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.

References

1.
Zegard
,
T.
, and
Paulino
,
G. H.
,
2016
, “
Bridging Topology Optimization and Additive Manufacturing
,”
Struct. Multidiscip. Optim.
,
53
(
1
), pp.
175
192
.
2.
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
3.
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.
4.
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.
5.
Jacobs
,
P. F.
,
1992
,
Rapid Prototyping & Manufacturing: Fundamentals of Stereolithography
,
Society of Manufacturing Engineers
, Dearborn, MI.
6.
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
.
7.
Gibson
,
I.
, and
Shi
,
D.
,
1997
, “
Material Properties and Fabrication Parameters in Selective Laser Sintering Process
,”
Rapid Prototyping J.
,
3
(
4
), pp.
129
136
.
8.
Kruth
,
J.
,
Wang
,
X.
,
Laoui
,
T.
, and
Froyen
,
L.
,
2003
, “
Lasers and Materials in Selective Laser Sintering
,”
Assem. Autom.
,
23
(
4
), pp.
357
371
.
9.
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
.
10.
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
.
11.
Lewis
,
G. K.
, and
Schlienger
,
E.
,
2000
, “
Practical Considerations and Capabilities for Laser Assisted Direct Metal Deposition
,”
Mater. Des.
,
21
(
4
), pp.
417
423
.
12.
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
.
13.
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
.
14.
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
.
15.
Chernov
,
N.
,
Stoyan
,
Y.
, and
Romanova
,
T.
,
2010
, “
Mathematical Model and Efficient Algorithms for Object Packing Problem
,”
Comput. Geom.
,
43
(
5
), pp.
535
553
.
16.
Gibson
,
I.
,
Rosen
,
D.
, and
Stucker
,
B.
,
2015
, “
Software Issues for Additive Manufacturing
,”
Additive Manufacturing Technologies SE - 15
,
Springer
,
New York
, pp.
351
374
.
17.
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
.
18.
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
.
19.
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.
20.
Jamieson
,
R.
, and
Hacker
,
H.
,
1995
, “
Direct Slicing of CAD Models for Rapid Prototyping
,”
Rapid Prototyping J.
,
1
(
2
), pp.
4
12
.
21.
Tata
,
K.
,
Fadel
,
G.
,
Bagchi
,
A.
, and
Aziz
,
N.
,
1998
, “
Efficient Slicing for Layered Manufacturing
,”
Rapid Prototyping J.
,
4
(
4
), pp.
151
167
.
22.
Tyberg
,
J.
, and
Bøhn
,
J. H.
,
1998
, “
Local Adaptive Slicing
,”
Rapid Prototyping J.
,
4
(
3
), pp.
118
127
.
23.
Ma
,
W.
, and
He
,
P.
,
1999
, “
Adaptive Slicing and Selective Hatching Strategy for Layered Manufacturing
,”
J. Mater. Process. Technol.
,
89–90
, pp.
191
197
.
24.
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
.
25.
Sabourin
,
E.
,
Houser
,
S. A.
, and
Bøhn
,
J. H.
,
1996
, “
Adaptive Slicing Using Stepwise Uniform Refinement
,”
Rapid Prototyping J.
,
2
(
4
), pp.
20
26
.
26.
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
.
27.
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
.
28.
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
.
29.
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
.
30.
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
.
31.
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
.
32.
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
.
33.
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
.
34.
Lefebvre
,
S.
,
2013
, “
IceSL: A GPU Accelerated CSG Modeler and Slicer
,”
18th European Forum on Additive Manufacturing (AEFA13)
, Paris, France.
35.
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.
36.
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
.
37.
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
.
38.
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
.
39.
Steuben
,
J. C.
,
Iliopoulos
,
A. P.
, and
Michopoulos
,
J. G.
,
2016
, “Implicit Slicing for Functionally Tailored Additive Manufacturing,”
ASME
Paper No. DETC2016-59638.
40.
Bendsoe
,
M. P.
, and
Sigmund
,
O.
,
2013
,
Topology Optimization: Theory, Methods, and Applications
,
Springer Science & Business Media
, Berlin.
41.
Eschenauer
,
H. A.
, and
Olhoff
,
N.
,
2001
, “
Topology Optimization of Continuum Structures: A Review
,”
ASME Appl. Mech. Rev.
,
54
(
4
), pp.
331
390
.
42.
Rozvany
,
G. I.
,
2009
, “
A Critical Review of Established Methods of Structural Topology Optimization
,”
Struct. Multidiscip. Optim.
,
37
(
3
), pp.
217
237
.
43.
Bendsøe
,
M. P.
,
1989
, “
Optimal Shape Design as a Material Distribution Problem
,”
Struct. Optim.
,
1
(
4
), pp.
193
202
.
44.
Sigmund
,
O.
,
2001
, “
A 99 Line Topology Optimization Code Written in Matlab
,”
Struct. Multidiscip. Optim.
,
21
(
2
), pp.
120
127
.
45.
Stolpe
,
M.
, and
Svanberg
,
K.
,
2001
, “
An Alternative Interpolation Scheme for Minimum Compliance Topology Optimization
,”
Struct. Multidiscip. Optim.
,
22
(
2
), pp.
116
124
.
46.
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
.
47.
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
.
48.
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
.
49.
Suresh
,
K.
,
2010
, “
A 199-Line Matlab Code for Pareto-Optimal Tracing in Topology Optimization
,”
Struct. Multidiscip. Optim.
,
42
(
5
), pp.
665
679
.
50.
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
.
51.
Stegmann
,
J.
, and
Lund
,
E.
,
2005
, “
Discrete Material Optimization of General Composite Shell Structures
,”
Int. J. Numer. Methods Eng.
,
62
(
14
), pp.
2009
2027
.
52.
Deng
,
S.
, and
Suresh
,
K.
,
2017
, “
Topology Optimization Under Thermo-Elastic Buckling
,”
Struct. Multidiscip. Optim.
,
55
(5), pp. 1759–1772.
53.
Harzheim
,
L.
, and
Graf
,
G.
,
2006
, “
A Review of Optimization of Cast Parts Using Topology Optimization
,”
Struct. Multidiscip. Optim.
,
31
(
5
), pp.
388
399
.
54.
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
.
55.
Alonso
,
J. J.
,
LeGresley
,
P.
, and
Pereyra
,
V.
,
2009
, “
Aircraft Design Optimization
,”
Math. Comput. Simul.
,
79
(
6
), pp.
1948
1958
.
56.
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
.
57.
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
.
58.
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
.
59.
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.
60.
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
.
61.
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.
62.
Comsol
,
2015
, “Comsol Multiphysics, Version 5,”
Comsol
,
Burlington, MA
.
63.
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
.
64.
Svanberg
,
K.
,
1987
, “
The Method of Moving Asymptotes—A New Method for Structural Optimization
,”
Int. J. Numer. Methods Eng.
,
24
(
2
), pp.
359
373
.
65.
Chew
,
L. P.
,
1989
, “
Constrained Delaunay Triangulation
,”
Algorithmica
,
4
(
1–4
), pp.
97
108
.
66.
Sloan
,
S. W.
,
1993
, “
A Fast Algorithm for Generating Constrained Delaunay Triangulations
,”
Comput. Struct.
,
47
(
3
), pp.
441
450
.
67.
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
.
68.
Si
,
H.
,
2015
, “
TetGen a Delaunay-Based Quality Tetrahedral Mesh Generator
,”
ACM Trans. Math. Software
,
41
(
2
), pp. 1--36.
69.
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
.
70.
Mirzendehdel
,
A. M.
, and
Suresh
,
K.
,
2015
, “
A Pareto-Optimal Approach to Multimaterial Topology Optimization
,”
ASME J. Mech. Des.
,
137
(
10
), p.
101701
.
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