(4), 393–408 (2004)
Svanberg, K.: The method of moving asymptotes—a new method for structural optimization. Int. J. Numer. Meth. Eng. 24(2), 359–373 (1987)
Bendsøe, M.P.: Optimal shape design as a material distribution problem. Struct. Optim. 1(4), 193–202 (1989)
Sigmund, O.: A 99 line topology optimization code written in matlab. Struct. Multidiscip. Optim. 21(2), 120–127 (2001)
Yin, X., Lee, S., Chen, W., Liu, W.K., Horstemeyer, M.F.: Efficient random field uncertainty propagation in design using multiscale analysis. J. Mech. Des. 131(2), 21006 (2009)
Zhao, Y.G., Ono, T.: Moment methods for structural reliability. Struct. Saf. 23(1), 47–75 (2001)
Lee, S.H., Chen, W.: A comparative study of uncertainty propagation methods for black-box-type problems. Struct. Multidiscip. Optim. 37(3), 239–253 (2009)
Lee, S.H., Chen, W., Kwak, B.M.: Robust design with arbitrary distributions using Gauss-type quadrature formula. Struct. Multidiscip. Optim. 39(3), 227–243 (2009)
Acknowledgements
This work was supported by the Walter P. Murphy Fellowship to Ms. Yu-Chin Chan at Northwestern University. The authors would also like to thank the Digital Manufacturing and Design Innovation Institute (DMDII) for their support through award number 15-07-07.
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Shintani, K., Chan, YC., Chen, W. (2018). Robust Multi-material Topology Optimization for Lattice Structure Under Material Uncertainties. In: Schumacher, A., Vietor, T., Fiebig, S., Bletzinger, KU., Maute, K. (eds) Advances in Structural and Multidisciplinary Optimization. WCSMO 2017. Springer, Cham. https://doi.org/10.1007/978-3-319-67988-4_84
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DOI: https://doi.org/10.1007/978-3-319-67988-4_84
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