This paper presents a two-step elastic modeling (TsEM) method for the topology optimization of compliant mechanisms aimed at eliminating de facto hinges. Based on the TsEM method, an alternative formulation is developed and incorporated with the level set method. An efficient algorithm is developed to solve the level set-based optimization problem for improving the computational efficiency. Two widely studied numerical examples are performed to demonstrate the validity of the proposed method. The proposed formulation can prevent hinges from occurring in the resulting mechanisms. Further, the proposed optimization algorithm can yield fewer design iterations and thus it can improve the overall computational efficiency.

References

References
1.
Howell
,
L. L.
,
2001
,
Compliant Mechanisms
,
Wiley-Interscience
,
New York
.
2.
Fatikow
,
S.
,
Wich
,
T.
,
Hulsen
,
H.
,
Sievers
,
T.
, and
Jahnisch
,
M.
,
2007
, “
Microrobot System for Automatic Nanohandling Inside a Scanning Electron Microscope
,”
IEEE/ASME Trans. Mechatron.
,
12
(
3
), pp.
244
252
.10.1109/TMECH.2007.897252
3.
Sardan
,
O.
,
Eichhorn
,
V.
,
Petersen
,
D. H.
,
Fatikow
,
S.
,
Sigmund
,
O.
, and
Bøgild
,
P.
,
2008
, “
Rapid Prototyping of Nanotube-Based Devices Using Topology-Optimized Microgrippers
,”
Nanotechnology
,
19
(
49
), pp.
495503
495511
.10.1088/0957-4484/19/49/495503
4.
Pucheta
,
M. A.
, and
Cardona
,
A.
,
2010
, “
Design of Bistable Compliant Mechanisms Using Precision-Position and Rigid-Body Replacement Methods
,”
Mech. Mach. Theory
,
45
(
2
), pp.
304
426
.10.1016/j.mechmachtheory.2009.09.009
5.
Bendsøe
,
M. P.
, and
Sigmund
,
O.
,
2003
,
Topology Optimization: Theory, Methods and Applications
,
Springer
,
New York
.
6.
Sigmund
,
O.
,
2007
, “
Morphology-Based Black and White Filters for Topology Optimization
,”
Struct. Multidiscip. Optim.
,
33
(
4–5
), pp.
401
424
.10.1007/s00158-006-0087-x
7.
Yamada
,
T.
,
Izui
,
K.
,
Nishiwaki
,
S.
, and
Takezawa
,
A.
,
2010
, “
A Topology Optimization Method Based on the Level Set Method Incorporating a Fictitious Interface Energy
,”
Comput. Methods Appl. Mech. Eng.
,
199
(
45–48
), pp.
2876
2891
.10.1016/j.cma.2010.05.013
8.
Choi
,
K. K.
, and
Kim
,
N. H.
,
2005
,
Structural Sensitivity Analysis and Optimization 1: Linear Systems
,
Springer
,
New York
.
9.
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
10.
Wang
,
M.
,
Wang
,
X. M.
, and
Guo
,
D. M.
,
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
11.
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
12.
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
13.
Sethian
,
J. A.
, and
Wiegmann
,
A.
,
2000
, “
Structural Boundary Design Via Level Set and Immersed Interface Methods
,”
J. Comput. Phys.
,
163
(
2
), pp.
489
528
.10.1006/jcph.2000.6581
14.
Osher
,
S.
, and
Santosa
,
F.
,
2001
, “
Level-Set Methods for Optimization Problem Involving Geometry and Constraints: I. Frequencies of a Two-Density Inhomogeneous drum
,”
J. Comput. Phys.
,
171
(
1
), pp.
272
288
.10.1006/jcph.2001.6789
15.
Chen
,
S. K.
,
Gonella
,
S.
,
Chen
,
W.
, and
Liu
,
W. K.
,
2010
, “
A Level Set Approach for Optimal Design of Smart Energy Harvesters
,”
Comput. Methods Appl. Mech. Eng.
,
199
(
37–40
), pp.
2532
2543
.10.1016/j.cma.2010.04.008
16.
Zhou
,
S. W.
,
Li
,
W.
,
Chen
,
Y. H.
,
Sun
,
G. Y.
, and
Li
,
Q.
,
2011
, “
Topology Optimization for Negative Permeability Metamaterials Using Level-Set Algorithm
,”
Acta Mater.
,
59
(
7
), pp.
2624
2636
.10.1016/j.actamat.2010.12.049
17.
Ha
,
S. H.
, and
Cho
,
S.
,
2008
, “
Level Set Based Topological Shape Optimization of Geometrically Nonlinear Structures Using Unstructured Mesh
,”
Comput. Struct.
,
86
, pp.
1447
1455
.10.1016/j.compstruc.2007.05.025
18.
Wang
,
X.
,
Wang
,
M.
, and
Guo
,
D.
,
2004
, “
Structural Shape and Topology Optimization in a Level-Set-Based Framework of Region Representation
,”
Structural and Multidisciplinary Optimization
,
27
(
1–2
), pp.
1
19
.10.1007/s00158-003-0363-y
19.
Luo
,
Z.
,
Tong
,
L.
,
Wang
,
M. Y.
, and
Wang
,
S.
,
2007
, “
Shape and Topology Optimization of Compliant Mechanisms Using a Parameterization Level Set Method
,”
J. Comput. Phys.
,
227
(
1
), pp.
680
705
.10.1016/j.jcp.2007.08.011
20.
Mei
,
Y.
, and
Wang
,
X.
,
2004
, “
A Level Set Method for Structural Topology Optimization and its Applications
,”
Adv. Eng. Software
,
35
(
7
), pp.
415
441
.10.1016/j.advengsoft.2004.06.004
21.
Zhu
,
B.
, and
Zhang
,
X.
,
2012
, “
A New Level Set Method for Topology Optimization of Distributed Compliant Mechanisms
,”
Int. J. Numer. Methods Eng.
,
91
(
8
), pp.
843
871
.10.1002/nme.4296
22.
Luo
,
J.
,
Luo
,
Z.
,
Chen
,
L.
,
Tong
,
L.
, and
Wang
,
M. Y.
,
2008
, “
A Semi-Implicit Level Set Method for Structural Shape and Topology Optimization
,”
J. Comput. Phys.
,
227
(
11
), pp.
5561
5581
.10.1016/j.jcp.2008.02.003
23.
Zhou
,
M.
, and
Wang
,
M. Y.
,
2012
, “
A Semi-Lagrangian Level Set Method for Structural Optimization
,”
Struct. Multidiscip. Optim.
,
46
(
4
), pp.
487
501
.10.1007/s00158-012-0842-0
24.
Deepak
,
S. R.
,
Dinesh
,
M.
,
Sahu
,
D. K.
, and
Ananthasuresh
,
G. K.
,
2009
, “
A Comparative Study of the Formulations and Benchmark Problems for the Topology Optimization of Compliant Mechanisms
,”
ASME J. Mech. Rob
,
1
(1), p.
011003
.10.1115/1.2959094
25.
Pedersen
,
C. B.
,
Buhl
,
T.
, and
Sigmund
,
O.
,
2001
, “
Topology Synthesis of Large-Displacement Compliant Mechanisms
,”
Int. J. Numer. Methods Eng.
,
50
(
12
), pp.
2683
2705
.10.1002/nme.148
26.
Wang
,
M. Y.
,
2009
, “
A Kinetoelastic Formulation of Compliant Mechanism Optimization
,”
ASME J. Mech. Rob.
,
1
(
2
), p.
021011
.10.1115/1.3056476
27.
Rahmatalla
,
S.
, and
Swan
,
C. C.
,
2005
, “
Sparse Monolithic Compliant Mechanisms Using Continuum Structural Topology Optimization
,”
Int. J. Numer. Methods Eng.
,
62
(
12
), pp.
1579
1605
.10.1002/nme.1224
28.
Chen
,
S. K.
,
2007
, “
Compliant Mechanisms With Distributed Compliance and Characteristic Stiffness: A Level Set Method
,” PhD thesis, The Chinese University of Hong Kong, China.
29.
Luo
,
Z.
,
Chen
,
L.
,
Yang
,
J.
,
Zhang
,
Y.
, and
Abdel-Malek
,
K.
,
2005
, “
Compliant Mechanism Design Using Multi-Objective Topology Optimization Scheme of Continuum Structures
,”
Struct. Multidiscip. Optim.
,
30
(
2
), pp.
142
154
.10.1007/s00158-004-0512-y
30.
Duysinx
,
P.
, and
Bendsøe
,
M. P.
,
1998
, “
Topology Optimization of Continuum Structures With Local Stress Constraints
,”
Int. J. Numer. Methods Eng.
,
43
, pp.
1453
1478
.10.1002/(SICI)1097-0207(19981230)43:8<1453::AID-NME480>3.0.CO;2-2
31.
Wang
,
N.
, and
Zhang
,
X.
,
2012
, “
Compliant Mechanisms Design Based on Pairs of Curves
,”
Sci. China Technol. Sci.
,
55
(
8
), pp.
2099
2106
.10.1007/s11431-012-4849-y
32.
Zhou
,
H.
,
2010
, “
Topology Optimization of Compliant Mechanisms Using Hybrid Discretization Model
,”
ASME J. Mech. Des.
,
132
(
11
), p.
111003
.10.1115/1.4002663
33.
Poulsen
,
T. A.
,
2003
, “
A New Scheme For Imposing a Minimum Length Scale in Topology Optimization
,”
Int. J. Numer. Methods Eng.
,
57
(
6
), pp.
741
760
.10.1002/nme.694
34.
Yin
,
L.
, and
Ananthasuresh
,
G. K.
,
2003
, “
Design of Distributed Compliant Mechanisms
,”
Mech. Based Des. Struct. Mach.
31
(
2
), pp.
151
179
.10.1081/SME-120020289
35.
Chen
,
S. K.
,
Wang
,
M. Y.
, and
Liu
,
A. Q.
,
2008
, “
Shape Feature Control in Structural Topology Optimization
,”
Computer-Aided Des.
,
40
, pp.
951
962
.10.1016/j.cad.2008.07.004
36.
Zhu
,
B.
,
Zhang
,
X.
, and
Wang
,
N.
,
2013
, “
Topology Optimization of Hinge-Free Compliant Mechanisms With Multiple Outputs Using Level Set Method
,”
Struct. Multidiscip. Optim.
,
47
(
5
), pp.
659
672
.10.1007/s00158-012-0841-1
37.
Luo
,
J.
,
Luo
,
Z.
,
Chen
,
S.
,
Tong
,
L.
, and
Wang
,
M. Y.
,
2008
, “
A New Level Set Method for Systematic Design of Hinge-Free Compliant Mechanisms
,”
Comput. Methods Appl. Mech. Eng.
,
198
, pp.
318
331
.10.1016/j.cma.2008.08.003
38.
Sigmund
,
O.
,
1997
, “
On the Design of Compliant Mechanisms Using Topology Optimization
,”
Mech. Struct. Mach.
,
25
(
4
), pp.
493
524
.10.1080/08905459708945415
39.
Nishiwaki
,
S.
,
Min
,
S.
,
Yoo
,
J.
, and
Kikuchi
,
N.
,
2001
, “
Optimal Structural Design Considering Flexibility
,”
Comput. Methods Appl. Mech. Eng.
,
190
(
34
), pp.
4457
4504
.10.1016/S0045-7825(00)00329-7
40.
Osher
,
S.
, and
Fedkiw
,
R.
,
2002
,
Level Set Methods and Dynamic Implicit Surfaces
,
Springer
,
New York
.
41.
Sethain
,
J. A.
,
1999
,
Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Version, and Material Science
,
Cambridge University Press
,
Cambridge
, UK.
42.
Sokolowski
,
J.
, and
Zolesio
,
J. P.
,
1992
,
Introduction to Shape Optimization: Shape Sensitivity Analysis
,
Springer
,
New York
.
43.
Belegundu
,
A. D.
, and
Chandrupatla
,
T. R.
,
1999
,
Optimization Concepts and Applications in Engineering
,
Prentice Hall
,
NJ
.
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