Abstract

Without an explicit formulation to minimize support structures, topology optimization may create complex shapes that require an intensive use of support material when additively manufactured. We propose a neural network-based approach to topology optimization that aims to reduce the use of support structures in additive manufacturing. Our approach uses a network architecture that allows the simultaneous determination of an optimized: (1) part segmentation, (2) the topology of each part, and (3) the build direction of each part that collectively minimize the amount of support structure. Through training, the network learns a material density and segment classification in the continuous 3D space. Given a problem domain with prescribed load and displacement boundary conditions, the neural network takes as input 3D coordinates of the voxelized domain as training samples and outputs a continuous density field. Since the neural network for topology optimization learns the density distribution field, analytical solutions to the density gradient can be obtained from the input–output relationship of the neural network. We demonstrate our approach on several compliance minimization problems with volume fraction constraints, where support volume minimization is added as an additional criterion to the objective function. We show that simultaneous optimization of part segmentation along with the topology and print angle optimization further reduces the support structure, compared to a combined print angle and topology optimization without segmentation.

References

1.
Nie
,
Z.
,
Jung
,
S.
,
Kara
,
L. B.
, and
Whitefoot
,
K. S.
,
2020
, “
Optimization of Part Consolidation for Minimum Production Costs and Time Using Additive Manufacturing
,”
ASME J. Mech. Des.
,
142
(
7
), p.
072001
.
2.
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
.
3.
Mirzendehdel
,
A. M.
, and
Suresh
,
K.
,
2016
, “
Support Structure Constrained Topology Optimization for Additive Manufacturing
,”
Comput. Aided Des.
,
81
, pp.
1
13
.
4.
Wang
,
C.
, and
Qian
,
X.
,
2020
, “
Simultaneous Optimization of Build Orientation and Topology for Additive Manufacturing
,”
Addit. Manuf.
,
34
, p.
101246
.
5.
Chandrasekhar
,
A.
, and
Suresh
,
K.
,
2021
, “
Tounn: Topology Optimization Using Neural Networks
,”
Struct. Multidiscipl. Optim.
,
63
, pp.
1135
1149
.
6.
Thompson
,
M. K.
,
Moroni
,
G.
,
Vaneker
,
T.
,
Fadel
,
G.
,
Campbell
,
R. I.
,
Gibson
,
I.
,
Bernard
,
A.
, et al.
2016
, “
Design for Additive Manufacturing: Trends, Opportunities, Considerations, and Constraints
,”
CIRP Ann. Manuf. Technol.
,
65
(
2
), pp.
737
760
.
7.
Brackett
,
D.
,
Ashcroft
,
I.
, and
Hague
,
R.
,
2011
, “
Topology Optimization for Additive Manufacturing
,”
2011 International Solid Freeform Fabrication Symposium
,
Austin, TX
,
Aug. 8–10
, pp.
348
362
.
8.
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
.
9.
Gaynor
,
A. T.
, and
Guest
,
J. K.
,
2014
, “
Topology Optimization for Additive Manufacturing: Considering Maximum Overhang Constraint
,”
AIAA Aviation 2014–15th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference
,
Atlanta, GA
,
June 16–20
10.
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
.
11.
Langelaar
,
M.
,
2016
, “
Topology Optimization of 3D Self-supporting Structures for Additive Manufacturing
,”
Addit. Manuf.
,
12
, pp.
60
70
.
12.
van de Ven
,
E.
,
Maas
,
R.
,
Ayas
,
C.
,
Langelaar
,
M.
, and
van Keulen
,
F.
,
2018
, “
Continuous Front Propagation-Based Overhang Control for Topology Optimization With Additive Manufacturing
,”
Struct. Multidiscipl. Optim.
,
57
(
5
), pp.
2075
2091
.
13.
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
.
14.
Cheng
,
L.
, and
To
,
A.
,
2019
, “
Part-Scale Build Orientation Optimization for Minimizing Residual Stress and Support Volume for Metal Additive Manufacturing: Theory and Experimental Validation
,”
Comput. Aided Des.
,
113
, pp.
1
23
.
15.
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
.
16.
Zhang
,
K.
,
Cheng
,
G.
, and
Xu
,
L.
,
2019
, “
Topology Optimization Considering Overhang Constraint in Additive Manufacturing
,”
Comput. Struct.
,
212
, pp.
86
100
.
17.
Mezzadri
,
F.
,
Bouriakov
,
V.
, and
Qian
,
X.
,
2018
, “
Topology Optimization of Self-supporting Support Structures for Additive Manufacturing
,”
Addit. Manuf.
,
21
, pp.
666
682
.
18.
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
.
19.
Chandrasekhar
,
A.
,
Kumar
,
T.
, and
Suresh
,
K.
,
2020
, “
Build Optimization of Fiber-Reinforced Additively Manufactured Components
,”
Struct. Multidiscipl. Optim.
,
61
, pp.
77
90
.
20.
Ulu
,
E.
,
Korkmaz
,
E.
,
Yay
,
K.
,
Ozdoganlar
,
O. B.
, and
Kara
,
L. B.
,
2015
, “
Enhancing the Structural Performance of Additively Manufactured Objects Through Build Orientation Optimization
,”
ASME J. Mech. Des.
,
137
(
11
), p. 111410.
21.
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.
111410
.
22.
Ulu
,
E.
,
Gecer Ulu
,
N.
,
Hsiao
,
W.
, and
Nelaturi
,
S.
,
2019
, “
Manufacturability Oriented Model Correction and Build Direction Optimization for Additive Manufacturing
,”
ASME J. Mech. Des.
,
142
(
6
), p.
062001
.
23.
Zhou
,
Y.
,
Nomura
,
T.
, and
Saitou
,
K.
,
2021
, “
Anisotropic Multicomponent Topology Optimization for Additive Manufacturing With Build Orientation Design and Stress-constrained Interfaces
,”
ASME J. Comput. Inf. Sci. Eng.
,
21
(
1
), p.
011007
.
24.
White
,
D. A.
,
Arrighi
,
W. J.
,
Kudo
,
J.
, and
Watts
,
S. E.
,
2019
, “
Multiscale Topology Optimization Using Neural Network Surrogate Models
,”
Comput. Methods Appl. Mech. Eng.
,
346
, pp.
1118
1135
.
25.
Banga
,
S.
,
Gehani
,
H.
,
Bhilare
,
S.
,
Patel
,
S.
, and
Kara
,
L.
,
2018
, “
3D Topology Optimization Using Convolutional Neural Networks
.” arXiv preprint arXiv:1808.07440.
26.
Behzadi
,
M. M.
, and
Ilieş
,
H. T.
,
2021
, “
Real-Time Topology Optimization in 3D Via Deep Transfer Learning
,”
Comput. Aided Des.
,
135
, p.
103014
.
27.
Zheng
,
S.
,
He
,
Z.
, and
Liu
,
H.
,
2021
, “
Generating Three-Dimensional Structural Topologies Via a U-net Convolutional Neural Network
,”
Thin-Walled Struct.
,
159
, p.
107263
.
28.
Cang
,
R.
,
Yao
,
H.
, and
Ren
,
Y.
,
2019
, “
One-Shot Generation of Near-Optimal Topology Through Theory-Driven Machine Learning
,”
Comput. Aided Des.
,
109
, pp.
12
21
.
29.
Nie
,
Z.
,
Lin
,
T.
,
Jiang
,
H.
, and
Kara
,
L. B.
,
2021
, “
Topologygan: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domain
,”
ASME J. Mech. Des.
,
143
(
3
), p.
031715
.
30.
Iyer
,
N. S.
,
Mirzendehdel
,
A. M.
,
Raghavan
,
S.
,
Jiao
,
Y.
,
Ulu
,
E.
,
Behandish
,
M.
,
Nelaturi
,
S.
, and
Robinson
,
D. M.
,
2021
, “
PATO: Producibility-Aware Topology Optimization Using Deep Learning for Metal Additive Manufacturing
,” CoRR,
abs/2112.04552
https://arxiv.org/abs/2112.04552
31.
Chi
,
H.
,
Zhang
,
Y.
,
Tang
,
T. L. E.
,
Mirabella
,
L.
,
Dalloro
,
L.
,
Song
,
L.
, and
Paulino
,
G. H.
,
2021
, “
Universal Machine Learning for Topology Optimization
,”
Comput. Methods Appl. Mech. Eng.
,
375
), p.
112739
.
32.
Chandrasekhar
,
A.
, and
Suresh
,
K.
,
2021
, “
Length Scale Control in Topology Optimization Using Fourier Enhanced Neural Networks
,” CoRR, abs/2109.01861.
33.
Chandrasekhar
,
A.
, and
Suresh
,
K.
,
2021
, “
Multi-material Topology Optimization Using Neural Networks
,”
Comput. Aided Des.
,
136
, p.
103017
.
34.
Abadi
,
M.
,
Agarwal
,
A.
,
Barham
,
P.
,
Brevdo
,
E.
,
Chen
,
Z.
,
Citro
,
C.
,
Corrado
,
G. S.
, et al.
2016
, “
Tensorflow: Large-Scale Machine Learning on Heterogeneous Distributed Systems
.”
35.
Orbay
,
G.
,
Fu
,
L.
, and
Kara
,
L. B.
,
2015
, “
Deciphering the Influence of Product Shape on Consumer Judgments Through Geometric Abstraction
,”
ASME J. Mech. Des.
,
137
(
8
), p.
081103
.
36.
Liu
,
K.
, and
Tovar
,
A.
,
2014
, “
An Efficient 3D Topology Optimization Code Written in Matlab
,”
Struct. Multidiscipl. Optim.
,
50
, pp.
1175
1196
.
37.
Kingma
,
D. P.
, and
Ba
,
J. L.
,
2015
, “
Adam: A Method for Stochastic Optimization
.”
38.
Ultimaker
,
2020
, “
Ultimaker Cura
,” Oct.12
You do not currently have access to this content.