Abstract

Most of the existing self-support topology optimization methods restrict the overhang inclination angle to be larger than the self-support threshold value. However, for some additive manufacturing processes, such as fused deposition modeling, horizontal overhangs with zero inclination angle could be successfully printed while the overhang size plays a key role in determining the printability. Therefore, the self-support threshold condition should be re-developed to comprehensively consider the overhang size and inclination angle. At the same time, there raises the challenges of formulating the self-support constraints based on the new threshold condition. To address this difficulty, a novel method is proposed in this work to realize the design with horizontal overhangs. To be specific, the new method employs a skeleton-based structure decomposition approach to divide the structure into components based on the connectivity condition. Then, each component will be evaluated about its self-support status based on its overhang length and inclination angle. Finally, the self-support constraint will be activated only for those components that violate the threshold condition. An excellent feature of the method is that it can be adapted to address the only inclination angle self-support condition, or the comprehensive self-support condition that simultaneously considers the overhang length and inclination angle. Therefore, the new method serves for general applications to different additive manufacturing (AM) processes. Numerical examples will be studied to demonstrate the effectiveness of the proposed method.

References

References
1.
Guo
,
P.
,
Zou
,
B.
,
Huang
,
C.
, and
Gao
,
H.
,
2017
, “
Study on Microstructure, Mechanical Properties and Machinability of Efficiently Additive Manufactured AISI 316L Stainless Steel by High-Power Direct Laser Deposition
,”
J. Mater. Process. Technol.
,
240
, pp.
12
22
. 10.1016/j.jmatprotec.2016.09.005
2.
Liang
,
X.
,
Cheng
,
L.
,
Chen
,
Q.
,
Yang
,
Q.
, and
To
,
A. C.
,
2018
, “
A Modified Method for Estimating Inherent Strains From Detailed Process Simulation of Additive Manufacturing
,”
Addit. Manuf.
,
23
, pp.
471
486
. 10.1016/j.addma.2018.08.029
3.
Li
,
C.
,
Liu
,
Z. Y.
,
Fang
,
X. Y.
, and
Guo
,
Y. B.
,
2018
, “
On the Simulation Scalability of Predicting Residual Stress and Distortion in Selective Laser Melting
,”
ASME J. Manuf. Sci. Eng.
,
140
(4), p.
041013
. 10.1115/1.4038893
4.
Baykasoglu
,
C.
,
Akyildiz
,
O.
,
Candemir
,
D.
,
Yang
,
Q.
, and
To
,
A. C.
,
2018
, “
Predicting Microstructure Evolution During Directed Energy Deposition Additive Manufacturing of Ti-6Al-4V
,”
ASME J. Manuf. Sci. Eng.
,
140
(
5
), p.
051003
. 10.1115/1.4038894
5.
Shamvedi
,
D.
,
McCarthy
,
O. J.
,
O’Donoghue
,
E.
,
Danilenkoff
,
C.
,
O’Leary
,
P.
, and
Raghavendra
,
R.
,
2018
, “
3D Metal Printed Heat Sinks With Longitudinally Varying Lattice Structure Sizes Using Direct Metal Laser Sintering
,”
Virtual Phys. Prototyp.
,
13
(
4
), pp.
301
310
. 10.1080/17452759.2018.1479528
6.
Brenken
,
B.
,
Barocio
,
E.
,
Favaloro
,
A.
,
Kunc
,
V.
, and
Pipes
,
R. B.
,
2018
, “
Fused Filament Fabrication of Fiber-Reinforced Polymers: A Review
,”
Addit. Manuf.
,
21
, pp.
1
16
. 10.1016/j.addma.2018.01.002
7.
Zhang
,
Y.
, and
Shapiro
,
V.
,
2018
, “
Linear-Time Thermal Simulation of As-Manufactured Fused Deposition Modeling Components
,”
ASME J. Manuf. Sci. Eng.
,
140
(7), p.
071002
. 10.1115/1.4039556
8.
Cattenone
,
A.
,
Morganti
,
S.
,
Alaimo
,
G.
, and
Auricchio
,
F.
,
2019
, “
Finite Element Analysis of Additive Manufacturing Based on Fused Deposition Modeling (FDM): Distortion Prediction and Comparison With Experimental Data
,”
ASME J. Manuf. Sci. Eng.
,
141
(
1
), p.
011010
. 10.1115/1.4041626
9.
Lu
,
Z.
,
Cao
,
J.
,
Song
,
Z.
,
Li
,
D.
, and
Lu
,
B.
,
2019
, “
Research Progress of Ceramic Matrix Composite Parts Based on Additive Manufacturing Technology
,”
Virtual Phys. Prototyp.
,
14
(
4
), pp.
333
348
. 10.1080/17452759.2019.1607759
10.
Mohan
,
N.
,
Senthil
,
P.
,
Vinodh
,
S.
, and
Jayanth
,
N.
,
2017
, “
A Review on Composite Materials and Process Parameters Optimisation for the Fused Deposition Modelling Process
,”
Virtual Phys. Prototyp.
,
12
(
1
), pp.
47
59
. 10.1080/17452759.2016.1274490
11.
Hamdan
,
B.
,
Lafi
,
S.
, and
Hassan
,
N. M.
,
2018
, “
Optimizing the Manufacturing Processes of Carbon Fiber Epoxy Resin Composite Panels
,”
ASME J. Manuf. Sci. Eng.
,
140
(
1
), p.
011003
. 10.1115/1.4037233
12.
Bos
,
F. P.
,
Bosco
,
E.
, and
Salet
,
T. A. M.
,
2019
, “
Ductility of 3D Printed Concrete Reinforced With Short Straight Steel Fibers
,”
Virtual Phys. Prototyp.
,
14
(
2
), pp.
160
174
. 10.1080/17452759.2018.1548069
13.
Rosen
,
D. W.
,
2014
, “
Research Supporting Principles for Design for Additive Manufacturing
,”
Virtual Phys. Prototyp.
,
9
(
4
), pp.
225
232
. 10.1080/17452759.2014.951530
14.
Rosen
,
D. W.
,
2016
, “
A Review of Synthesis Methods for Additive Manufacturing
,”
Virtual Phys. Prototyp.
,
11
(
4
), pp.
305
317
. 10.1080/17452759.2016.1240208
15.
Ponche
,
R.
,
Hascoet
,
J. Y.
,
Kerbrat
,
O.
, and
Mognol
,
P.
,
2012
, “
A New Global Approach to Design for Additive Manufacturing
,”
Virtual Phys. Prototyp.
,
7
(
2
), pp.
93
105
. 10.1080/17452759.2012.679499
16.
Segonds
,
F.
,
2018
, “
Design by Additive Manufacturing: An Application in Aeronautics and Defence
,”
Virtual Phys. Prototyp.
,
13
(
4
), pp.
237
245
. 10.1080/17452759.2018.1498660
17.
Li
,
L.
,
Liu
,
J.
,
Ma
,
Y.
,
Ahmad
,
R.
, and
Qureshi
,
A.
,
2019
, “
Multi-view Feature Modeling for Design-for-Additive Manufacturing
,”
Adv. Eng. Inform.
,
39
, pp.
144
156
. 10.1016/j.aei.2018.12.004
18.
Chowdhury
,
S.
,
Mhapsekar
,
K.
, and
Anand
,
S.
,
2018
, “
Part Build Orientation Optimization and Neural Network-Based Geometry Compensation for Additive Manufacturing Process
,”
ASME J. Manuf. Sci. Eng.
,
140
(
3
), p.
031009
. 10.1115/1.4038293
19.
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
20.
Bendsøe
,
M. P.
, and
Sigmund
,
O.
,
2004
,
Topology Optimization
,
Springer
,
Berlin
, http://link.springer.com/10.1007/978-3-662-05086-6, Accessed on May 27, 2016)
21.
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
22.
Liu
,
J.
, and
Ma
,
Y.
,
2016
, “
A Survey of Manufacturing Oriented Topology Optimization Methods
,”
Adv. Eng. Softw.
,
100
, pp.
161
175
. 10.1016/j.advengsoft.2016.07.017
23.
Zhang
,
P.
,
Toman
,
J.
,
Yu
,
Y.
,
Biyikli
,
E.
,
Kirca
,
M.
,
Chmielus
,
M.
, and
To
,
A. C.
,
2015
, “
Efficient Design-Optimization of Variable-Density Hexagonal Cellular Structure by Additive Manufacturing: Theory and Validation
,”
ASME J. Manuf. Sci. Eng.
,
137
(
2
), p.
021004
. 10.1115/1.4028724
24.
Xia
,
L.
, and
Breitkopf
,
P.
,
2017
, “
Recent Advances on Topology Optimization of Multiscale Nonlinear Structures
,”
Arch. Comput. Methods Eng.
,
24
(
2
), pp.
227
249
. 10.1007/s11831-016-9170-7
25.
Wang
,
Y.
,
Zhang
,
L.
,
Daynes
,
S.
,
Zhang
,
H.
,
Feih
,
S.
, and
Wang
,
M. Y.
,
2018
, “
Design of Graded Lattice Structure With Optimized Mesostructures for Additive Manufacturing
,”
Mater. Des.
,
142
, pp.
114
123
. 10.1016/j.matdes.2018.01.011
26.
Li
,
H.
,
Luo
,
Z.
,
Gao
,
L.
, and
Walker
,
P.
,
2018
, “
Topology Optimization for Functionally Graded Cellular Composites With Metamaterials by Level Sets
,”
Comput. Methods Appl. Mech. Eng.
,
328
, pp.
340
364
. 10.1016/j.cma.2017.09.008
27.
Liu
,
J.
,
Zheng
,
Y.
,
Ahmad
,
R.
,
Tang
,
J.
, and
Ma
,
Y.
,
2019
, “
Minimum Length Scale Constraints in Multi-Scale Topology Optimisation for Additive Manufacturing
,”
Virtual Phys. Prototyp.
,
14
(
3
), pp.
229
241
. 10.1080/17452759.2019.1584944
28.
Zhang
,
H.
,
Wang
,
Y.
, and
Kang
,
Z.
,
2019
, “
Topology Optimization for Concurrent Design of Layer-Wise Graded Lattice Materials and Structures
,”
Int. J. Eng. Sci.
,
138
, pp.
26
49
. 10.1016/j.ijengsci.2019.01.006
29.
Yu
,
H.
,
Huang
,
J.
,
Zou
,
B.
,
Shao
,
W.
, and
Liu
,
J.
,
2020
, “
Stress-Constrained Shell-Lattice Infill Structural Optimization for Additive Manufacturing
,”
Virtual Phys. Prototyp.
,
15
(
1
), pp.
35
48
. 10.1080/17452759.2019.1647488
30.
Takezawa
,
A.
,
Kobashi
,
M.
,
Koizumi
,
Y.
, and
Kitamura
,
M.
,
2017
, “
Porous Metal Produced by Selective Laser Melting With Effective Isotropic Thermal Conductivity Close to the Hashin–Shtrikman Bound
,”
Int. J. Heat Mass Transfer
,
105
, pp.
564
572
. 10.1016/j.ijheatmasstransfer.2016.10.006
31.
Takezawa
,
A.
,
Koizumi
,
Y.
, and
Kobashi
,
M.
,
2017
, “
High-Stiffness and Strength Porous Maraging Steel via Topology Optimization and Selective Laser Melting
,”
Addit. Manuf.
,
18
, pp.
194
202
. 10.1016/j.addma.2017.10.004
32.
Vogiatzis
,
P.
,
Chen
,
S.
,
Wang
,
X.
,
Li
,
T.
, and
Wang
,
L.
,
2017
, “
Topology Optimization of Multi-material Negative Poisson’s Ratio Metamaterials Using a Reconciled Level Set Method
,”
Comput.-Aided Des.
,
83
, pp.
15
32
. 10.1016/j.cad.2016.09.009
33.
Niu
,
J.
,
Choo
,
H. L.
,
Sun
,
W.
, and
Mok
,
S. H.
,
2018
, “
Analytical Solution and Experimental Study of Effective Young’s Modulus of Selective Laser Melting-Fabricated Lattice Structure With Triangular Unit Cells
,”
ASME J. Manuf. Sci. Eng.
,
140
(9), p.
091008
. 10.1115/1.4040159
34.
Liu
,
J.
, and
Yu
,
H.
,
2017
, “
Concurrent Deposition Path Planning and Structural Topology Optimization for Additive Manufacturing
,”
Rapid Prototyp. J.
,
23
(
5
), pp.
930
942
. 10.1108/RPJ-05-2016-0087
35.
Zhang
,
P.
,
Liu
,
J.
, and
To
,
A. C.
,
2017
, “
Role of Anisotropic Properties on Topology Optimization of Additive Manufactured Load Bearing Structures
,”
Scr. Mater.
,
135
, pp.
148
152
. 10.1016/j.scriptamat.2016.10.021
36.
Dapogny
,
C.
,
Estevez
,
R.
,
Faure
,
A.
, and
Michailidis
,
G.
,
2019
, “
Shape and Topology Optimization Considering Anisotropic Features Induced by Additive Manufacturing Processes
,”
Comput. Methods Appl. Mech. Eng.
,
344
, pp.
626
665
. 10.1016/j.cma.2018.09.036
37.
Montemurro
,
M.
, and
Catapano
,
A.
,
2019
, “
A General B-Spline Surfaces Theoretical Framework for Optimisation of Variable Angle-tow Laminates
,”
Compos. Struct.
,
209
, pp.
561
578
. 10.1016/j.compstruct.2018.10.094
38.
Montemurro
,
M.
, and
Catapano
,
A.
,
2017
, “
On the Effective Integration of Manufacturability Constraints Within the Multi-scale Methodology for Designing Variable Angle-Tow Laminates
,”
Compos. Struct.
,
161
, pp.
145
159
. 10.1016/j.compstruct.2016.11.018
39.
Catapano
,
A.
,
Montemurro
,
M.
,
Balcou
,
J.-A.
, and
Panettieri
,
E.
,
2019
, “
Rapid Prototyping of Variable Angle-Tow Composites
,”
Aerotec. Missili Spaz.
,
98
(
4
), pp.
257
271
. 10.1007/s42496-019-00019-0
40.
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
41.
Langelaar
,
M.
,
2019
, “
Topology Optimization for Multi-axis Machining
,”
Comput. Methods Appl. Mech. Eng.
,
351
, pp.
226
252
. 10.1016/j.cma.2019.03.037
42.
Morris
,
N.
,
Butscher
,
A.
, and
Iorio
,
F.
,
2020
, “
A Subtractive Manufacturing Constraint for Level set Topology Optimization
,”
Struct. Multidiscip. Optim.
,
61
(
4
), pp.
1573
1588
. 10.1007/s00158-019-02436-y
43.
Liu
,
S.
,
Li
,
Q.
,
Liu
,
J.
,
Chen
,
W.
, and
Zhang
,
Y.
,
2018
, “
Realization Method for Transforming Topology Optimization Design to Additive Manufacturing Structures
,”
Engineering.
,
4
(
2
), pp.
277
285
. 10.1016/j.eng.2017.09.002
44.
Vogiatzis
,
P.
,
Chen
,
S.
, and
Zhou
,
C.
,
2017
, “
An Open Source Framework For Integrated Additive Manufacturing and Level-Set Based Topology Optimization
,”
ASME J. Comput. Inf. Sci. Eng.
,
17
(
4
), p.
041012
. 10.1115/1.4037738
45.
Jiang
,
L.
,
Ye
,
H.
,
Zhou
,
C.
, and
Chen
,
S.
,
2019
, “
Parametric Topology Optimization Toward Rational Design and Efficient Prefabrication for Additive Manufacturing
,”
ASME J. Manuf. Sci. Eng.
,
141
(4), p.
041007
. 10.1115/1.4042580
46.
Ulu
,
E.
,
Huang
,
R.
,
Kara
,
L. B.
, and
Whitefoot
,
K. S.
,
2019
, “
Concurrent Structure and Process Optimization for Minimum Cost Metal Additive Manufacturing
,”
ASME J. Mech. Des.
,
141
(
6
), p.
061701
. 10.1115/1.4042112
47.
Liu
,
J.
,
Chen
,
Q.
,
Liang
,
X.
, and
To
,
A. C.
,
2019
, “
Manufacturing Cost Constrained Topology Optimization for Additive Manufacturing
,”
Front. Mech. Eng.
,
14
(
2
), pp.
213
221
. 10.1007/s11465-019-0536-z
48.
Guo
,
X.
,
Zhang
,
W.
, and
Zhong
,
W.
,
2014
, “
Explicit Feature Control in Structural Topology Optimization via Level Set Method
,”
Comput. Methods Appl. Mech. Eng.
,
272
, pp.
354
378
. 10.1016/j.cma.2014.01.010
49.
Allaire
,
G.
,
Jouve
,
F.
, and
Michailidis
,
G.
,
2016
, “
Thickness Control in Structural Optimization via a Level set Method
,”
Struct. Multidiscip. Optim.
,
53
(
6
), pp.
1349
1382
. 10.1007/s00158-016-1453-y
50.
Liu
,
J.
,
Li
,
L.
, and
Ma
,
Y.
,
2018
, “
Uniform Thickness Control Without Pre-specifying the Length Scale Target Under the Level Set Topology Optimization Framework
,”
Adv. Eng. Software
,
115
, pp.
204
216
. 10.1016/j.advengsoft.2017.09.013
51.
Liu
,
J.
, and
Ma
,
Y.
,
2018
, “
A New Multi-material Level Set Topology Optimization Method With the Length Scale Control Capability
,”
Comput. Methods Appl. Mech. Eng.
,
329
, pp.
444
463
. 10.1016/j.cma.2017.10.011
52.
Costa
,
G.
,
Montemurro
,
M.
, and
Pailhès
,
J.
,
2018
, “
A 2D Topology Optimisation Algorithm in NURBS Framework With Geometric Constraints
,”
Int. J. Mech. Mater. Des.
,
14
(
4
), pp.
669
696
. 10.1007/s10999-017-9396-z
53.
Costa
,
G.
,
Montemurro
,
M.
, and
Pailhès
,
J.
,
2019
, “
NURBS Hyper-Surfaces for 3D Topology Optimization Problems
,”
Mech. Adv. Mater. Struct.
, pp.
1
20
.
in press
. 10.1080/15376494.2019.1582826
54.
Costa
,
G.
,
Montemurro
,
M.
,
Pailhès
,
J.
, and
Perry
,
N.
,
2019
, “
Maximum Length Scale Requirement in a Topology Optimisation Method Based on NURBS Hyper-Surfaces
,”
CIRP Ann.
,
68
(
1
), pp.
153
156
. 10.1016/j.cirp.2019.04.048
55.
Costa
,
G.
,
Montemurro
,
M.
, and
Pailhès
,
J.
,
2019
, “
Minimum Length Scale Control in a NURBS-Based SIMP Method
,”
Comput. Methods Appl. Mech. Eng.
,
354
, pp.
963
989
. 10.1016/j.cma.2019.05.026
56.
Liu
,
J.
,
2019
, “
Piecewise Length Scale Control for Topology Optimization With an Irregular Design Domain
,”
Comput. Methods Appl. Mech. Eng.
,
351
, pp.
744
765
. 10.1016/j.cma.2019.04.014
57.
Gaynor
,
A. T.
,
Meisel
,
N. A.
,
Williams
,
C. B.
, and
Guest
,
J. K.
,
2014
, “
Multiple-Material Topology Optimization of Compliant Mechanisms Created via PolyJet Three-Dimensional Printing
,”
ASME J. Manuf. Sci. Eng.
,
136
(
6
), p.
061015
. 10.1115/1.4028439
58.
Ranjan
,
R.
,
Samant
,
R.
, and
Anand
,
S.
,
2017
, “
Integration of Design for Manufacturing Methods With Topology Optimization in Additive Manufacturing
,”
ASME J. Manuf. Sci. Eng.
,
139
(
6
), p.
061007
. 10.1115/1.4035216
59.
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
60.
Rodriguez
,
T.
,
Montemurro
,
M.
,
Le Texier
,
P.
, and
Pailhès
,
J.
,
2020
, “
Structural Displacement Requirement in a Topology Optimization Algorithm Based on Isogeometric Entities
,”
J. Optim. Theory Appl.
,
184
(
1
), pp.
250
276
. 10.1007/s10957-019-01622-8
61.
Jiang
,
J.
,
Lou
,
J.
, and
Hu
,
G.
,
2019
, “
Effect of Support on Printed Properties in Fused Deposition Modelling Processes
,”
Virtual Phys. Prototyp.
,
14
(
4
), pp.
308
315
. 10.1080/17452759.2019.1568835
62.
Jiang
,
J.
,
Stringer
,
J.
,
Xu
,
X.
, and
Zhong
,
R. Y.
,
2018
, “
Investigation of Printable Threshold Overhang Angle in Extrusion-Based Additive Manufacturing for Reducing Support Waste
,”
Int. J. Comput. Integr. Manuf.
,
31
(
10
), pp.
961
969
. 10.1080/0951192X.2018.1466398
63.
Wei
,
C.
,
Chueh
,
Y.-H.
,
Zhang
,
X.
,
Huang
,
Y.
,
Chen
,
Q.
, and
Li
,
L.
,
2019
, “
Easy-to-Remove Composite Support Material and Procedure in Additive Manufacturing of Metallic Components Using Multiple Material Laser-Based Powder Bed Fusion
,”
ASME J. Manuf. Sci. Eng.
,
141
(7), p.
071002
. 10.1115/1.4043536
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.
Gaynor
,
A. T.
, and
Guest
,
J. K.
,
2016
, “
Topology Optimization Considering Overhang Constraints: Eliminating Sacrificial Support Material in Additive Manufacturing Through Design
,”
Struct. Multidiscip. Optim.
,
54
(
5
), pp.
1157
1172
. 10.1007/s00158-016-1551-x
66.
Johnson
,
T. E.
, and
Gaynor
,
A. T.
,
2018
, “
Three-Dimensional Projection-Based Topology Optimization for Prescribed-Angle Self-Supporting Additively Manufactured Structures
,”
Addit. Manuf.
,
24
, pp.
667
686
. 10.1016/j.addma.2018.06.011
67.
Langelaar
,
M.
,
2017
, “
An Additive Manufacturing Filter for Topology Optimization of Print-Ready Designs
,”
Struct. Multidiscip. Optim.
,
55
(
3
), pp.
871
883
. 10.1007/s00158-016-1522-2
68.
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
69.
Wang
,
C.
,
Qian
,
X.
,
Gerstler
,
W. D.
, and
Shubrooks
,
J.
,
2019
, “
Boundary Slope Control in Topology Optimization for Additive Manufacturing: For Self-Support and Surface Roughness
,”
ASME J. Manuf. Sci. Eng.
,
141
(9), p.
091001
. 10.1115/1.4043978
70.
Guo
,
X.
,
Zhou
,
J.
,
Zhang
,
W.
,
Du
,
Z.
,
Liu
,
C.
, and
Liu
,
Y.
,
2017
, “
Self-Supporting Structure Design in Additive Manufacturing Through Explicit Topology Optimization
,”
Comput. Methods Appl. Mech. Eng.
,
323
, pp.
27
63
. 10.1016/j.cma.2017.05.003
71.
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
72.
Zhang
,
W.
,
Yang
,
W.
,
Zhou
,
J.
,
Li
,
D.
, and
Guo
,
X.
,
2016
, “
Structural Topology Optimization Through Explicit Boundary Evolution
,”
ASME J. Appl. Mech.
,
84
(
1
), p.
011011
. 10.1115/1.4034972
73.
Zhang
,
W.
, and
Zhou
,
L.
,
2018
, “
Topology Optimization of Self-Supporting Structures With Polygon Features for Additive Manufacturing
,”
Comput. Methods Appl. Mech. Eng.
,
334
, pp.
56
78
. 10.1016/j.cma.2018.01.037
74.
Zhang
,
W.
,
Zhou
,
Y.
, and
Zhu
,
J.
,
2017
, “
A Comprehensive Study of Feature Definitions With Solids and Voids for Topology Optimization
,”
Comput. Methods Appl. Mech. Eng.
,
325
, pp.
289
313
. 10.1016/j.cma.2017.07.004
75.
Liu
,
J.
, and
To
,
A. C.
,
2017
, “
Deposition Path Planning-Integrated Structural Topology Optimization for 3D Additive Manufacturing Subject to Self-Support Constraint
,”
Comput.-Aided Des.
,
91
, pp.
27
45
. 10.1016/j.cad.2017.05.003
76.
Allaire
,
G.
,
Dapogny
,
C.
,
Estevez
,
R.
,
Faure
,
A.
, and
Michailidis
,
G.
,
2017
, “
Structural Optimization Under Overhang Constraints Imposed by Additive Manufacturing Technologies
,”
J. Comput. Phys.
,
351
, pp.
295
328
. 10.1016/j.jcp.2017.09.041
77.
Wang
,
Y.
,
Gao
,
J.
, and
Kang
,
Z.
,
2018
, “
Level Set-Based Topology Optimization With Overhang Constraint: Towards Support-Free Additive Manufacturing
,”
Comput. Methods Appl. Mech. Eng.
,
339
, pp.
591
614
. 10.1016/j.cma.2018.04.040
78.
Allaire
,
G.
, and
Bogosel
,
B.
,
2018
, “
Optimizing Supports for Additive Manufacturing
,”
Struct. Multidiscip. Optim.
,
58
(
6
), pp.
2493
2515
. 10.1007/s00158-018-2125-x
79.
Hu
,
K.
,
Jin
,
S.
, and
Wang
,
C. C. L.
,
2015
, “
Support Slimming for Single Material Based Additive Manufacturing
,”
Comput.-Aided Des.
,
65
, pp.
1
10
. 10.1016/j.cad.2015.03.001
80.
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
81.
Osher
,
S.
, and
Sethian
,
J. A.
,
1988
, “
Fronts Propagating With Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations
,”
J. Comput. Phys.
,
79
(
1
), pp.
12
49
. 10.1016/0021-9991(88)90002-2
82.
Osher
,
S.
, and
Fedkiw
,
R.
,
2003
,
Level Set Methods and Dynamic Implicit Surfaces
,
Springer
,
New York
, http://link.springer.com/10.1007/b98879, Accessed on May 27, 2016).
83.
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
84.
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
. 10.1016/j.jcp.2003.09.032
85.
Zhang
,
L.
,
He
,
Q.
,
Ito
,
S.
, and
Kita
,
K.
,
2010
, “
Euclidean Distance-Ordered Thinning for Skeleton Extraction
,”
Proceedings of 2nd International Conference on Education Technology and Computer
,
Shanghai
,
June 22–24
.
86.
Palágyi
,
K.
, and
Kuba
,
A.
,
1999
, “
A Parallel 3D 12-Subiteration Thinning Algorithm
,”
Graph. Models Image Process.
,
61
(
4
), pp.
199
221
. 10.1006/gmip.1999.0498
87.
Arcelli
,
C.
,
di Baja
,
G. S.
, and
Serino
,
L.
,
2011
, “
Distance-Driven Skeletonization in Voxel Images
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
33
(
4
), pp.
709
720
. 10.1109/TPAMI.2010.140
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