An identification method for enclosed voids restriction in manufacturability design for additive manufacturing structures

Abstract

Additive manufacturing (AM) technologies, such as selective laser sintering (SLS) and fused deposition modeling (FDM), have become the powerful tools for direct manufacturing of complex parts. This breakthrough in manufacturing technology makes the fabrication of new geometrical features and multiple materials possible. Past researches on designs and design methods often focused on how to obtain desired functional performance of the structures or parts, specific manufacturing capabilities as well as manufacturing constraints of AM were neglected. However, the inherent constraints in AM processes should be taken into account in design process. In this paper, the enclosed voids, one type of manufacturing constraints of AM, are investigated. In mathematics, enclosed voids restriction expressed as the solid structure is simply-connected. We propose an equivalent description of simply-connected constraint for avoiding enclosed voids in structures, named as virtual temperature method (VTM). In this method, suppose that the voids in structure are filled with a virtual heating material with high heat conductivity and solid areas are filled with another virtual material with low heat conductivity. Once the enclosed voids exist in structure, the maximum temperature value of structure will be very high. Based upon this method, the simply-connected constraint is equivalent to maximum temperature constraint. And this method can be easily used to formulate the simply-connected constraint in topology optimization. The effectiveness of this description method is illustrated by several examples. Based upon topology optimization, an example of 3D cantilever beam is used to illustrate the trade-off between manufacturability and functionality. Moreover, the three optimized structures are fabricated by FDM technology to indicate further the necessity of considering the simply-connected constraint in design phase for AM.

Key words： additive manufacturing, topology optimization, manufacturability constraints, design for additive manufacturing, simply-connected constraint

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11332004, 11172052 and 11402046), the National Basic Research Program of China (Grant No. 2011CB610304), the Fundamental Research Funds for the Central Universities of China (2342013DUT13RC(3)28) and the 111 Project (B14013). These financial supports are gratefully acknowledged.

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11332004, 11172052 and 11402046) and the National Basic Research Program of China (Grant No. 2011CB610304). These financial supports are gratefully acknowledged.

References

1 Kruth J P, Leu M C, Nakagawa T. Progress in additive manufacturing and rapid prototyping. CIRP Annals-Manufacturing Technology, 1998, 47(2): 525–540

2 Gibson I, Rosen D W, Stucker B. Additive Manufacturing Technologies. New York: Springer, 2010

3 Murr L E, Gaytan S M, Ramirez D A, . Metal fabrication by additive manufacturing using laser and electron beam melting technologies. Journal of Materials Science and Technology, 2012, 28(1): 1–14

4 Gu D, Meiners W, Wissenbach K, . Laser additive manufacturing of metallic components: Materials, processes and mechanisms. International Materials Reviews, 2012, 57(3): 133–164

5 Turner B N, Strong R, Gold S A. A review of melt extrusion additive manufacturing processes: I. Process design and modeling. Rapid Prototyping Journal, 2014, 20: 192–204

6 Kim D S, Bae S W, Choi K H. Development of industrial SFF system using dual laser and optimal process. Robotics and Computer-Integrated Manufacturing, 2007, 23(6): 659–666

7 Kruth J, Vandenbroucke B, van Vaerenbergh J, . Digital manufacturing of biocompatible metal frameworks for complex dental prostheses by means of SLS/SLM. In: Proceedings of Virtual Prototyping and Rapid Manufacturing-Advanced Research in Virtual and Rapid Prototyping, Taylor & Francis. London, 2005, 139–146

8 Rosen D. Design for additive manufacturing: Past, present, and future directions. Journal of Mechanical Design, 2014, 136(9): 090301

9 Sigmund O, Maute K. Topology optimization approaches. Structural and Multidisciplinary Optimization, 2013, 48(6): 1031–1055

10 Cheng K T, Olhoff N. An investigation concerning optimal design of solid elastic plates. International Journal of Solids and Structures, 1981, 17(3): 305–323

11 Bendsøe M P, Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, 1988, 71(2): 197–224

12 Zhou M, Rozvany G. The COC algorithm, Part II: Topological, geometrical and generalized shape optimization. Computer Methods in Applied Mechanics and Engineering, 1991, 89(1–3): 309–336

13 Bendsøe M P, Sigmund O. Material interpolation schemes in topology optimization. Archive of Applied Mechanics, 1999, 69(9–10): 635–654

14 Allaire G, Jouve F, Toader A M. A level-set method for shape optimization. Comptes Rendus Mathematique, 2002, 334(12): 1125–1130

15 Wang M Y, Wang X, Guo D. A level set method for structural topology optimization. Computer Methods in Applied Mechanics and Engineering, 2003, 192(1–2): 227–246

16 Xie Y, Steven G P. A simple evolutionary procedure for structural optimization. Computers & Structures, 1993, 49(5): 885–896

17 Sokolowski J, Zochowski A. Topological derivative in shape optimization. In: Floudas C A, Pardalos P M, eds. Encyclopedia of Optimization. New York: Springer, 2009, 3908–3918

18 Sobieszczanski-Sobieski J, Haftka R T. Multidisciplinary aerospace design optimization: Survey of recent developments. Structural Optimization, 1997, 14(1): 1–23

19 Bendsoe M P, Sigmund O. Topology Optimization: Theory, Methods and Applications. Berlin: Springer, 2004

20 Zhang Y, Liu S. Design of conducting paths based on topology optimization. Heat and Mass Transfer, 2008, 44(10): 1217–1227

21 Zhu J, Zhang W, Beckers P. Integrated layout design of multi-component system. International Journal for Numerical Methods in Engineering, 2009, 78(6): 631–651

22 Sigmund O. Tailoring materials with prescribed elastic properties. Mechanics of Materials, 1995, 20(4): 351–368

23 Nomura T, Nishiwaki S, Sato K, et al. Topology optimization for the design of periodic microstructures composed of electromagnetic materials. Finite Elements in Analysis and Design, 2009, 45(3): 210–226

24 Radman A, Huang X, Xie Y. Topological optimization for the design of microstructures of isotropic cellular materials. Engineering Optimization, 2013, 45(11): 1331–1348

25 Larsen U D, Sigmund O, Bouwstra S. Design and fabrication of compliant micromechanisms and structures with negative Poisson’s ratio. In: Proceedings of Micro Electro Mechanical Systems, the Ninth Annual International Workshop on an Investigation of Micro Structures, Sensors, Actuators, Machines and Systems. San Diego: IEEE, 1996, 365–371

26 Chen W, Liu S. Topology optimization of microstructures of viscoelastic damping materials for a prescribed shear modulus. Structural and Multidisciplinary Optimization, 2014, 50(2): 287–296

27 Andreassen E, Lazarov B S, Sigmund O. Design of manufacturable 3D extremal elastic microstructure. Mechanics of Materials, 2014, 69(1): 1–10

28 Brackett D, Ashcroft I, Hague R. A dithering based method to generate variable volume lattice cells for additive manufacturing. In: 22nd Annual international solid freeform fabrication symposium. 2011, 671–679

29 Aremu A, Ashcroft I, Hague R, . Suitability of SIMP and BESO topology optimization algorithms for additive manufacture. In: 21st Annual International Solid Freeform Fabrication Symposium (SFF)—An Additive Manufacturing Conference. 2010, 679–692

30 Gaynor A T, Meisel N A, Williams C B, . Multiple material topology optimization of compliant mechanisms created via polyJet 3D printing. Journal of Manufacturing Science and Engineering, 2014, 136(6): 061015

31 Hu Y, Blouin V Y, Fadel G M. Design for manufacturing of 3D heterogeneous objects with processing time consideration. Journal of Mechanical Design, 2008, 130(3): 031701

32 Tomlin M, Meyer J. Topology optimization of an additive layer manufactured (ALM) aerospace part. In: Proceedings of 7th Altair CAE Technology Conference. 2011

33 Vayre B, Vignat F, Villeneuve F. Designing for additive manufacturing. Procedia CIRP, 2012, 3: 632–637

34 Diegel O, Singamneni S, Reay S, . Tools for sustainable product design: Additive manufacturing. Journal of Sustainable Development, 2010, 3(3): 68–75

35 Kruth J P, Mercelis P, van Vaerenbergh J, . Binding mechanisms in selective laser sintering and selective laser melting. Rapid Prototyping Journal, 2005, 11(1): 26–36

36 Zein I, Hutmacher D W, Tan K C, . Fused deposition modeling of novel scaffold architectures for tissue engineering applications. Biomaterials, 2002, 23(4): 1169–1185

PMID

37 Hutmacher D W, Schantz T, Zein I, . Mechanical properties and cell cultural response of polycaprolactone scaffolds designed and fabricated via fused deposition modeling. Journal of Biomedical Materials Research, 2001, 55(2): 203–216

PMID

38 Myers S B. Connections between differential geometry and topology. I. Simply connected surfaces. Duke Mathematical Journal, 1935, 1(3): 376–391

39 Bondy J A, Murty U S R. Graph Theory with Applications. London: Macmillan, 1976

40 Golumbic M C. Algorithmic Graph Theory and Perfect Graphs. 2nd. North Holland, 2004

41 West D B. Introduction to Graph Theory. Upper Saddle River: Prentice hall, 2001

42 Korf R E. Depth-first iterative-deepening: An optimal admissible tree search. Artificial Intelligence, 1985, 27(1): 97–109

43 Zhou R, Hansen E A. Breadth-first heuristic search. Artificial Intelligence, 2006, 170(4–5): 385–408

44 Bader D A, Madduri K. Designing multithreaded algorithms for breadth-first search and st-connectivity on the Cray MTA-2. In: International Conference on Parallel Processing. Columbus: IEEE, 2006, 523–530

45 Gabow H N, Tarjan R E. A linear-time algorithm for a special case of disjoint set union. In: Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing. Baltimore: ACM, 1983, 246–251

46 Tarjan R E. Efficiency of a good but not linear set union algorithm. Journal of the ACM, 1975, 22(2): 215–225

47 Dhatt G, Lefrançois E, Touzot G. Finite Element Method. New York: John Wiley & Sons, 2012

48 Bathe K J. Finite element method. In: Wah B W, ed. Wiley encyclopedia of computer science and engineering. New York: John Wiley & Sons, 2008, 1–12

49 Raithby G, Chui E. A finite-volume method for predicting a radiant heat transfer in enclosures with participating media. Journal of Heat Transfer, 1990, 112(2): 415–423

50 Liszka T, Orkisz J. The finite difference method at arbitrary irregular grids and its application in applied mechanics. Computers & Structures, 1980, 11(1–2): 83–95