0
Research Papers

Multiscale Topology Optimization for Additively Manufactured Objects

[+] Author and Article Information
John C. Steuben

Mem. ASME
Computational Multiphysics Systems Laboratory,
Center of Materials Physics and Technology,
U.S. Naval Research Laboratory,
Washington, DC 20375

Athanasios P. Iliopoulos

Mem. ASME
Computational Multiphysics Systems Laboratory,
Center of Materials Physics and Technology
U.S. Naval Research Laboratory,
Washington, DC 20375

John G. Michopoulos

Fellow ASME
Computational Multiphysics Systems Laboratory,
Center of Materials Physics and Technology,
U.S. Naval Research Laboratory,
Washington, DC 20375

1Corresponding author.

Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received October 15, 2017; final manuscript received January 23, 2018; published online June 12, 2018. Assoc. Editor: Jitesh H. Panchal.

J. Comput. Inf. Sci. Eng 18(3), 031002 (Jun 12, 2018) (10 pages) Paper No: JCISE-17-1229; doi: 10.1115/1.4039312 History: Received October 15, 2017; Revised January 23, 2018

The precise control of mass and energy deposition associated with additive manufacturing (AM) processes enables the topological specification and realization of how space can be filled by material in multiple scales. Consequently, AM can be pursued in a manner that is optimized such that fabricated objects can best realize performance specifications. In the present work, we propose a computational multiscale method that utilizes the unique meso-scale structuring capabilities of implicit slicers for AM, in conjunction with existing topology optimization (TO) tools for the macro-scale, in order to generate structurally optimized components. The use of this method is demonstrated on two example objects including a load bearing bracket and a hand tool. This paper also includes discussion concerning the applications of this methodology, its current limitations, a recasting of the AM digital thread, and the future work required to enable its widespread use.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Zegard, T. , and Paulino, G. H. , 2016, “Bridging Topology Optimization and Additive Manufacturing,” Struct. Multidiscip. Optim., 53(1), pp. 175–192. [CrossRef]
Brackett, D. , Ashcroft, I. , and Hague, R. , 2011, “Topology Optimization for Additive Manufacturing,” Solid Freeform Fabrication Symposium, Austin, TX, pp. 348–362. https://sffsymposium.engr.utexas.edu/Manuscripts/2011/2011-27-Brackett.pdf
Steuben, J. C. , Iliopoulos, A. P. , and Michopoulos, J. G. , 2017, “Towards Multiscale Topology Optimization for Additively Manufactured Components Using Implicit Slicing,” ASME Paper No. DETC2017-67596.
Steuben, J. C. , Michopoulos, J. G. , Iliopoulos, A. P. , and Birnbaum, A. J. , 2017, “Functional Performance Tailoring of Additively Manufactured Components Via Topology Optimization,” ASME Paper No. DETC2017-67600.
Jacobs, P. F. , 1992, Rapid Prototyping & Manufacturing: Fundamentals of Stereolithography, Society of Manufacturing Engineers, Dearborn, MI.
Hutmacher, D. W. , Schantz, T. , Zein, I. , Ng, K. W. , Teoh, S. H. , and Tan, K. C. , 2001, “Mechanical Properties and Cell Cultural Response of Polycaprolactone Scaffolds Designed and Fabricated Via Fused Deposition Modeling,” J. Biomed. Mater. Res., 55(2), pp. 203–216. [CrossRef] [PubMed]
Gibson, I. , and Shi, D. , 1997, “Material Properties and Fabrication Parameters in Selective Laser Sintering Process,” Rapid Prototyping J., 3(4), pp. 129–136. [CrossRef]
Kruth, J. , Wang, X. , Laoui, T. , and Froyen, L. , 2003, “Lasers and Materials in Selective Laser Sintering,” Assem. Autom., 23(4), pp. 357–371. [CrossRef]
Kruth, J. , Mercelis, P. , Vaerenbergh, J. V. , Froyen, L. , and Rombouts, M. , 2005, “Binding Mechanisms in Selective Laser Sintering and Selective Laser Melting,” Rapid Prototyping J., 11(1), pp. 26–36. [CrossRef]
Murr, L. E. , Gaytan, S. M. , Ramirez, D. A. , Martinez, E. , Hernandez, J. , Amato, K. N. , Shindo, P. W. , Medina, F. R. , and Wicker, R. B. , 2012, “Metal Fabrication by Additive Manufacturing Using Laser and Electron Beam Melting Technologoies,” J. Mater. Sci. Technol., 28(1), pp. 1–14. [CrossRef]
Lewis, G. K. , and Schlienger, E. , 2000, “Practical Considerations and Capabilities for Laser Assisted Direct Metal Deposition,” Mater. Des., 21(4), pp. 417–423. [CrossRef]
Mazumder, J. , Dutta, D. , Kikuchi, N. , and Ghosh, A. , 2000, “Closed Loop Direct Metal Deposition: Art to Part,” Opt. Lasers Eng., 34(4–6), pp. 397–414. [CrossRef]
Livesu, M. , Ellero, S. , Martínez, J. , Lefebvre, S. , and Attene, M. , 2017, “From 3D Models to 3D Prints: An Overview of the Processing Pipeline,” Computer Graphics Forum, Vol. 36, Wiley, Hoboken, NJ, pp. 537–564. [CrossRef]
Huotilainen, E. , Jaanimets, R. , Valášek, J. , Marcián, P. , Salmi, M. , Tuomi, J. , Mäkitie, A. , and Wolff, J. , 2014, “Inaccuracies in Additive Manufactured Medical Skull Models Caused by the DICOM to STL Conversion Process,” J. Cranio-Maxillofacial Surg., 42(5), pp. e259–e265. [CrossRef]
Chernov, N. , Stoyan, Y. , and Romanova, T. , 2010, “Mathematical Model and Efficient Algorithms for Object Packing Problem,” Comput. Geom., 43(5), pp. 535–553. [CrossRef]
Gibson, I. , Rosen, D. , and Stucker, B. , 2015, “Software Issues for Additive Manufacturing,” Additive Manufacturing Technologies SE - 15, Springer, New York, pp. 351–374.
Gao, W. , Zhang, Y. , Ramanujan, D. , Ramani, K. , Chen, Y. , Williams, C. B. , Wang, C. C. , Shin, Y. C. , Zhang, S. , and Zavattieri, P. D. , 2015, “The Status, Challenges, and Future of Additive Manufacturing in Engineering,” Comput.-Aided Des., 69, pp. 65–89. [CrossRef]
Pandey, P. M. , Reddy, N. V. , and Dhande, S. G. , 2003, “Slicing Procedures in Layered Manufacturing: A Review,” Rapid Prototyping J., 9(5), pp. 274–288. [CrossRef]
Luo, R. , and Ma, Y. , 1995, “A Slicing Algorithm for Rapid Prototyping and Manufacturing,” IEEE International Conference on Robotics and Automation (ICRA), Nagoya, Japan, May 21–27.
Jamieson, R. , and Hacker, H. , 1995, “Direct Slicing of CAD Models for Rapid Prototyping,” Rapid Prototyping J., 1(2), pp. 4–12. [CrossRef]
Tata, K. , Fadel, G. , Bagchi, A. , and Aziz, N. , 1998, “Efficient Slicing for Layered Manufacturing,” Rapid Prototyping J., 4(4), pp. 151–167. [CrossRef]
Tyberg, J. , and Bøhn, J. H. , 1998, “Local Adaptive Slicing,” Rapid Prototyping J., 4(3), pp. 118–127. [CrossRef]
Ma, W. , and He, P. , 1999, “Adaptive Slicing and Selective Hatching Strategy for Layered Manufacturing,” J. Mater. Process. Technol., 89–90, pp. 191–197. [CrossRef]
Hope, R. L. , Roth, R. N. , and Jacobs, P. A. , 1997, “Adaptive Slicing With Sloping Layer Surfaces,” Rapid Prototyping J., 3(3), pp. 89–98. [CrossRef]
Sabourin, E. , Houser, S. A. , and Bøhn, J. H. , 1996, “Adaptive Slicing Using Stepwise Uniform Refinement,” Rapid Prototyping J., 2(4), pp. 20–26. [CrossRef]
Xu, F. , Wong, Y. S. , Loh, H. T. , Fuh, J. Y. H. , and Miyazawa, T. , 1997, “Optimal Orientation With Variable Slicing in Stereolithography,” Rapid Prototyping J., 3(3), pp. 76–88. [CrossRef]
Yang, P. , and Qian, X. , 2008, “Adaptive Slicing of Moving Least Squares Surfaces: Toward Direct Manufacturing of Point Set Surfaces,” ASME J. Comput. Inf. Sci. Eng., 8(3), p. 031003. [CrossRef]
Yang, Y. , Loh, H. , Fuh, J. , and Wang, Y. , 2002, “Equidistant Path Generation for Improving Scanning Efficiency in Layered Manufacturing,” Rapid Prototyping J., 8(1), pp. 30–37. [CrossRef]
Qiu, D. , and Langrana, N. A. , 2002, “Void Eliminating Toolpath for Extrusion-Based Multi-Material Layered Manufacturing,” Rapid Prototyping J., 8(1), pp. 38–45. [CrossRef]
Siraskar, N. , Paul, R. , and Anand, S. , 2015, “Adaptive Slicing in Additive Manufacturing Process Using a Modified Boundary Octree Data Structure,” ASME J. Manuf. Sci. Eng., 137(1), p. 011007. [CrossRef]
Qiu, Y. , Zhou, X. , and Qian, X. , 2011, “Direct Slicing of Cloud Data With Guaranteed Topology for Rapid Prototyping,” Int. J. Adv. Manuf. Technol., 53(1–4), pp. 255–265. [CrossRef]
Huang, P. , Wang, C. C. L. , and Chen, Y. , 2013, “Intersection-Free and Topologically Faithful Slicing of Implicit Solid,” ASME J. Comput. Inf. Sci. Eng., 13(2), p. 021009. [CrossRef]
Huang, P. , Wang, C. C. L. , and Chen, Y. , 2014, Advances in Computers and Information in Engineering Research, Vol. 1, American Society of Mechanical Engineers, New York, pp. 377–409. [PubMed] [PubMed]
Lefebvre, S. , 2013, “IceSL: A GPU Accelerated CSG Modeler and Slicer,” 18th European Forum on Additive Manufacturing (AEFA13), Paris, France.
Schumacher, C. , Bickel, B. , Rys, J. , Marschner, S. , Daraio, C. , and Gross, M. , 2015, “Microstructures to Control Elasticity in 3D Printing,” ACM Trans. Graph., 34(4), p. 136.
Martínez, J. , Song, H. , Dumas, J. , and Lefebvre, S. , 2017, “Orthotropic k-Nearest Foams for Additive Manufacturing,” ACM Trans. Graph. (TOG), 36(4), p. 121. [CrossRef]
Cramer, A. D. , Challis, V. J. , and Roberts, A. P. , 2017, “Physically Realizable Three-Dimensional Bone Prosthesis Design With Interpolated Microstructures,” ASME J. Biomech. Eng., 139(3), p. 031013. [CrossRef]
Steuben, J. C. , Iliopoulos, A. P. , and Michopoulos, J. G. , 2016, “Implicit Slicing for Functionally Tailored Additive Manufacturing,” Comput.-Aided Des., 77, pp. 107–119. [CrossRef]
Steuben, J. C. , Iliopoulos, A. P. , and Michopoulos, J. G. , 2016, “Implicit Slicing for Functionally Tailored Additive Manufacturing,” ASME Paper No. DETC2016-59638.
Bendsoe, M. P. , and Sigmund, O. , 2013, Topology Optimization: Theory, Methods, and Applications, Springer Science & Business Media, Berlin.
Eschenauer, H. A. , and Olhoff, N. , 2001, “Topology Optimization of Continuum Structures: A Review,” ASME Appl. Mech. Rev., 54(4), pp. 331–390. [CrossRef]
Rozvany, G. I. , 2009, “A Critical Review of Established Methods of Structural Topology Optimization,” Struct. Multidiscip. Optim., 37(3), pp. 217–237. [CrossRef]
Bendsøe, M. P. , 1989, “Optimal Shape Design as a Material Distribution Problem,” Struct. Optim., 1(4), pp. 193–202. [CrossRef]
Sigmund, O. , 2001, “A 99 Line Topology Optimization Code Written in Matlab,” Struct. Multidiscip. Optim., 21(2), pp. 120–127. [CrossRef]
Stolpe, M. , and Svanberg, K. , 2001, “An Alternative Interpolation Scheme for Minimum Compliance Topology Optimization,” Struct. Multidiscip. Optim., 22(2), pp. 116–124. [CrossRef]
Munk, D. J. , Vio, G. A. , and Steven, G. P. , 2015, “Topology and Shape Optimization Methods Using Evolutionary Algorithms: A Review,” Struct. Multidiscip. Optim., 52(3), pp. 613–631. [CrossRef]
Sethian, J. A. , and Wiegmann, A. , 2000, “Structural Boundary Design Via Level Set and Immersed Interface Methods,” J. Comput. Phys., 163(2), pp. 489–528. [CrossRef]
Allaire, G. , Jouve, F. , and Toader, A.-M. , 2004, “Structural Optimization Using Sensitivity Analysis and a Level-Set Method,” J. Comput. Phys., 194(1), pp. 363–393. [CrossRef]
Suresh, K. , 2010, “A 199-Line Matlab Code for Pareto-Optimal Tracing in Topology Optimization,” Struct. Multidiscip. Optim., 42(5), pp. 665–679. [CrossRef]
Chen, J. , Shapiro, V. , Suresh, K. , and Tsukanov, I. , 2007, “Shape Optimization With Topological Changes and Parametric Control,” Int. J. Numer. Methods Eng., 71(3), pp. 313–346. [CrossRef]
Stegmann, J. , and Lund, E. , 2005, “Discrete Material Optimization of General Composite Shell Structures,” Int. J. Numer. Methods Eng., 62(14), pp. 2009–2027. [CrossRef]
Deng, S. , and Suresh, K. , 2017, “Topology Optimization Under Thermo-Elastic Buckling,” Struct. Multidiscip. Optim., 55(5), pp. 1759–1772.
Harzheim, L. , and Graf, G. , 2006, “A Review of Optimization of Cast Parts Using Topology Optimization,” Struct. Multidiscip. Optim., 31(5), pp. 388–399. [CrossRef]
Coverstone-Carroll, V. , Hartmann, J. , and Mason, W. , 2000, “Optimal Multi-Objective Low-Thrust Spacecraft Trajectories,” Comput. Methods Appl. Mech. Eng., 186(2–4), pp. 387–402. [CrossRef]
Alonso, J. J. , LeGresley, P. , and Pereyra, V. , 2009, “Aircraft Design Optimization,” Math. Comput. Simul., 79(6), pp. 1948–1958. [CrossRef]
Wang, X. , Xu, S. , Zhou, S. , Xu, W. , Leary, M. , Choong, P. , Qian, M. , Brandt, M. , and Xie, Y. M. , 2016, “Topological Design and Additive Manufacturing of Porous Metals for Bone Scaffolds and Orthopaedic Implants: A Review,” Biomaterials, 83, pp. 127–141. [CrossRef] [PubMed]
Robbins, J. , Owen, S. , Clark, B. , and Voth, T. , 2016, “An Efficient and Scalable Approach for Generating Topologically Optimized Cellular Structures for Additive Manufacturing,” Addit. Manuf., 12(Pt. B), pp. 296–304. [CrossRef]
Quan, Z. , Larimore, Z. , Wu, A. , Yu, J. , Qin, X. , Mirotznik, M. , Suhr, J. , Byun, J.-H. , Oh, Y. , and Chou, T.-W. , 2016, “Microstructural Design and Additive Manufacturing and Characterization of 3D Orthogonal Short Carbon Fiber/Acrylonitrile-Butadiene-Styrene Preform and Composite,” Compos. Sci. Technol., 126, pp. 139–148. [CrossRef]
Gaynor, A. T. , Meisel, N. A. , Williams, C. B. , and Guest, J. K. , 2014, “Topology Optimization for Additive Manufacturing: Considering Maximum Overhang Constraint,” AIAA Paper No. 2014-2036.
Wu, J. , Clausen, A. , and Sigmund, O. , 2017, “Minimum Compliance Topology Optimization of Shell-Infill Composites for Additive Manufacturing,” Comput. Methods Appl. Mech. Eng., 326, pp. 358–375. [CrossRef]
Jiang, L. , Ye, H. , Zhou, C. , Chen, S. , and Xu, W. , 2017, “Parametric Topology Optimization Toward Rational Design and Efficient Prefabrication for Additive Manufacturing,” ASME Paper No. MSEC2017-2954.
Comsol, 2015, “Comsol Multiphysics, Version 5,” Comsol, Burlington, MA.
Amestoy, P. R. , Duff, I. S. , LExcellent, J.-Y. , and Koster, J. , 2000, “Mumps: A General Purpose Distributed Memory Sparse Solver,” International Workshop on Applied Parallel Computing, Bergen, Norway, June 18–20, pp. 121–130.
Svanberg, K. , 1987, “The Method of Moving Asymptotes—A New Method for Structural Optimization,” Int. J. Numer. Methods Eng., 24(2), pp. 359–373. [CrossRef]
Chew, L. P. , 1989, “Constrained Delaunay Triangulation,” Algorithmica, 4(1–4), pp. 97–108. [CrossRef]
Sloan, S. W. , 1993, “A Fast Algorithm for Generating Constrained Delaunay Triangulations,” Comput. Struct., 47(3), pp. 441–450. [CrossRef]
Shewchuk, J. R. , 1996, “Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator,” Applied Computational Geometry Towards Geometric Engineering, Vol. 1148, Springer, Berlin, pp. 203–222. [CrossRef]
Si, H. , 2015, “TetGen a Delaunay-Based Quality Tetrahedral Mesh Generator,” ACM Trans. Math. Software, 41(2), pp. 1--36.
Kruskal, J. B. , 1956, “On the Shortest Spanning Subtree of a Graph and the Traveling Salesman Problem,” Proc. Am. Math. Soc., 7(1), pp. 48–50. [CrossRef]
Mirzendehdel, A. M. , and Suresh, K. , 2015, “A Pareto-Optimal Approach to Multimaterial Topology Optimization,” ASME J. Mech. Des., 137(10), p. 101701. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

An overview of the AM “digital thread” concept

Grahic Jump Location
Fig. 2

Illustration of toolpath concepts. Note the perimeter shells (black) that enclose a sparse infill pattern (red); this combination of path types is commonly used in AM applications.

Grahic Jump Location
Fig. 3

Example of implicit slicing. At top, the input geometry and applied force F. At center, the von Mises stress in the part, as calculated using FEA. At bottom, the toolpath produced by the implicit slicer.

Grahic Jump Location
Fig. 4

Flowchart of the workflow demonstrating the stages of the proposed multiscale methodology for TO

Grahic Jump Location
Fig. 5

TO example. At top (a) the original domain and boundary conditions are shown. At center (b), the output ρd is shown, with the cutoff value ρd=ρmin highlighted. At the bottom (c), the output domain Ω corresponding to ρd≥ρmin is highlighted: (a) TO domain, (b) results of TO, and (c) output domain from TO.

Grahic Jump Location
Fig. 6

Steps for computing the 2D and 3D domains: (a) 2Γρ, (b) 2Γρ ∪ 2Γ0, (c) Γ=2Γρ ∪ 2Γ0¯, and (d) 2Ω, and (e) 3Γ

Grahic Jump Location
Fig. 7

TO example. (a) the density field from the topology optimizer. (b, c) the corresponding linear infill function defined over the first and second layers. (d, e) the modulated infill function for the first and second layers. (f) contours corresponding to the infill for the first two layers superimposed, along with the perimeter contours: (a) ρd(x), (b) Hlin(x) for z = 0, (c) Hlin(x) for z=lt, (d) Hin(x) for z = 0, (e) Hin(x) for z=lt, and (f) superimposed infill for first two layers.

Grahic Jump Location
Fig. 8

Complete bracket toolpath in 3D space. All slices are of the same bounding geometry, resulting in a 2.5D part.

Grahic Jump Location
Fig. 9

Illustration of the graph formulation for optimal toolpath sequencing. The original toolpath segments are shown in bold, with the vertices Vi on either end. The negative-weight edges connecting the endpoints of the original segments are bold and dashed. The positive weight edges representing movement between toolpath segments are shown by light dashed lines.

Grahic Jump Location
Fig. 10

The fastener that the spanner must drive (top), and the corresponding dimensions and boundary conditions on the outer envelope of the spanner wrench

Grahic Jump Location
Fig. 11

Multiscale TO of the wrench. At top (a), the density function is computed by the topology optimizer. Below (b) is the domain Ω upon which the implicit slicer operates. The infill function Hin is shown, for the first two layers, in (c). In (d) and (e) the output toolpath can be seen. At bottom (f), the FDM-manufactured wrench is photographed: (a) ρd(x), (b) Ω, (c) Hin for z = 0 and z=lt, (d) ρd(x) with gin∪gpr superimposed, (e) output toolpath, and (f) photograph of as-manufactured wrench.

Grahic Jump Location
Fig. 12

The reinterpreted digital thread incorporating an optimization environment

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In