Additive manufacturing processes, of which Selective Laser Melting (SLM) is one, provide an increased design freedom and the ability to build structures directly from CAD models. There is a growing interest in using optimization methods to design structures in place of manual designs. Three design optimization problems were addressed in this paper. The first related to axisymmetric structures and the other two addressing important design constraints when manufacturing using SLM. These solutions were developed and applied to a case study of a turbine containment ring. Firstly, many structural components such as a turbine containment ring are axisymmetric while they are subjected to a non-axisymmetric load. A solution was presented in this paper to generate optimized axisymmetric designs for a problem in which the mechanical model was not axisymmetric. The solution also worked equally well for generating a prismatic geometry with a uniform cross section, requiring no change in the procedure from axisymmetric designs to achieve this. Secondly, the SLM process experiences difficulties manufacturing structures with internal voids larger than a certain upper limit. A method was developed that allowed the designer to provide a value for this upper limit to the optimization method which would prevent the generation of internal voids larger than this value in any optimized design. The method calculated the sizes of all the voids and did not increase their size once they reached this limit. It was also aware of voids near each other, providing a minimum distance between them. Finally, in order to remove the metal powder, that fills the internal voids of structures built using SLM to reduce unnecessary weight, a method was developed to build paths to join the internal voids created during the optimization process. It allowed the analyst to nominate suitable path entrance locations from which powder could be removed, then found the shortest path connecting all voids and these locations. For axisymmetric structures it also distributed this path around the circumference to avoid generating weak points.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
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. doi:10.1016/j.cma.2015.02.028
Allaire G, Jouve E, Michailidis G (2016) Thickness control in structural optimization via a level set method. Struct Multidiscip Optim 53(6):1349–1382. doi:10.1007/s00158-016-1453-y
ASM International (1967) Inconel Alloy 625. Alloy Digest.
Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1(4):193–202. doi:10.1007/BF01650949
Brackett D, Ashcroft I, Hague R (2001) Topology optimization for additive manufacturing. In: Twenty second solid Freeform Fabrication (SFF) Symposium. University of Texas, Austin, pp 348–362
Brooks W, Sutcliffe C, Cantwell W, Fox P, Todd J, Mines R (August 2005) Rapid design and manufacture of ultralight cellular materials. In: Sixteenth solid Freeform Fabrication (SFF) Symposium. University of Texas, Austin, pp 231–241
Bruns TE, Tortorelli DA (2001) Topology optimization of non-linear elastic structures and compliant mechanisms. Comput Methods Appl Mech Eng 190(26–27):3443–3459. doi:10.1016/S0045-7825(00)00278-4
Bruns TE, Tortorelli DA (2003) An element removal and reintroduction strategy for the topology optimization of structures and compliant mechanisms. Int J Numer Methods Eng 57(10):1413–1430. doi:10.1002/nme.783
Challis VJ, Roberts AP, Grotowski JF, Zhang L-C, Sercombe TB (2010) Prototypes for bone implant scaffolds designed via topology optimization and manufactured by solid Freeform Fabrication. Adv Eng Mater 12(11):1106–1110. doi:10.1002/adem.201000154
Chen Y (2006) A mesh-based geometric modeling method for general structures. ASME Conf Proc 2006(42578):269–281. doi:10.1115/DETC2006-99513
Chen S, Wang MY, Liu AQ (2008) Shape feature control in structural topology optimization. Comput Aided Des 40(9):951–962. doi:10.1016/j.cad.2008.07.004
Chu DN, Xie YM, Hira A, Steven GP (1996) Evolutionary structural optimization for problems with stiffness constraints. Finite Elem Anal Des 21(4):239–251. doi:10.1016/0168-874X(95)00043-S
Chu C, Graf G, Rosen DW (2008) Design for Additive Manufacturing of cellular structures. Comput-Aided Des Applic 5(5):686–696. doi:10.3722/cadaps.2008.686-696
Deaton J, Grandhi RV (2013) A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct Multidiscip Optim 49(1):1–38. doi:10.1007/s00158-013-0956-z
Du J, Olhoff N (2007) Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps. Struct Multidiscip Optim 34(2):91–110. doi:10.1007/s00158-007-0101-y
Field DA (1988) Laplacian smoothing and Delaunay triangulations. Commun Appl Numer Methods 4:709–712
Forsberg J, Nilsson L (2007) Topology optimization in crashworthiness design. Struct Multidiscip Optim 33(1):1–12. doi:10.1007/s00158-006-0040-z
Guest JK (2009) Imposing maximum length scale in topology optimization. Struct Multidiscip Optim 37(5):463–473. doi:10.1007/s00158-008-0250-7
Guest JK, Prévost JH, Belytschko T (2004) Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int J Numer Methods Eng 61(2):238–254. doi:10.1002/nme.1064
Haber, R.B., Jog, C.S., and Bendsøe, M.P. (1996) A new approach to variable-topology shape design using a constraint on perimeter. Struct Optim, 11(1):1–12, doi:10.1007/BF01279647.
Hagg AC, Sankey GO (1974) The containment of disk burst fragments by cylindrical shells. J Eng Power 96(2):114–123. doi:10.1115/1.3445758
Haynes International Inc. (2001) Haynes 625 alloy. Technical Report H-3073D, Kokomo, Indiana 46904–9013 (USA). <http://www.haynesintl.com/pdf/h3073.pdf> Retrieved 28-Dec-2012.
Hopkinson, N, Hague, RJM, and Dickens, PM (editors) (2006) Rapid manufacturing: an industrial revolution for the digital age. John Wiley & Sons, ltd, west Sussex PO19 8SQ, England, ISBN:978-0-4700-3399-9, doi:10.1002/0470033991.
Huang X, Xie YM (2007) Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite Elem Anal Des 43(14):1039–1049. doi:10.1016/j.finel.2007.06.006
Huang X, Xie YM (2010) A further review of ESO type methods for topology optimization. Struct Multidiscip Optim 41(5):671–683. doi:10.1007/s00158-010-0487-9
Huang X, Xie YM, Burry MC (2006) A new algorithm for bi-directional evolutionary structural optimization. JSME international journal. Series C 49(4):1091–1099. doi:10.1299/jsmec.49.1091
Huang X, Xie YM, Lu G (2007) Topology optimization of energy-absorbing structures. Int J Crashworthiness 12(6):663–675. doi:10.1080/13588260701497862
Jung D, Gea HC (2006) Design of an energy-absorbing structure using topology optimization with a multimaterial model. Struct Multidiscip Optim 32(3):251–257. doi:10.1007/s00158-006-0011-4
Kato J, Hoshiba H, Takase S, Terada K, Kyoya T (2015) Analytical sensitivity in topology optimization for elastoplastic composites. Struct Multidiscip Optim 52(3):507–526
Kobayashi T, Simons JW, Brown CS, Shockey DA (2008) Plastic flow behavior of Inconel 718 under dynamic shear loads. Int J Impact Eng 35(5):389–396. doi:10.1016/j.ijimpeng.2007.03.005
Li Q, Steven GP, Xie YM, Querin OM (2004) Evolutionary topology optimization for temperature reduction of heat conducting fields. Int J Heat Mass Transf 47(23):5071–5083. doi:10.1016/j.ijheatmasstransfer.2004.06.010
Lin S, Kernighan BW (1973) An effective heuristic algorithm for the traveling-salesman problem. Oper Res 21(2):498–516
Maute K, Schwarz S, Ramm E (1998) Adaptive topology optimization of elastoplastic structures. Struct Optim 15(2):81–91. doi:10.1007/BF01278493
Mayer RR, Kikuchi N, Scott RA (1996) Application of topological optimization techniques to structural crashworthiness. Int J Numer Methods Eng 39(8):1383–1403. doi:10.1002/(SICI)1097-0207(19960430)39:8<1383::AID-NME909>3.0.CO;2-3
Naing MW, Chua CK, Leong KF, Wang Y (2005) Fabrication of customised scaffolds using computer-aided design and rapid prototyping techniques. Rapid Prototyp J 11(4):249–259. doi:10.1108/13552540510612938
Neves MM, Rodrigues H, Guedes JM (1995) Generalized topology design of structures with a buckling load criterion. Struct Optim 10(2):71–78. doi:10.1007/BF01743533
Pedersen CBW (2003) Topology optimization design of crushed 2D-frames for desired energy absorption history. Struct Multidiscip Optim 25(5–6):368–382. doi:10.1007/s00158-003-0282-y
Pereira JM, Lerch BA (2001) Effects of heat treatment on the ballistic impact properties of INCONEL718 for jet engine fan containment applications. Int J Impact Eng 25(8):715–733. doi:10.1016/S0734-743X(01)00018-5
Poulsen TA (2003) A new scheme for imposing a minimum length scale in topology optimization. Int J Numer Methods Eng 57(6):741–760. doi:10.1002/nme.694
Prasad B, Emerson JF (1984) Optimal structural remodeling of multi-objective systems. Comput Struct 18(4):619–628. doi:10.1016/0045-7949(84)90007-5
Querin OM, Young V, Steven GP, Xie YM (2000) Computational efficiency and validation of bi-directional evolutionary structural optimisation. Comput Methods Appl Mech Eng 189(2):559–573. doi:10.1016/S0045-7825(99)00309-6
Rosen DW (2007) Computer-aided design for additive manufacturing of cellular structures. Comput-Aided Des Appl 4(1–6):585–594. doi:10.1080/16864360.2007.10738493
Rozvany GIN (2009) A critical review of established methods of structural topology optimization. Struct Multidiscip Optim 37(3):217–237. doi:10.1007/s00158-007-0217-0
Rozvany GIN, Zhou M, Birker T (1992) Generalized shape optimization without homogenization. Structural optimization 4(3–4):250–252. doi:10.1007/BF01742754
Samanta, A., Teli, M., and Singh, R.K. (2012) Surface integrity in laser assisted mechanical micro-machining of (LAMM) of Inconel 625. In Proceedings of international Conference on Micromanufacturing, Chicago, USA.
Schroeder C, Regli WC, Shokoufandeh A, Sun W (2005) Computer-aided design of porous artifacts. Comput Aided Des 37(3):339–353. doi:10.1016/j.cad.2004.03.008
Sorkine, O., Cohen-Or, D., Lipman, Y., Alexa, M., Rössl, C., and Seidel, H.-P. (2004) Laplacian surface editing. In Proceedings of the 2004 Eurographics/ACM SIGGRAPH Symposium on geometry processing, SGP’04, pages 175–184, New York, ACM.
Special Metals Corporation (2006) Inconel alloy 625. Technical Report SMC-063, Huntington, WV 25705–1771 (USA). <http://www.specialmetals.com/documents/Inconel%20alloy%20625.pdf> Retrieved 30-Dec-2012.
Stojanov D, Falzon BG, Wu X, Yan W (2016) Implementing a structural continuity constraint and a halting method for the topology optimization of energy absorbers. Struct Multidiscip Optim 54:429-448 doi:10.1007/s00158-016-1451-0
Sun W, Starly B, Nam J, Darling A (2005) Bio-CAD modeling and its applications in computer-aided tissue engineering. Comput Aided Des 37(11):1097–1114. doi:10.1016/j.cad.2005.02.002
Wallin M, Jönsson V, Wingren E (2016) Topology optimization based on finite strain plasticity. Struct Multidiscip Optim 54(4):783–793
Wang H, Chen Y, Rosen DW (2005) A hybrid geometric modeling method for large scale conformal cellular structures. ASME Conf Proc 2005(47403):421–427. doi:10.1115/DETC2005-85366
Watts DM, Hague RJ (2006) Exploiting the design freedom of rm. In: Seventeenth solid Freeform Fabrication (SFF) Symposium. University of Texas, Austin, pp 656–667
Wu C-Y, Tseng K-Y (2010) Topology optimization of structures using modified binary differential evolution. Struct Multidiscip Optim 42(6):939–953. doi:10.1007/s00158-010-0523-9
Yang XY, Xie YM, Liu JS, Parks GT, Clarkson PJ (2002) Perimeter control in the bidirectional evolutionary optimization method. Struct Multidiscip Optim 24(6):430–440. doi:10.1007/s00158-002-0256-5
Yoon GH, Kim YY (2007) Topology optimization of material-nonlinear continuum structures by the element connectivity parameterization. Int J Numer Methods Eng 69(10):2196–2218. doi:10.1002/nme.1843
Yuge K, Kikuchi N (1995) Optimization of a frame structure subjected to a plastic deformation. Struct Optim 10(3):197–208. doi:10.1007/BF01742592
Zhang, G., Li, L., Khandelwal, K. (2016) Topology optimization of structures with anisotropic plastic materials using enhanced assumed strain elements. Struct Multidiscip Optim. doi:10.1007/s00158-016-1612-1
Funding for this research was provided by Microturbo, a member of the Safran group. Computational resources were provided by the Australian Government through the National Computational Infrastructure.
Brian G. Falzon acknowledges the financial support of Bombardier and the Royal Academy of Engineering. X Wu and W Yan acknowledge the support of Australian Research Council through the ITRH project IH130100008 and the support of the Australian Science and Industry Endowment Fund through the SIEF project RP04-153 (Aero-Engine).
About this article
Cite this article
Stojanov, D., Wu, X., Falzon, B.G. et al. Axisymmetric structural optimization design and void control for selective laser melting. Struct Multidisc Optim 56, 1027–1043 (2017). https://doi.org/10.1007/s00158-017-1700-x
- Axisymmetric structure
- Void control
- Bi-directional evolutionary structural optimization
- Additive manufacturing