Abstract

This paper presents a multicomponent topology optimization method for designing structures assembled from additively manufactured components, considering anisotropic material behavior for each component due to its build orientation, distinct material behavior, and stress constraints at component interfaces (i.e., joints). Based upon the multicomponent topology optimization (MTO) framework, the simultaneous optimization of structural topology, its partitioning, and the build orientations of each component is achieved, which maximizes an assembly-level structural stiffness performance subject to maximum stress constraints at component interfaces. The build orientations of each component are modeled by its orientation tensor that avoids numerical instability experienced by the conventional angular representation. A new joint model is introduced at component interfaces, which enables the identification of the interface location, the specification of a distinct material tensor, and imposing maximum stress constraints during optimization. Both 2D and 3D numerical examples are presented to illustrate the effect of the build orientation anisotropy and the component interface behavior on the resulting multicomponent assemblies.

References

References
1.
Mark Two Desktop 3D Printer, Markforged
. https://markforged.com/mark-two/, Accessed Sep. 29, 2019.
2.
CBAM-2, Impossible Object
. https://www.impossible-objects.com/systems-services/, Accessed: Sep. 29, 2019.
3.
Frazier
,
W. E.
,
2014
, “
Metal Additive Manufacturing: a Review
,”
J. Mater. Eng. Perform.
,
23
(
6
), pp.
1917
1928
. 10.1007/s11665-014-0958-z
4.
Carroll
,
B. E.
,
Palmer
,
T. A.
, and
Beese
,
A. M.
,
2015
, “
Anisotropic Tensile Behavior of Ti–6al–4v Components Fabricated with Directed Energy Deposition Additive Manufacturing
,”
Acta. Mater.
,
87
, pp.
309
320
. 10.1016/j.actamat.2014.12.054
5.
Popovich
,
V.
,
Borisov
,
E.
,
Popovich
,
A.
,
Sufiiarov
,
V. S.
,
Masaylo
,
D.
, and
Alzina
,
L.
,
2017
, “
Functionally Graded Inconel 718 Processed by Additive Manufacturing: Crystallographic Texture, Anisotropy of Microstructure and Mechanical Properties
,”
Mater. Des.
,
114
, pp.
441
449
. 10.1016/j.matdes.2016.10.075
6.
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
. 10.1115/1.4030998
7.
Chandrasekhar
,
A.
,
Kumar
,
T.
, and
Suresh
,
K.
,
2020
, “
Build Optimization of Fiber-reinforced Additively Manufactured Components
,”
Struct. Multidiscipl. Optim.
,
61
(
1
), pp.
77
90
. 10.1007/s00158-019-02346-z
8.
Liu
,
J.
,
Gaynor
,
A. T.
,
Chen
,
S.
,
Kang
,
Z.
,
Suresh
,
K.
,
Takezawa
,
A.
,
Li
,
L.
,
Kato
,
J.
,
Tang
,
J.
,
Wang
,
C. C.
et al.,
2018
, “
Current and Future Trends in Topology Optimization for Additive Manufacturing
,”
Struct. Multidiscipl. Optim.
,
57
(
6
), pp.
2457
2483
. 10.1007/s00158-018-1994-3
9.
Alexander
,
P.
,
Allen
,
S.
, and
Dutta
,
D.
,
1998
, “
Part Orientation and Build Cost Determination in Layered Manufacturing
,”
Comput.-Aided Design
,
30
(
5
), pp.
343
356
. 10.1016/S0010-4485(97)00083-3
10.
Pandey
,
P. M.
,
Thrimurthulu
,
K.
, and
Reddy
,
N. V.
,
2004
, “
Optimal Part Deposition Orientation in FDM by Using a Multicriteria Genetic Algorithm
,”
Int. J. Product. Res.
,
42
(
19
), pp.
4069
4089
. 10.1080/00207540410001708470
11.
Gao
,
W.
,
Zhang
,
Y.
,
Nazzetta
,
D. C.
,
Ramani
,
K.
, and
Cipra
,
R. J.
,
2015
, “
Revomaker: Enabling Multi-directional and Functionally-embedded 3D Printing Using a Rotational Cuboidal Platform
,”
Proceedings of the 28th Annual ACM Symposium on User Interface Software & Technology
,
Charlotte, NC
, ACM, pp.
437
446
.
12.
Langelaar
,
M.
,
2018
, “
Combined Optimization of Part Topology, Support Structure Layout and Build Orientation for Additive Manufacturing
,”
Struct. Multidiscipl. Optim.
,
57
(
5
), pp.
1985
2004
. 10.1007/s00158-017-1877-z
13.
Jaiswal
,
P.
,
Patel
,
J.
, and
Rai
,
R.
,
2018
, “
Build Orientation Optimization for Additive Manufacturing of Functionally Graded Material Objects
,”
Int. J. Adv. Manuf. Technol.
,
96
, pp.
1
13
. 10.1007/s00170-018-1586-9
14.
Wu
,
C.
,
Dai
,
C.
,
Fang
,
G.
,
Liu
,
Y.-J.
, and
Wang
,
C. C.
,
2019
, “
General Support-effective Decomposition for Multi-directional 3-D Printing
,”
IEEE Trans. Autom. Sci. Eng.
,
17
(
2
), pp.
599
610
. 10.1109/TASE.2019.2938219
15.
Song
,
P.
,
Deng
,
B.
,
Wang
,
Z.
,
Dong
,
Z.
,
Li
,
W.
,
Fu
,
C.-W.
, and
Liu
,
L.
,
2016
, “
CofiFab: Coarse-to-fine Fabrication of Large 3D Objects
,”
ACM Trans. Graphics (TOG)
,
35
(
4
), p.
45
. 10.1145/2897824.2925876
16.
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
17.
Zegard
,
T.
, and
Paulino
,
G. H.
,
2016
, “
Bridging Topology Optimization and Additive Manufacturing
,”
Struct. Multidiscipl. Optim.
,
53
(
1
), pp.
175
192
. 10.1007/s00158-015-1274-4
18.
Zhu
,
B.
,
Skouras
,
M.
,
Chen
,
D.
, and
Matusik
,
W.
,
2017
, “
Two-scale Topology Optimization with Microstructures
,”
ACM Trans. Graphics
,
36
(
5
), pp.
164
.
19.
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
20.
Zhou
,
Y.
,
Nomura
,
T.
, and
Saitou
,
K.
,
2019
, “
Multicomponent Topology Optimization for Additive Manufacturing with Build Volume and Cavity Free Constraints
,”
ASME J. Comput. Inf. Sci. Eng.
,
19
(
2
), p.
021011
. 10.1115/1.4042640
21.
Lyu
,
N.
, and
Saitou
,
K.
,
2005
, “
Topology Optimization of Multicomponent Beam Structure Via Decomposition-based Assembly Synthesis
,”
ASME J. Mech. Des.
,
127
(
2
), pp.
170
183
. 10.1115/1.1814671
22.
Yildiz
,
A. R.
, and
Saitou
,
K.
,
2011
, “
Topology Synthesis of Multicomponent Structural Assemblies in Continuum Domains
,”
ASME J. Mech. Des.
,
133
(
1
), p.
011008
. 10.1115/1.4003038
23.
Guirguis
,
D.
,
Hamza
,
K.
,
Aly
,
M.
,
Hegazi
,
H.
, and
Saitou
,
K.
,
2015
, “
Multi-objective Topology Optimization of Multi-component Continuum Structures Via a Kriging-interpolated Level Set Approach
,”
Struct. Multidiscipl. Optim.
,
51
(
3
), pp.
733
748
. 10.1007/s00158-014-1154-3
24.
Zhou
,
Y.
, and
Saitou
,
K.
,
2018
, “
Gradient-based Multi-component Topology Optimization for Stamped Sheet Metal Assemblies (MTO-S)
,”
Struct. Multidiscipl. Optim.
,
58
(
1
), pp.
83
94
. 10.1007/s00158-017-1878-y
25.
Zhou
,
H.
,
Zhang
,
J.
,
Zhou
,
Y.
, and
Saitou
,
K.
,
2019
, “
Multi-component Topology Optimization for Die Casting (MTO-D)
,”
Struct. Multidiscipl. Optim.
,
60
(
6
), pp.
2265
2279
. 10.1007/s00158-019-02317-4
26.
Liu
,
P.
,
Luo
,
Y.
, and
Kang
,
Z.
,
2016
, “
Multi-material Topology Optimization Considering Interface Behavior Via XFEM and Level Set Method
,”
Comput. Methods Appl. Mech. Eng.
,
308
, pp.
113
133
. 10.1016/j.cma.2016.05.016
27.
Woischwill
,
C.
, and
Kim
,
I. Y.
,
2018
, “
Multimaterial Multijoint Topology Optimization
,”
Int. J. Num. Methods Eng.
,
115
(
13
), pp.
1552
1579
. 10.1002/nme.5908
28.
Liu
,
P.
, and
Kang
,
Z.
,
2018
, “
Integrated Topology Optimization of Multi-component Structures Considering Connecting Interface Behavior
,”
Computer Methods Appl. Mech. Eng.
,
341
, pp.
851
887
. 10.1016/j.cma.2018.07.001
29.
Florea
,
V.
,
Pamwar
,
M.
,
Sangha
,
B.
, and
Kim
,
I. Y.
,
2019
, “
3D Multi-material and Multi-joint Topology Optimization with Tooling Accessibility Constraints
,”
Struct. Multidiscipl. Optim.
,
60
(
6
), pp.
2531
2558
. 10.1007/s00158-019-02344-1
30.
Chu
,
S.
,
Xiao
,
M.
,
Gao
,
L.
,
Li
,
H.
,
Zhang
,
J.
, and
Zhang
,
X.
,
2019
, “
Topology Optimization of Multi-material Structures with Graded Interfaces
,”
Comput. Methods Appl. Mech. Eng.
,
346
, pp.
1096
1117
. 10.1016/j.cma.2018.09.040
31.
Zhou
,
Y.
,
Nomura
,
T.
, and
Saitou
,
K.
,
2018
, “
Multi-component Topology and Material Orientation Design of Composite Structures (MTO-C)
,”
Comput. Methods Appl. Mech. Eng.
,
342
, pp.
438
457
. 10.1016/j.cma.2018.07.039
32.
Nomura
,
T.
,
Kawamoto
,
A.
,
Kondoh
,
T.
,
Dede
,
E. M.
,
Lee
,
J.
,
Song
,
Y.
, and
Kikuchi
,
N.
,
2019
, “
Inverse Design of Structure and Fiber Orientation by Means of Topology Optimization with Tensor Field Variables
,”
Composites Part B: Eng.
,
176
. 10.1016/j.compositesb.2019.107187
33.
Bendsøe
,
M. P.
, and
Sigmund
,
O.
,
2004
,
Topology Optimization Theory, Methods, and Applications
,
Springer
.
34.
Stegmann
,
J.
, and
Lund
,
E.
,
2005
, “
Discrete Material Optimization of General Composite Shell Structures
,”
Int. J. Numer. Methods Eng.
,
62
(
14
), pp.
2009
2027
. 10.1002/nme.1259
35.
Kawamoto
,
A.
,
Matsumori
,
T.
,
Yamasaki
,
S.
,
Nomura
,
T.
,
Kondoh
,
T.
, and
Nishiwaki
,
S.
,
2011
, “
Heaviside Projection Based Topology Optimization by a PDE-filtered Scalar Function
,”
Struct. Multidiscipl. Optim.
,
44
(
1
), pp.
19
24
. 10.1007/s00158-010-0562-2
36.
Le
,
C.
,
Norato
,
J.
,
Bruns
,
T.
,
Ha
,
C.
, and
Tortorelli
,
D.
,
2010
, “
Stress-based Topology Optimization for Continua
,”
Struct. Multidiscipl. Optim.
,
41
(
4
), pp.
605
620
. 10.1007/s00158-009-0440-y
37.
Wang
,
C.
, and
Qian
,
X.
,
2018
, “
Heaviside Projection–based Aggregation in Stress-constrained Topology Optimization
,”
Int. J. Numer. Methods Eng.
,
115
(
7
), pp.
849
871
. 10.1002/nme.5828
38.
Advani
,
S. G.
, and
Tucker III
,
C. L.
,
1987
, “
The Use of Tensors to Describe and Predict Fiber Orientation in Short Fiber Composites
,”
J. Rheol.
,
31
(
8
), pp.
751
784
. 10.1122/1.549945
39.
Svanberg
,
K.
,
1987
, “
The Method of Moving Asymptotes – a New Method for Structural Optimization
,”
Int. J. Numer. Methods Eng.
,
24
(
2
), pp.
359
373
. 10.1002/nme.1620240207
You do not currently have access to this content.