Abstract

We address a central issue that arises within element-based topology optimization. To achieve a sufficiently well-defined material interface, one requires a highly refined finite element mesh; however, this leads to an increased computational cost due to the solution of the finite element analysis problem. By generating an optimal structure on a coarse mesh and using an artificial neural network to map this coarse solution to a refined mesh, we can greatly reduce computational time. This approach resulted in time savings of up to 85% for test cases considered. This significant advantage in computational time also preserves the structural integrity when compared with a fine-mesh optimization with limited error. Along with the savings in computational time, the boundary edges become more refined during the process, allowing for a sharp transition from solid to void. This improved boundary edge can be leveraged to improve the manufacturability of the optimized designs.

References

References
1.
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
2.
Nanthakumar
,
S.
,
Lahmer
,
T.
,
Zhuang
,
X.
,
Park
,
H. S.
, and
Rabczuk
,
T.
,
2016
, “
Topology Optimization of Piezoelectric Nanostructures
,”
J. Mech. Phys. Solids
,
94
(
Sep.
), pp.
316
335
. 10.1016/j.jmps.2016.03.027
3.
Jensen
,
K. E.
,
Szabo
,
P.
, and
Okkels
,
F.
,
2013
, “
Optimization of Bistable Viscoelastic Systems
,”
Struct. Multidiscipl. Optim.
,
49
(
5
), pp.
733
742
. 10.1007/s00158-013-1020-8
4.
Kutylowski
,
R.
, and
Rasiak
,
B.
,
2008
, “
Influence of Various Design Parameters on the Quality of Optimal Shape Design in Topology Optimization Analysis
,”
PAMM
,
8
(
1
), pp.
10797
10798
. 10.1002/pamm.200810797
5.
Sigmund
,
O.
, and
Peterson
,
J.
,
1998
, “
Numerical Instabilities in Topology Optimization: A Survey on Procedures Dealing With Checkerboards, Mesh-Dependencies and Local Minima
,”
Struct. Optim.
,
16
(
1
), pp.
68
75
. 10.1007/BF01214002
6.
Le
,
C.
,
Norato
,
J.
,
Bruns
,
T.
,
Ha
,
C.
, and
Tortorelli
,
D.
,
2009
, “
Stress-Based Topology Optimization for Continua
,”
Struct. Multidiscipl. Optim.
,
41
(
4
), pp.
605
620
. 10.1007/s00158-009-0440-y
7.
Guest
,
J. K.
,
Prévost
,
J. H.
, and
Belytschko
,
T.
,
2004
, “
Achieving Minimum Length Scale in Topology Optimization Using Nodal Design Variables and Projection Functions
,”
Int. J. Numer. Methods Eng.
,
61
(
2
), pp.
238
254
. 10.1002/nme.1064
8.
James
,
K. A.
, and
Waisman
,
H.
,
2014
, “
Failure Mitigation in Optimal Topology Design Using a Coupled Nonlinear Continuum Damage Model
,”
Comput. Methods Appl. Mech. Eng.
,
268
(
Jan.
), pp.
614
631
. 10.1016/j.cma.2013.10.022
9.
James
,
K. A.
, and
Waisman
,
H.
,
2015
, “
Topology Optimization of Viscoelastic Structures Using a Time-Dependent Adjoint Method
,”
Comput. Methods Appl. Mech. Eng.
,
285
(
Mar.
), pp.
166
187
. 10.1016/j.cma.2014.11.012
10.
Wang
,
S.
,
de Sturler
,
E.
, and
Paulino
,
G. H.
,
2010
, “
Dynamic Adaptive Mesh Refinement for Topology Optimization
,” ResearchGate.
11.
Wang
,
Y.
,
Kang
,
Z.
, and
He
,
Q.
,
2013
, “
An Adaptive Refinement Approach for Topology Optimization Based on Separated Density Field Description
,”
Comput. Struct.
,
117
(
Feb.
), pp.
10
22
. 10.1016/j.compstruc.2012.11.004
12.
Allaire
,
G. C. A.
,
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
13.
James
,
K. A.
, and
Martins
,
J. R.
,
2012
, “
An Isoparametric Approach to Level Set Topology Optimization Using a Body-Fitted Finite-Element Mesh
,”
Comput. Struct.
,
90–91
(
Jan.
), pp.
97
106
. 10.1016/j.compstruc.2011.10.004
14.
Zhou
,
H.
, and
Mohammed
,
S. A.
,
2013
, “
The Boundary Smoothing in Discrete Topology Optimization of Structures
,”
Volume 3A: 39th Design Automation Conference
,
New Orleans, LA
,
June 10–14, 2002
.
15.
Kim
,
J.
,
Lee
,
J. K.
, and
Lee
,
K. M.
,
2016
, “
Accurate Image Super-Resolution Using Very Deep Convolutional Networks
,”
IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
,
Las Vegas, NV
,
June 26–July 1
.
16.
Dong
,
C.
,
Loy
,
C. C.
,
He
,
K.
, and
Tang
,
X.
,
2016
, “
Image Super-Resolution Using Deep Convolutional Networks
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
38
(
2
), pp.
295
307
. 10.1109/TPAMI.2015.2439281
17.
Burel
,
G.
,
Pottier
,
I.
, and
Catros
,
J.-Y.
,
1992
, “
Recognition of Handwritten Digits by Image Processing and Neural Network
,”
Proceedings 1992: IJCNN International Joint Conference on ANNs
,
Baltimore, MD
,
June 7–11
.
18.
Karlik
,
B.
, and
Sarioz
,
M.
,
2009
, “
Coloring Gray-Scale Image Using Artificial ANNs
,”
2nd International Conference on Adaptive Science & Technology (ICAST)
,
Accra, Ghana
,
Dec. 14–16
.
19.
Bishop
,
C. M.
,
2013
,
Pattern Recognition and Machine Learning
,
Springer
,
New Delhi
.
20.
Wang
,
G. G.
, and
Shan
,
S.
,
2006
, “
Review of Metamodeling Techniques in Support of Engineering Design Optimization
,”
Volume 1: 32nd Design Automation Conference, Parts A and B
,
Philadelphia, PA
,
Sept. 10–13
.
21.
Gorrisen
,
D.
,
Couckuyt
,
I.
,
Demeester
,
P.
,
Dhaene
,
T.
, and
Crombecq
,
K.
,
2010
, “
A Surrogate Modeling and Adaptive Sampling Toolbox for Computer Based Design
,”
J. Mach. Learn. Res.
,
11
, pp.
2051
2055
.
22.
Chojaczyk
,
A. A.
,
Teixeira
,
A. P.
,
Neves
,
L. C.
,
Cardoso
,
J. B.
, and
Soares
,
C. G.
,
2015
, “
Review and Application of Artificial Neural Networks Models in Reliability Analysis of Steel Structures
,”
Struct. Saf.
,
52
(
Part A
), pp.
78
89
. 10.1016/j.strusafe.2014.09.002
23.
Quan
,
W.
, and
Pimentel
,
A. D.
,
2014
, “
Towards Exploring Vast MPSoC Mapping Design Spaces Using a Bias-Elitist Evolutionary Approach
,”
17th Euromicro Conference on Digital System Design
,
Verona, Italy
,
Aug. 27–29
.
24.
Yadav
,
V.
,
Malik
,
P.
,
Sahoo
,
G.
, and
Chauhan
,
A. S.
,
2014
, “
Energy Efficient Virtual Machine Optimization
,”
Int. J. Comput. Appl.
,
106
(
7
), pp.
23
28
.
25.
Zadpoor
,
A. A.
,
2013
, “
Open Forward and Inverse Problems in Theoretical Modeling of Bone Tissue Adaptation
,”
J. Mech. Behav. Biomed. Mater.
,
27
(
Nov.
), pp.
249
261
. 10.1016/j.jmbbm.2013.05.017
26.
Mohri
,
M.
,
Rostamizadeh
,
A.
, and
Talwalkar
,
A.
,
2012
,
Foundations of Machine Learning
,
The MIT Press
,
Cambridge, MA
.
27.
Malsburg
,
C. V. D.
,
1986
, “Frank Rosenblatt: Principles of Neurodynamics: Perceptrons and the Theory of Brain Mechanisms,”
Brain Theory
,
P.
Günther
, and
Ad.
Aertsen
, eds.,
Springer-Verlag Berlin Heidelberg
,
Berlin, Germany
, pp.
245
248
.
28.
Nair
,
V.
, and
Hinton
,
G. E.
,
2010
, “
Rectified Linear Units Improve Restricted Boltzmann Machines
,”
27th International Conference on Machine Learning
,
Haifa, Israel
,
June 21–24
.
29.
Bengio
,
Y.
,
Courville
,
A.
, and
Vincent
,
P.
,
2013
, “
Representation Learning: A Review and New Perspectives
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
35
(
8
), pp.
1798
1828
. 10.1109/TPAMI.2013.50
30.
Sigmund
,
O.
,
2001
, “
A 99 Line Topology Optimization Code Written in Matlab
,”
Struct. Multidiscipl. Optim.
,
21
(
2
), pp.
120
127
. 10.1007/s001580050176
31.
Pedersen
,
C.
,
Lund
,
J.
,
Damkilde
,
L.
, and
Kristensen
,
A.
,
2006
,
Topology Optimization—Improved Checkerboard Filtering With Sharp Contours
,
Aalborg University
,
Aalborg
.
32.
Kang
,
Z.
, and
James
,
K. A.
,
2019
, “
Multimaterial Topology Design for Optimal Elastic and Thermal Response With Materials-Specific Temperature Constraints
,”
Int. J. Numer. Methods Eng.
,
117
(
10
), pp.
1019
1037
. 10.1002/nme.5989
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