Abstract

Topology optimization (TO) has rapidly evolved from an academic exercise into an exciting discipline with numerous industrial applications. Various TO algorithms have been established, and several commercial TO software packages are now available. However, a major challenge in TO is the post-processing of the optimized models for downstream applications. Typically, optimal topologies generated by TO are faceted (triangulated) models, extracted from an underlying finite element mesh. These triangulated models are dense, poor quality, and lack feature/parametric control. This poses serious challenges to downstream applications such as prototyping/testing, design validation, and design exploration. One strategy to address this issue is to directly impose downstream requirements as constraints in the TO algorithm. However, this not only restricts the design space, it may even lead to TO failure. Separation of post-processing from TO is more robust and flexible. The objective of this paper is to provide a critical review of various post-processing methods and categorize them based both on targeted applications and underlying strategies. The paper concludes with unresolved challenges and future work.

References

1.
Bendsoe
,
M. P.
, and
Sigmund
,
O.
,
2004
,
Topology Optimization: Theory, Methods, and Applications
,
Springer-Verlag Berlin Heidelberg
.
2.
Bendsøe
,
M. P.
,
1995
,
Optimization of Structural Topology, Shape and Material
,
Springer-Verlag Berlin Heidelberg
.
3.
Sigmund
,
O.
, and
Maute
,
K.
,
2013
, “
Topology Optimization Approaches
,”
Struct. Multidiscip. Optim.
,
48
(
6
), pp.
1031
1055
. 10.1007/s00158-013-0978-6
4.
Zhu
,
J.-H.
,
Zhang
,
W.-H.
, and
Xia
,
L.
,
2016
, “
Topology Optimization in Aircraft and Aerospace Structures Design
,”
Arch. Comput. Methods Eng.
,
23
(
4
), pp.
595
622
. 10.1007/s11831-015-9151-2
5.
Zhu
,
J.-H.
,
Gu
,
X.-J.
,
Zhang
,
W.-H.
, and
Beckers
,
P.
,
2013
, “
Structural Design of Aircraft Skin Stretch-Forming Die Using Topology Optimization
,”
J. Comput. Appl. Math.
,
246
, pp.
278
288
. 10.1016/j.cam.2012.09.001
6.
Dunning
,
P. D.
,
Stanford
,
B. K.
, and
Kim
,
H. A.
,
2015
, “
Coupled Aerostructural Topology Optimization Using a Level Set Method for 3d Aircraft Wings
,”
Struct. Multidiscip. Optim.
,
51
(
5
), pp.
1113
1132
. 10.1007/s00158-014-1200-1
7.
Walker
,
D.
, and
Liu
,
D.
,
2015
, “
Topology Optimization of An Aircraft Wing
,”
56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
,
Kissimmee, FL
,
Jan. 5–9
, p.
0976
.
8.
Kesseler
,
E.
, and
Vankan
,
W.
,
2006
, “
Multidisciplinary Design Analysis and Multi-Objective Optimisation Applied to Aircraft Wing
,”
WSEAS Trans. Syst. Control
,
1
(
2
), pp.
221
227
.
9.
Alonso
,
J. J.
,
LeGresley
,
P.
, and
Pereyra
,
V.
,
2009
, “
Aircraft Design Optimization
,”
Math. Comput. Simul.
,
79
(
6
), pp.
1948
1958
. 10.1016/j.matcom.2007.07.001
10.
Li
,
C.
,
Kim
,
I. Y.
, and
Jeswiet
,
J.
,
2015
, “
Conceptual and Detailed Design of An Automotive Engine Cradle by Using Topology, Shape, and Size Optimization
,”
Struct. Multidiscip. Optim.
,
51
(
2
), pp.
547
564
. 10.1007/s00158-014-1151-6
11.
Xiao
,
D.
,
Liu
,
X.
,
Du
,
W.
,
Wang
,
J.
, and
He
,
T.
,
2012
, “
Application of Topology Optimization to Design An Electric Bicycle Main Frame
,”
Struct. Multidiscip. Optim.
,
46
(
6
), pp.
913
929
. 10.1007/s00158-012-0803-7
12.
Chuang
,
C.-H.
,
Chen
,
S.
,
Yang
,
R.-J.
, and
Vogiatzis
,
P.
,
2018
, “
Topology Optimization With Additive Manufacturing Consideration for Vehicle Load Path Development
,”
Int. J. Numer. Methods Eng.
,
113
(
8
), pp.
1434
1445
. 10.1002/nme.5549
13.
Wu
,
J.
,
Aage
,
N.
,
Westermann
,
R.
, and
Sigmund
,
O.
,
2017
, “
Infill Optimization for Additive Manufacturing–Approaching Bone-Like Porous Structures
,”
IEEE Trans. Visual. Comput. Graphics
,
24
(
2
), pp.
1127
1140
. 10.1109/TVCG.2017.2655523
14.
Sutradhar
,
A.
,
Park
,
J.
,
Carrau
,
D.
,
Nguyen
,
T. H.
,
Miller
,
M. J
, and
Paulino
,
G. H.
,
2016
, “
Designing Patient-Specific 3d Printed Craniofacial Implants Using a Novel Topology Optimization Method
,”
Med. Biol. Eng. Comput.
,
54
(
7
), pp.
1123
1135
. 10.1007/s11517-015-1418-0
15.
Coelho
,
P. G.
,
Hollister
,
S. J.
,
Flanagan
,
C. L.
, and
Fernandes
,
P. R.
,
2015
, “
Bioresorbable Scaffolds for Bone Tissue Engineering: Optimal Design, Fabrication, Mechanical Testing and Scale-Size Effects Analysis
,”
Med. Eng. Phys.
,
37
(
3
), pp.
287
296
. 10.1016/j.medengphy.2015.01.004
16.
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
. 10.1016/j.biomaterials.2016.01.012
17.
Park
,
J.
,
Sutradhar
,
A.
,
Shah
,
J. J.
, and
Paulino
,
G. H.
,
2018
, “
Design of Complex Bone Internal Structure Using Topology Optimization With Perimeter Control
,”
Comput. Biol. Med.
,
94
, pp.
74
84
. 10.1016/j.compbiomed.2018.01.001
18.
Ma
,
H.
,
Wang
,
J.
,
Lu
,
Y.
, and
Guo
,
Y.
,
2019
, “
Lightweight Design of Turnover Frame of Bridge Detection Vehicle Using Topology and Thickness Optimization
,”
Struct. Multidiscip. Optim.
,
59
(
3
), pp.
1007
1019
. 10.1007/s00158-018-2113-1
19.
Chun
,
J.
,
Song
,
J.
, and
Paulino
,
G. H.
,
2016
, “
Structural Topology Optimization Under Constraints on Instantaneous Failure Probability
,”
Struct. Multidiscip. Optim.
,
53
(
4
), pp.
773
799
. 10.1007/s00158-015-1296-y
20.
Kociecki
,
M.
, and
Adeli
,
H.
,
2015
, “
Shape Optimization of Free-Form Steel Space-Frame Roof Structures With Complex Geometries Using Evolutionary Computing
,”
Eng. Appl. Artif. Intell.
,
38
, pp.
168
182
. 10.1016/j.engappai.2014.10.012
21.
Briseghella
,
B.
,
Fenu
,
L.
,
Lan
,
C.
,
Mazzarolo
,
E.
, and
Zordan
,
T.
,
2012
, “
Application of Topological Optimization to Bridge Design
,”
J. Bridge Eng.
,
18
(
8
), pp.
790
800
. 10.1061/(ASCE)BE.1943-5592.0000416
22.
Zuo
,
Z. H.
,
Huang
,
X.
,
Black
,
T.
, and
Felicetti
,
P.
,
2014
, “
Application of Topological Optimisation Technology to Bridge Design
,”
Struct. Eng. Int.
,
24
(
2
), pp.
185
191
. 10.2749/101686614X13830790993366
23.
Zhou
,
M.
,
Lazarov
,
B. S.
,
Wang
,
F.
, and
Sigmund
,
O.
,
2015
, “
Minimum Length Scale in Topology Optimization by Geometric Constraints
,”
Comput. Methods Appl. Mech. Eng.
,
293
, pp.
266
282
. 10.1016/j.cma.2015.05.003
24.
Krishnakumar
,
A.
, and
Suresh
,
K.
,
2015
, “
Hinge-Free Compliant Mechanism Design Via the Topological Level-Set
,”
ASME J. Mech. Des.
,
137
(
3
), p.
031406
. 10.1115/1.4029335
25.
Chu
,
S.
,
Gao
,
L.
,
Xiao
,
M.
,
Luo
,
Z.
, and
Li
,
H.
,
2018
, “
Stress-Based Multi-Material Topology Optimization of Compliant Mechanisms
,”
Int. J. Numer. Methods Eng.
,
113
(
7
), pp.
1021
1044
. 10.1002/nme.5697
26.
Xia
,
Q.
, and
Shi
,
T.
,
2016
, “
Topology Optimization of Compliant Mechanism and Its Support Through a Level Set Method
,”
Comput. Methods Appl. Mech. Eng.
,
305
, pp.
359
375
. 10.1016/j.cma.2016.03.017
27.
Makhija
,
D. S.
, and
Beran
,
P. S.
,
2019
, “
Concurrent Shape and Topology Optimization for Steady Conjugate Heat Transfer
,”
Struct. Multidiscip. Optim.
,
59
(
3
), pp.
919
940
. 10.1007/s00158-018-2110-4
28.
Wu
,
S.
,
Zhang
,
Y.
, and
Liu
,
S.
,
2019
, “
Topology Optimization for Minimizing the Maximum Temperature of Transient Heat Conduction Structure
,”
Struct. Multidiscip. Optim.
,
60
(
1
), pp.
69
82
. 10.1007/s00158-019-02196-9
29.
Yaji
,
K.
,
Yamada
,
T.
,
Yoshino
,
M.
,
Matsumoto
,
T.
,
Izui
,
K.
, and
Nishiwaki
,
S.
,
2016
, “
Topology Optimization in Thermal-Fluid Flow Using the Lattice Boltzmann Method
,”
J. Comput. Phys.
,
307
, pp.
355
377
. 10.1016/j.jcp.2015.12.008
30.
Yaji
,
K.
,
Yamada
,
T.
,
Kubo
,
S.
,
Izui
,
K.
, and
Nishiwaki
,
S.
,
2015
, “
A Topology Optimization Method for a Coupled Thermal–Fluid Problem Using Level Set Boundary Expressions
,”
Int. J. Heat Mass Transfer
,
81
, pp.
878
888
. 10.1016/j.ijheatmasstransfer.2014.11.005
31.
Haertel
,
J. H. K.
, and
Nellis
,
G. F.
,
2017
, “
A Fully Developed Flow Thermofluid Model for Topology Optimization of 3d-Printed Air-Cooled Heat Exchangers
,”
Appl. Therm. Eng.
,
119
, pp.
10
24
. 10.1016/j.applthermaleng.2017.03.030
32.
Coffin
,
P.
, and
Maute
,
K.
,
2016
, “
Level Set Topology Optimization of Cooling and Heating Devices Using a Simplified Convection Model
,”
Struct. Multidiscip. Optim.
,
53
(
5
), pp.
985
1003
. 10.1007/s00158-015-1343-8
33.
Qian
,
X.
, and
Dede
,
E. M.
,
2016
, “
Topology Optimization of a Coupled Thermal-Fluid System Under a Tangential Thermal Gradient Constraint
,”
Struct. Multidiscip. Optim.
,
54
(
3
), pp.
531
551
. 10.1007/s00158-016-1421-6
34.
Dede
,
E. M.
,
Joshi
,
S. N.
, and
Zhou
,
F.
,
2015
, “
Topology Optimization, Additive Layer Manufacturing, and Experimental Testing of An Air-Cooled Heat Sink
,”
ASME J. Mech. Des.
,
137
(
11
), p.
111403
. 10.1115/1.4030989
35.
Wang
,
M. Y.
,
Wang
,
X.
, and
Guo
,
D.
,
2003
, “
A Level Set Method for Structural Topology Optimization
,”
Comput. Methods Appl. Mech. Eng.
,
192
(
1–2
), pp.
227
246
. 10.1016/S0045-7825(02)00559-5
36.
Huang
,
X.
, and
Xie
,
M.
,
2010
,
Evolutionary Topology Optimization of Continuum Structures: Methods and Applications
,
John Wiley & Sons
.
37.
Querin
,
O. M.
,
Steven
,
G. P.
, and
Xie
,
Y. M.
,
1998
, “
Evolutionary Structural Optimisation Using a Bi-Directional Algorithm
,”
Eng. Comput.
,
15
(
8
), pp.
1031
1048
. 10.1108/02644409810244129
38.
Gea
,
H. C.
,
1996
, “
Topology Optimization: a New Microstructure-Based Design Domain Method
,”
Comput. Struct.
,
61
(
5
), pp.
781
788
. 10.1016/0045-7949(96)00092-2
39.
Suresh
,
K.
,
2010
, “
A 199-Line Matlab Code for Pareto-Optimal Tracing in Topology Optimization
,”
Struct. Multidiscip. Optim.
,
42
(
5
), pp.
665
679
. 10.1007/s00158-010-0534-6
40.
Suresh
,
K.
, and
Takalloozadeh
,
M.
,
2013
, “
Stress-Constrained Topology Optimization: a Topological Level-Set Approach
,”
Struct. Multidiscip. Optim.
,
48
(
2
), pp.
295
309
. 10.1007/s00158-013-0899-4
41.
Bendsøe
,
M. P.
, and
Kikuchi
,
N.
,
1988
, “
Generating Optimal Topologies in Structural Design Using a Homogenization Method
,”
Comput. Methods Appl. Mech. Eng.
,
71
(
2
), pp.
197
224
. 10.1016/0045-7825(88)90086-2
42.
Kumar
,
A. V.
, and
Parthasarathy
,
A.
,
2011
, “
Topology Optimization Using B-Spline Finite Elements
,”
Struct. Multidiscip. Optim.
,
44
(
4
), p.
471
. 10.1007/s00158-011-0650-y
43.
Kumar
,
T.
, and
Suresh
,
K.
,
2020
, “
A Density-and-Strain-based K-Clustering Approach to Microstructural Topology Optimization
,”
Struct. Multidiscip. Optim.
,
61
(
4
), pp.
1399
1415
. 10.1007/s00158-019-02422-4
44.
Taheri
,
A. H.
, and
Suresh
,
K.
,
2017
, “
An Isogeometric Approach to Topology Optimization of Multi-Material and Functionally Graded Structures
,”
Int. J. Numer. Methods Eng.
,
109
(
5
), pp.
668
696
. 10.1002/nme.5303
45.
Bartsch
,
M.
,
Weiland
,
T.
, and
Witting
,
M.
,
1996
, “
Generation of 3d Isosurfaces by Means of the Marching Cube Algorithm
,”
IEEE Trans. Magn.
,
32
(
3
), pp.
1469
1472
. 10.1109/20.497526
46.
Topology Optimization Roundtable
,
2019
, http://paulino.ce.gatech.edu/TopOpt%20Workshop%20Website/, Accessed December 21, 2019.
47.
Suresh
,
K.
,
2015
, “
Topology Optimization on the Cloud: a Confluence of Technologies
,”
Proceedings of the ASME 2015 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference
,
Boston, MA
,
Aug. 2–5
.
48.
Deng
,
S.
, and
Suresh
,
K.
,
2016
, “
Multi-Constrained 3d Topology Optimization Via Augmented Topological Level-Set
,”
Comput. Struct.
,
170
, pp.
1
12
. 10.1016/j.compstruc.2016.02.009
49.
Harzheim
,
L.
, and
Graf
,
G.
,
2005
, “
A Review of Optimization of Cast Parts Using Topology Optimization
,”
Struct. Multidiscip. Optim.
,
30
(
6
), pp.
491
497
. 10.1007/s00158-005-0553-x
50.
Harzheim
,
L.
, and
Graf
,
G.
,
2006
, “
A Review of Optimization of Cast Parts Using Topology Optimization
,”
Struct. Multidiscip. Optim.
,
31
(
5
), pp.
388
399
. 10.1007/s00158-005-0554-9
51.
Liu
,
J.
, and
Ma
,
Y.
,
2016
, “
A Survey of Manufacturing Oriented Topology Optimization Methods
,”
Adv. Eng. Software
,
100
, pp.
161
175
. 10.1016/j.advengsoft.2016.07.017
52.
Zuo
,
K.-T.
,
Chen
,
L.-P.
,
Zhang
,
Y.-Q.
, and
Yang
,
J.
,
2006
, “
Manufacturing-and Machining-Based Topology Optimization
,”
Int. J. Adv. Manuf. Technol.
,
27
(
5–6
), pp.
531
536
. 10.1007/s00170-004-2210-8
53.
Li
,
H.
,
Li
,
P.
,
Gao
,
L.
,
Zhang
,
L.
, and
Wu
,
T.
,
2015
, “
A Level Set Method for Topological Shape Optimization of 3d Structures With Extrusion Constraints
,”
Comput. Methods Appl. Mech. Eng.
,
283
, pp.
615
635
. 10.1016/j.cma.2014.10.006
54.
Liu
,
Y.
,
Li
,
Z.
,
Wei
,
P.
, and
Wang
,
W.
,
2018
, “
Parameterized Level-Set Based Topology Optimization Method Considering Symmetry and Pattern Repetition Constraints
,”
Comput. Methods Appl. Mech. Eng.
,
340
, pp.
1079
1101
. 10.1016/j.cma.2018.04.034
55.
Li
,
Q.
,
Chen
,
W.
,
Liu
,
S.
, and
Fan
,
H.
,
2018
, “
Topology Optimization Design of Cast Parts Based on Virtual Temperature Method
,”
Comput.-Aided Des.
,
94
, pp.
28
40
. 10.1016/j.cad.2017.08.002
56.
Vatanabe
,
S. L.
,
Lippi
,
T. N.
,
de Lima
,
C. R.
,
Paulino
,
G. H.
, and
Silva
,
E. C. N.
,
2016
, “
Topology Optimization with Manufacturing Constraints: A Unified Projection-Based Approach
,”
Adv. Eng. Software
,
100
, pp.
97
112
. 10.1016/j.advengsoft.2016.07.002
57.
Liu
,
J.
, and
Ma
,
Y.-S.
,
2015
, “
3d Level-Set Topology Optimization: a Machining Feature-Based Approach
,”
Struct. Multidiscip. Optim.
,
52
(
3
), pp.
563
582
. 10.1007/s00158-015-1263-7
58.
Groen
,
J. P.
, and
Sigmund
,
O.
,
2018
, “
Homogenization-Based Topology Optimization for High-Resolution Manufacturable Microstructures
,”
Int. J. Numer. Methods Eng.
,
113
(
8
), pp.
1148
1163
. 10.1002/nme.5575
59.
Mirzendehdel
,
A. M.
,
Behandish
,
M.
, and
Nelaturi
,
S.
,
2019
, “
Exploring Feasible Design Spaces for Heterogeneous Constraints
,”
Comput.-Aided Des.
,
115
, pp.
323
347
. 10.1016/j.cad.2019.06.005
60.
Gao
,
W.
,
Zhang
,
Y.
,
Ramanujan
,
D.
,
Ramani
,
K.
,
Chen
,
Y.
,
Williams
,
C. B.
,
Wang
,
C. C. L.
,
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
. 10.1016/j.cad.2015.04.001
61.
Zegard
,
T.
, and
Paulino
,
G. H.
,
2016
, “
Bridging Topology Optimization and Additive Manufacturing
,”
Struct. Multidiscip. Optim.
,
53
(
1
), pp.
175
192
. 10.1007/s00158-015-1274-4
62.
Doutre
,
P.-T.
,
Morretton
,
E.
,
Vo
,
T. H.
,
Marin
,
P.
,
Pourroy
,
F.
,
Prudhomme
,
G.
, and
Vignat
,
F.
,
2017
,
Advances on Mechanics, Design Engineering and Manufacturing
,
Springer
,
Cham, Switzerland
, pp.
233
240
.
63.
Liu
,
J.
, and
To
,
A. C.
,
2017
, “
Topology Optimization for Hybrid Additive-Subtractive Manufacturing
,”
Struct. Multidiscip. Optim.
,
55
(
4
), pp.
1281
1299
. 10.1007/s00158-016-1565-4
64.
Leary
,
M.
,
Merli
,
L.
,
Torti
,
F.
,
Mazur
,
M.
, and
Brandt
,
M.
,
2014
, “
Optimal Topology for Additive Manufacture: A Method for Enabling Additive Manufacture of Support-Free Optimal Structures
,”
Mater. Des.
,
63
, pp.
678
690
. 10.1016/j.matdes.2014.06.015
65.
Mirzendehdel
,
A. M.
, and
Suresh
,
K.
,
2016
, “
Support Structure Constrained Topology Optimization for Additive Manufacturing
,”
Comput.-Aided Des.
,
81
, pp.
1
13
. 10.1016/j.cad.2016.08.006
66.
Mass
,
Y.
, and
Amir
,
O.
,
2017
, “
Topology Optimization for Additive Manufacturing: Accounting for Overhang Limitations Using a Virtual Skeleton
,”
Addit. Manuf.
,
18
, pp.
58
73
. 10.1016/j.addma.2017.08.001
67.
Garaigordobil
,
A.
,
Ansola
,
R.
,
Santamaría
,
J.
, and
de Bustos
,
I. F.
,
2018
, “
A New Overhang Constraint for Topology Optimization of Self-Supporting Structures in Additive Manufacturing
,”
Struct. Multidiscip. Optim.
,
58
(
5
), pp.
2003
2017
. 10.1007/s00158-018-2010-7
68.
Garaigordobil
,
A.
,
Ansola
,
R.
,
Veguería
,
E.
, and
Fernandez
,
I.
,
2019
, “
Overhang Constraint for Topology Optimization of Self-Supported Compliant Mechanisms Considering Additive Manufacturing
,”
Comput.-Aided Des.
,
109
, pp.
33
48
. 10.1016/j.cad.2018.12.006
69.
Kwok
,
T.-H.
,
Li
,
Y.
, and
Chen
,
Y.
,
2016
, “
A Structural Topology Design Method Based on Principal Stress Line
,”
Comput.-Aided Des.
,
80
, pp.
19
31
. 10.1016/j.cad.2016.07.005
70.
Mhapsekar
,
K.
,
McConaha
,
M.
, and
Anand
,
S.
,
2018
, “
Additive Manufacturing Constraints in Topology Optimization for Improved Manufacturability
,”
ASME J. Manuf. Sci. Eng.
,
140
(
5
), p.
051017
. 10.1115/1.4039198
71.
Qian
,
X.
,
2017
, “
Undercut and Overhang Angle Control in Topology Optimization: A Density Gradient Based Integral Approach
,”
Int. J. Numer. Methods Eng.
,
111
(
3
), pp.
247
272
. 10.1002/nme.5461
72.
Mezzadri
,
F.
,
Bouriakov
,
V.
, and
Qian
,
X.
,
2018
, “
Topology Optimization of Self-Supporting Support Structures for Additive Manufacturing
,”
Addit. Manuf.
,
21
, pp.
666
682
. 10.1016/j.addma.2018.04.016
73.
Langelaar
,
M.
,
2016
, “
Topology Optimization of 3d Self-Supporting Structures for Additive Manufacturing
,”
Addit. Manuf.
,
12
(
Part A
), pp.
60
70
. 10.1016/j.addma.2016.06.010
74.
Chandrasekhar
,
A.
,
Kumar
,
T.
, and
Suresh
,
K.
,
2020
, “
Build Optimization of Fiber-Reinforced Additively Manufactured Components
,”
Struct. Multidiscip. Optim.
,
61
(
1
), pp.
77
90
. 10.1007/s00158-019-02346-z
75.
Steuben
,
J. C.
,
Iliopoulos
,
A. P.
, and
Michopoulos
,
J. G.
,
2018
, “
Multiscale Topology Optimization for Additively Manufactured Objects
,”
ASME J. Comput. Inf. Sci. Eng.
,
18
(
3
), p.
031002
. 10.1115/1.4039312
76.
Liu
,
J.
,
Gaynor
,
A. T.
,
Chen
,
S.
,
Kang
,
Z.
,
Suresh
,
K.
,
Takezawa
,
A.
,
Li
,
L.
,
Kato
,
J.
,
Tang
,
J.
,
Wang
,
C.C.L.
,
Cheng
,
L.
,
Liang
,
X.
, and
To
,
A.C.
,
2018
, “
Current and Future Trends in Topology Optimization for Additive Manufacturing
,”
Struct. Multidiscip. Optim.
,
57
(
6
), pp.
2457
2483
. 10.1007/s00158-018-1994-3
77.
Bendsøe
,
M. P.
, and
Rodrigues
,
H. C.
,
1991
, “
Integrated Topology and Boundary Shape Optimization of 2-d Solids
,”
Comput. Methods Appl. Mech. Eng.
,
87
(
1
), pp.
15
34
. 10.1016/0045-7825(91)90144-U
78.
Olhoff
,
N.
,
Bendsøe
,
M. P.
, and
Rasmussen
,
J.
,
1991
, “
On CAD-Integrated Structural Topology and Design Optimization
,”
Comput. Methods Appl. Mech. Eng.
,
89
(
1–3
), pp.
259
279
. 10.1016/0045-7825(91)90044-7
79.
Zhou
,
M.
, and
Wang
,
M. Y.
,
2013
, “
Engineering Feature Design for Level Set Based Structural Optimization
,”
Comput.-Aided Des.
,
45
(
12
), pp.
1524
1537
. 10.1016/j.cad.2013.06.016
80.
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
. 10.1002/nme.1943
81.
Tang
,
P.-S.
, and
Chang
,
K.-H.
,
2001
, “
Integration of Topology and Shape Optimization for Design of Structural Components
,”
Struct. Multidiscip. Optim.
,
22
(
1
), pp.
65
82
. 10.1007/PL00013282
82.
Lin
,
C.-Y.
, and
Chao
,
L.-S.
,
2000
, “
Automated Image Interpretation for Integrated Topology and Shape Optimization
,”
Struct. Multidiscip. Optim.
,
20
(
2
), pp.
125
137
. 10.1007/s001580050144
83.
Zhang
,
Y.
, and
Kwok
,
T.-H.
,
2019
, “
Customization and Topology Optimization of Compression Casts/braces on Two-Manifold Surfaces
,”
Comput.-Aided Des.
,
111
, pp.
113
122
. 10.1016/j.cad.2019.02.005
84.
Christiansen
,
A. N.
,
Bærentzen
,
J. A.
,
Nobel-Jørgensen
,
M.
,
Aage
,
N.
, and
Sigmund
,
O.
,
2015
, “
Combined Shape and Topology Optimization of 3D Structures
,”
Computers & Graphics
,
46
, pp.
25
35
. 10.1016/j.cag.2014.09.021
85.
Guo
,
X.
,
Zhang
,
W.
, and
Zhong
,
W.
,
2014
, “
Doing Topology Optimization Explicitly and Geometrically - A New Moving Morphable Components Based Framework
,”
ASME J. Appl. Mech.
,
81
(
8
), p.
081009
. 10.1115/1.4027609
86.
Zhang
,
W.
,
Yuan
,
J.
,
Zhang
,
J.
, and
Guo
,
X.
,
2016
, “
A New Topology Optimization Approach Based on Moving Morphable Components (MMC) and the Ersatz Material Model
,”
Struct. Multidiscip. Optim.
,
53
(
6
), pp.
1243
1260
. 10.1007/s00158-015-1372-3
87.
Zhang
,
W.
,
Li
,
D.
,
Yuan
,
J.
,
Song
,
J.
, and
Guo
,
X.
,
2017
, “
A New Three-Dimensional Topology Optimization Method Based on Moving Morphable Components (MMCS)
,”
Comput. Mech.
,
59
(
4
), pp.
647
665
. 10.1007/s00466-016-1365-0
88.
Bell
,
B.
,
Norato
,
J.
, and
Tortorelli
,
D.
,
2012
, “
A Geometry Projection Method for Continuum-based Topology Optimization of Structures
,”
12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference
,
Indianapolis, IN
,
Sept. 17–19
, p.
5485
.
89.
Norato
,
J. A.
,
Bell
,
B. K.
, and
Tortorelli
,
D. A.
,
2015
, “
A Geometry Projection Method for Continuum-Based Topology Optimization with Discrete Elements
,”
Comput. Methods Appl. Mech. Eng.
,
293
, pp.
306
327
. 10.1016/j.cma.2015.05.005
90.
Lin
,
H.-Y.
,
Rayasam
,
M.
, and
Subbarayan
,
G.
,
2015
, “
Isocomp: Unified Geometric and Material Composition for Optimal Topology Design
,”
Struct. Multidiscip. Optim.
,
51
(
3
), pp.
687
703
. 10.1007/s00158-014-1164-1
91.
Gao
,
Y.
,
Guo
,
Y.
, and
Zheng
,
S.
,
2019
, “
A Nurbs-Based Finite Cell Method for Structural Topology Optimization Under Geometric Constraints
,”
Comput. Aided Geom. Des.
,
72
, pp.
1
18
. 10.1016/j.cagd.2019.05.001
92.
Zhang
,
W.
,
Zhao
,
L.
,
Gao
,
T.
, and
Cai
,
S.
,
2017
, “
Topology Optimization with Closed B-Splines and Boolean Operations
,”
Comput. Methods Appl. Mech. Eng.
,
315
, pp.
652
670
. 10.1016/j.cma.2016.11.015
93.
Norato
,
J. A.
,
2018
, “
Topology Optimization with Supershapes
,”
Struct. Multidiscip. Optim.
,
58
(
2
), pp.
415
434
. 10.1007/s00158-018-2034-z
94.
Da
,
D.
,
Xia
,
L.
,
Li
,
G.
, and
Huang
,
X.
,
2018
, “
Evolutionary Topology Optimization of Continuum Structures with Smooth Boundary Representation
,”
Struct. Multidiscip. Optim.
,
57
(
6
), pp.
2143
2159
. 10.1007/s00158-017-1846-6
95.
Jahangiry
,
H. A.
, and
Mehdi Tavakkoli
,
S.
,
2017
, “
An Isogeometrical Approach to Structural Level Set Topology Optimization
,”
Comput. Methods Appl. Mech. Eng.
,
319
, pp.
240
257
. 10.1016/j.cma.2017.02.005
96.
Kang
,
P.
, and
Youn
,
S.-K.
,
2016
, “
Isogeometric Topology Optimization of Shell Structures Using Trimmed Nurbs Surfaces
,”
Finite Elem. Anal. Des.
,
120
, pp.
18
40
. 10.1016/j.finel.2016.06.003
97.
Seo
,
Y.-D.
,
Kim
,
H.-J.
, and
Youn
,
S.-K.
,
2010
, “
Isogeometric Topology Optimization Using Trimmed Spline Surfaces
,”
Comput. Methods Appl. Mech. Eng.
,
199
(
49–52
), pp.
3270
3296
. 10.1016/j.cma.2010.06.033
98.
Gai
,
Y.
,
Zhu
,
X.
,
Zhang
,
Y.
,
Hou
,
W.
, and
Hu
,
P.
,
2019
, “
Explicit Isogeometric Topology Optimization Based on Moving Morphable Voids with Closed B-Spline Boundary Curves
,”
Struct. Multidiscip. Optim.
,
61
(
3
), pp.
963
982
. 10.1007/s00158-019-02398-1
99.
Gao
,
J.
,
Gao
,
L.
,
Luo
,
Z.
, and
Li
,
P.
,
2019
, “
Isogeometric Topology Optimization for Continuum Structures Using Density Distribution Function
,”
Int. J. Numer. Methods Eng.
,
119
(
10
), pp.
991
1017
. 10.1002/nme.6081
100.
Sosnovik
,
I.
, and
Oseledets
,
I.
,
2019
, “
Neural Networks for Topology Optimization
,”
Russ. J. Numer. Anal. Math. Modell.
,
34
(
4
), pp.
215
223
. 10.1515/rnam-2019-0018
101.
Herman Shen
,
M.-H.
, and
Chen
,
L.
,
2019
, “
A New CGAN Technique for Constrained Topology Design Optimization
,”
arXiv preprint arXiv:1901.07675
.
102.
Rawat
,
S.
, and
Herman Shen
,
M. H.
,
2019
, “
Application of Adversarial Networks for 3d Structural Topology Optimization
,”
Technical report, SAE Technical Paper
.
103.
Lei
,
X.
,
Liu
,
C.
,
Du
,
Z.
,
Zhang
,
W.
, and
Guo
,
X.
,
2019
, “
Machine Learning-Driven Real-Time Topology Optimization Under Moving Morphable Component-Based Framework
,”
ASME J. Appl. Mech.
,
86
(
1
), p.
011004
. 10.1115/1.4041319
104.
Fabio
,
R.
,
2003
, “
From Point Cloud to Surface: the Modeling and Visualization Problem
,”
Int. Arch. Photogram. Remote Sens. Spatial Inf. Sci.
,
34
(
5
), pp.
W10
. 10.3929/ethz-a-004655782
105.
Thakur
,
A.
,
Banerjee
,
A. G.
, and
Gupta
,
S. K.
,
2009
, “
A Survey of Cad Model Simplification Techniques for Physics-Based Simulation Applications
,”
Comput.-Aided Des.
,
41
(
2
), pp.
65
80
. 10.1016/j.cad.2008.11.009
106.
Alliez
,
P.
,
Ucelli
,
G.
,
Gotsman
,
C.
, and
Attene
,
M.
,
2008
, “Recent Advances in Remeshing of Surfaces,”
Shape Analysis and Structuring
,
Springer
, pp.
53
82
.
107.
PMP Library
www.pmp.library.org, Accessed 12 December, 2019.
108.
Jakob
,
W.
,
Tarini
,
M.
,
Panozzo
,
D.
, and
Sorkine-Hornung
,
O.
,
2015
, “
Instant Field-Aligned Meshes
,”
ACM Trans. Graphics
,
34
(
6
), pp.
1
15
. 10.1145/2816795.2818078
109.
Kazhdan
,
M.
,
Bolitho
,
M.
, and
Hoppe
,
H.
,
2006
, “
Poisson Surface Reconstruction
,”
Fourth Eurographics Symposium on Geometry Processing
,
Cagliari, Sardinia, Italy
,
June 26–28
, pp.
61
70
.
110.
Attene
,
M.
,
Falcidieno
,
B.
,
Rossignac
,
J.
, and
Spagnuolo
,
M.
,
2003
, “
Edge-sharpener: Recovering Sharp Features in Triangulations of Non-adaptively Re-meshed Surfaces
,”
Proceedings of the 2003 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, SGP ’03
,
Aire-la-Ville, Switzerland
,
Eurographics Association
, pp.
62
69
.
111.
Nielson
,
G. M.
,
2004
, “
Dual Marching Cubes
,”
IEEE Visualization
,
Austin, TX, USA
,
10-15 Oct.
.
112.
Lewiner
,
T.
,
Lopes
,
H.
,
Vieira
,
A. W.
, and
Tavares
,
G.
,
2003
, “
Efficient Implementation of Marching Cubes’ Cases with Topological Guarantees
,”
J. Graphics Tools
,
8
(
2
), pp.
1
15
. 10.1080/10867651.2003.10487582
113.
Shewchuk
,
J. R.
,
1998
, “
Tetrahedral Mesh Generation by Delaunay Refinement
,”
SoCG98: 14th ACM Symposium on Computational Geometry
,
Minneapolis, MN
,
June 7–10
, pp.
86
95
.
114.
Si
,
H.
,
2015
, “
Tetgen, A Delaunay-Based Quality Tetrahedral Mesh Generator
,”
ACM Trans. Math. Software (TOMS)
,
41
(
2
), p.
11
. 10.1145/2629697
115.
Dey
,
T. K.
, and
Goswami
,
S.
,
2003
, “
Tight Cocone: a Water-tight Surface Reconstructor
,”
Proceedings of the Eighth ACM symposium on Solid modeling and applications
,
Seattle, WA
,
June 16–20
, ACM, pp.
127
134
.
116.
Cheng
,
S.-W.
,
Dey
,
T. K.
, and
Ramos
,
E. A.
,
2010
, “
Delaunay Refinement for Piecewise Smooth Complexes
,”
Discrete Comput. Geom.
,
43
(
1
), pp.
121
166
. 10.1007/s00454-008-9109-3
117.
Nan
,
L.
, and
Wonka
,
P.
,
2017
, “
Polyfit: Polygonal Surface Reconstruction From Point Clouds
,”
Proceedings of the IEEE International Conference on Computer Vision
,
Venice, Italy
,
Oct. 22–29
, pp.
2353
2361
.
118.
Yi
,
G.
, and
Kim
,
N. H.
,
2017
, “
Identifying Boundaries of Topology Optimization Results Using Basic Parametric Features
,”
Struct. Multidiscip. Optim.
,
55
(
5
), pp.
1641
1654
. 10.1007/s00158-016-1597-9
119.
Li
,
Y.
,
Wu
,
X.
,
Chrysanthou
,
Y.
,
Sharf
,
A.
,
Cohen-Or
,
D.
, and
Mitra
,
N. J.
,
2011
, “
Globfit: Consistently Fitting Primitives by Discovering Global Relations
,”
ACM Trans. Graphics
,
30
(
4
), pp.
52:1
52:12
. 10.1145/2010324.1964947
120.
Schnabel
,
R.
,
Wahl
,
R.
, and
Klein
,
R.
,
2007
, “
Efficient Ransac for Point-Cloud Shape Detection
,”
Comput. Graphics Forum
,
26
(
2
), pp.
214
226
. 10.1111/j.1467-8659.2007.01016.x
121.
Joshi
,
S.
,
Medina
,
J. C.
,
Wannerberg
,
E.
,
Yurova
,
A.
,
Reiz
,
S.
, and
Rüth
,
B.
,
2016
,
Cad-integrated topology optimization
.
BGCE Honor. Proj. Report, Bavar. Grad. Sch. Comput. Eng
.
122.
Liu
,
S.
,
Li
,
Q.
,
Liu
,
J.
,
Chen
,
W.
, and
Zhang
,
Y.
,
2018
, “
A Realization Method for Transforming a Topology Optimization Design Into Additive Manufacturing Structures
,”
Engineering
,
4
(
2
), pp.
277
285
. 10.1016/j.eng.2017.09.002
123.
Chacón
,
J. M.
,
Bellido
,
J. C.
, and
Donoso
,
A.
,
2014
, “
Integration of Topology Optimized Designs Into CAD/CAM Via An Iges Translator
,”
Struct. Multidiscip. Optim.
,
50
(
6
), pp.
1115
1125
. 10.1007/s00158-014-1099-6
124.
Koguchi
,
A.
, and
Kikuchi
,
N.
,
2006
, “
A Surface Reconstruction Algorithm for Topology Optimization
,”
Eng. Comput.
,
22
(
1
), pp.
1
10
. 10.1007/s00366-006-0023-0
125.
Marsan
,
A. L.
, and
Dutta
,
D.
,
1996
, “
Construction of a Surface Model and Layered Manufacturing Data From 3d Homogenization Output
,”
ASME J. Mech. Des.
,
118
(
3
), pp.
412
418
. 10.1115/1.2826901
126.
Yoely
,
Y. M.
,
Amir
,
O.
, and
Hanniel
,
I.
,
2018
, “
Topology and Shape Optimization with Explicit Geometric Constraints Using a Spline-Based Representation and a Fixed Grid
,”
Procedia Manuf.
,
21
, pp.
189
196
. 10.1016/j.promfg.2018.02.110
127.
Zhao
,
W.
,
Gao
,
S.
, and
Lin
,
H.
,
2007
, “
A Robust Hole-Filling Algorithm for Triangular Mesh
,”
Vis. Comput.
,
23
(
12
), pp.
987
997
. 10.1007/s00371-007-0167-y
128.
Branch
,
J.
,
Prieto
,
F.
,
Boulanger
,
P.
, and
Pébay
,
P. P.
,
2006
, “
A Hole-filling Algorithm for Triangular Meshes Using Local Radial Basis Function
,”
Proceedings of the 15th International Meshing Roundtable
,
Birmingham, AL
,
Sept. 17–20
, Springer, pp.
411
431
.
129.
Curless
,
B.
, and
Levoy
,
M.
,
1996
, “
A Volumetric Method for Building Complex Models From Range Images
,”
Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’96
,
New Orleans, LA
,
Aug. 4–9
, ACM, pp.
303
312
.
130.
Liepa
,
P.
,
2003
, “
Filling Holes in Meshes
,”
Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, SGP ’03
,
Aachen, Germany
,
June 23–25
, pp.
200
205
.
131.
Catmull
,
E.
, and
Clark
,
J.
,
1978
, “
Recursively Generated B-Spline Surfaces on Arbitrary Topological Meshes
,”
Comput.-Aided Des.
,
10
(
6
), pp.
350
355
. 10.1016/0010-4485(78)90110-0
132.
Doo
,
D.
, and
Sabin
,
M.
,
1978
, “
Behaviour of Recursive Division Surfaces Near Extraordinary Points
,”
Comput.-Aided Des.
,
10
(
6
), pp.
356
360
. 10.1016/0010-4485(78)90111-2
133.
Loop
,
C.
,
1987
, “
Smooth Subdivision Surfaces Based on Triangles
,” Master’s thesis,
University of Utah, Department of Mathematics
.
134.
Edelsbrunner
,
H.
, and
Grayson
,
D. R.
,
2000
, “
Edgewise Subdivision of a Simplex
,”
Discrete Comput. Geom.
,
24
(
4
), pp.
707
719
. 10.1007/s4540010063
135.
Marinov
,
M.
,
Amagliani
,
M.
,
Barback
,
T.
,
Flower
,
J.
,
Barley
,
S.
,
Furuta
,
S.
,
Charrot
,
P.
,
Henley
,
I.
,
Santhanam
,
N.
,
Finnigan
,
G.T.
,
Meshkat
,
S.
,
Hallet
,
J.
,
Sapun
,
M.
, and
Wolski
,
P.
,
2019
, “
Generative Design Conversion to Editable and Watertight Boundary Representation
,”
Comput.-Aided Des.
,
115
, pp.
194
205
. 10.1016/j.cad.2019.05.016
136.
Sederberg
,
T. W.
,
Zheng
,
J.
,
Bakenov
,
A.
, and
Nasri
,
A.
,
2003
, “
T-splines and T-nurccs
,”
ACM SIGGRAPH 2003
,
San Diego, CA
,
July 27–31
, Vol.
22
, ACM, pp.
477
484
.
137.
Hsu
,
M.-H.
, and
Hsu
,
Y.-L.
,
2005
, “
Interpreting Three-Dimensional Structural Topology Optimization Results
,”
Comput. Struct.
,
83
(
4–5
), pp.
327
337
. 10.1016/j.compstruc.2004.09.005
138.
Hsu
,
Y.-L.
,
Hsu
,
M.-S.
, and
Chen
,
C.-T.
,
2001
, “
Interpreting Results From Topology Optimization Using Density Contours
,”
Comput. Struct.
,
79
(
10
), pp.
1049
1058
. 10.1016/S0045-7949(00)00194-2
139.
Cuillière
,
J.-C.
,
Francois
,
V.
, and
Drouet
,
J.-M.
,
2014
, “
Towards the Integration of Topology Optimization Into the Cad Process
,”
Comput.-Aided Des. Appl.
,
11
(
2
), pp.
120
140
. 10.1080/16864360.2014.846067
140.
Cuillière
,
J.-C.
,
Francois
,
V.
, and
Drouet
,
J.-M.
,
2013
, “
Automatic Mesh Generation and Transformation for Topology Optimization Methods
,”
Comput.-Aided Des.
,
45
(
12
), pp.
1489
1506
. 10.1016/j.cad.2013.07.004
141.
Larsen
,
S.
, and
Jensen
,
C. G.
,
2009
, “
Converting Topology Optimization Results Into Parametric Cad Models
,”
Comput.-Aided Des. Appl.
,
6
(
3
), pp.
407
418
. 10.3722/cadaps.2009.407-418
142.
Duu
,
T.
,
Inala
,
J. P.
,
Puu
,
Y.
,
Spielberg
,
A.
,
Schulz
,
A.
,
Rus
,
D.
,
Solar-Lezama
,
A.
, and
Matusik
,
W.
,
2018
, “
InverseCSG: Automatic conversion of 3d models to CSG trees
,”
ACM Trans. Graph.
,
37
(
6
), pp.
213:1
213:16
. 10.1145/3272127.3275006
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