The material mask overlay strategy employs negative masks to create material voids within the design region to synthesize perfectly binary (0-1), well connected continua. Previous implementations use either a constant number of circular masks or increase the latter via a sequence of subsearches making the procedure computationally expensive. Here, a modified algorithm is presented wherein the number of masks is adaptively varied within a single search, in addition to their positions and sizes, thereby generating material voids, both efficiently and effectively. A stochastic, mutation-only search with different mutation strategies is employed. The honeycomb parameterization naturally eliminates all subregion connectivity anomalies without requiring additional suppression methods. Boundary smoothening as a new preprocessing step further facilitates accurate evaluations of intermediate and final designs with moderated notches. Thus, both material and contour boundary interpretation steps, that can alter the synthesized solutions, are avoided during postprocessing. Various features, e.g., (i) effective use of the negative masks, (ii) convergence, (iii) mesh dependency, (iv) solution dependence on the reaction force, and (v) parallel search are investigated through the synthesis of small deformation fully compliant mechanisms that are designed to be robust under the specified loads. The proposed topology search algorithm shows promise for design of single-material large deformation continua as well.

References

References
1.
Bendsøe
,
M. P.
, and
Kikuchi
,
N.
, 1998, “
Generating Optimal Topologies in Structural Design Using a Homogenization Method
,”
Comput. Methods Appl. Mech. Eng.
,
71
(
2
), pp.
197
224
.
2.
Bendsøe
,
M. P.
, 1995,
Optimization of Structural Topology, Shape, and Material,
Springer
,
Berlin
.
3.
Diaz
,
A.
, and
Sigmund
,
O.
, 1995, “
Checkerboard Patterns in Layout Optimization
,”
Struct. Optim.
,
10
, pp.
40
45
.
4.
Jog
,
C. S.
, and
Haber
,
R. B.
, 1996, “
Stability of Finite Element Models for Distributed-Parameter Optimization and Topology Design
,”
Comput. Methods Appl. Mech. Eng.
,
130
, pp.
203
226
.
5.
Sigmund
,
O.
, 1994, “
Design of Material Structures Using Topology Optimization
,” DCAMM Report S.69, Department of Solid Mechanics, Ph.D. thesis, DTU, Denmark.
6.
Sigmund
,
O.
, 2007, “
Morphology-Based Black and White Filters for Topology Optimization
,”
Struct. Multidiscip. Optim.
,
33
, pp.
401
424
.
7.
Poulsen
,
T. A.
, 2003, “
A New Scheme for Imposing a Minimum Length Scale in Topology Optimization
,”
Int. J. Numer. Methods Eng.
,
57
, pp.
741
760
.
8.
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
, pp.
238
254
.
9.
Rahmatalla
,
S. F.
, and
Swan
,
C. C
, 2004, “
A Q4/Q4 Continuum Structural Topology Optimization Implementation
,”
Struct. Multidiscip. Optim.
,
27
, pp.
130
135
.
10.
Yoon
,
G. H.
,
Kim
,
Y. Y.
,
Bendsøe
,
M. P.
, and
Sigmund
,
O.
, 2004, “
Hinge-Free Topology Optimization With Embedded Translation-Invariant Differentiable Wavelet Shrinkage
,”
Struct. Multidiscip. Optim.
,
27
, pp.
139
150
.
11.
Saxena
,
R.
, and
Saxena
,
A.
, 2003, “
On Honeycomb Parameterization for Topology Optimization of Compliant Mechanisms
,”
ASME Design Engineering Technical Conferences, Design Automation Conference
,
Chicago, IL
, Sep. 2–6, 2003, Paper No. DETC2002/DAC-48806.
12.
Saxena
,
R.
, and
Saxena
,
A.
, 2007, “
On Honeycomb Representation and SIGMOID Material Assignment in Optimal Topology Synthesis of Compliant Mechanisms
,”
Finite Elem. Anal. Design
,
43
(
14
), pp.
1082
1098
.
13.
Langelaar
,
M.
, 2007, “
The Use of Convex Uniform Honeycomb Tessellations in Structural Topology Optimization
,”
Proceedings of the 7th World Congress on Structural and Multidisciplinary Optimization
,
Seoul, South Korea
, May 21–25, 2007.
14.
Talischi
,
C.
,
Paulino
,
G. H.
, and
Chau
,
H. Le
, 2009, “
Honeycomb Wachspress Finite Elements for Structural Topology Optimization
,”
Struct. Multidiscip. Optim.
,
37
(
6
), pp.
569
583
.
15.
Cook
,
R. D.
, 1995,
Finite Element Modeling For Stress Analysis
,
Wiley
,
New York
.
16.
Yin
,
L.
, and
Ananthasuresh
,
G. K.
, 2001, “
Topology Optimization of Compliant Mechanisms With Multiple Materials Using a Peak Function Material Interpolation Scheme
,”
Struct. Multidiscip. Optim.
,
23
, pp.
49
62
.
17.
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
.
18.
Wang
,
M. Y.
,
Chen
,
S. K.
,
Wang
,
X. M.
, and
Mei
,
Y. L.
, 2005, “
Design of Multimaterial Compliant Mechanisms Using Level-Set Methods
,”
ASME J. Mech. Des.
,
127
, pp.
941
956
.
19.
Luo
,
J. Z.
,
Luo
,
Z.
,
Chen
,
S. K.
,
Tong
,
L. Y.
, 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
.
20.
Allaire
,
G.
,
Jouve
,
F.
, and
Toader
,
A-M.
, 2004, “
Structural Optimization Using Sensitivity Analysis and a Level-Set Method
,”
J. Comput. Phys.
,
194
, pp.
363
393
.
21.
Hull
,
P. V.
, and
Canfield
,
S.
, 2006, “
Optimal Synthesis of Compliant Mechanisms Using Subdivision and Commercial FEA
,”
ASME J. Mech. Des.
,
128
, pp.
337
348
.
22.
Svanberg
,
K.
, and
Werme
,
M.
, 2007, “
Sequential Integer Programming Methods for Stress Constrained Topology Optimization
,”
Struct. Multidiscip. Optim.
,
34
, pp.
277
299
.
23.
Stolpe
,
M.
, and
Svanberg
,
K.
, 2003, “
Modelling Topology Optimization Problems as Linear Mixed 0–1 Programs
,”
Int. J. Numer. Methods Eng.
,
57
, pp.
723
739
.
24.
Saxena
,
A.
, 2009, “
A Material-Mask Overlay Strategy for Continuum Topology Optimization of Compliant Mechanisms Using Honeycomb Discretization
,”
ASME J. Mech. Des.
,
130
(
8
), p.
082304
.
25.
Jakiela
,
M. J.
,
Chapman
,
C.
,
Duda
,
J.
,
Adewuya
,
A.
, and
Saitou
,
K.
, 2000, “
Continuum Structural Topology Design With Genetic Algorithms
,”
Comput. Methods Appl. Mech. Eng.
,
186
, pp.
339
356
.
26.
Jain
,
C.
, and
Saxena
,
A.
, 2009, “
An Improved Material-Mask Overlay Strategy for Topology Optimization of Structures and Compliant Mechanisms
,”
ASME J. Mech. Des.
,
132
, p.
061006
.
27.
Gilat
,
A.
, 2004,
MATLAB: An Introduction With Applications
,
2nd ed.
,
Wiley
,
New York
.
28.
Kreyszig
,
E.
, 1999,
Advanced Engineering Mathematics
,
8th ed.
,
Wiley
,
New York
.
29.
Rai
,
A. K.
,
Saxena
,
A.
, and
Mankame
,
N. D.
, 2009, “
Unified Synthesis of Compact Planar Path-Generating Linkages With Rigid and Deformable Members
,”
Struct. Multidiscip. Optim.
,
41
, pp.
863
879
.
30.
Rai
,
A. K.
,
Saxena
,
A.
, and
Mankame
,
N. D.
, 2007, “
Synthesis of Path Generating Compliant Mechanisms Using Initially Curved Frame Elements
,”
ASME J. Mech. Des.
,
129
, pp.
1056
1063
.
31.
Reddy
,
B. V. S.
,
Nagendra
, and
Saxena.
,
A.
, 2010, “
Automated Design Of Contact-Aided Compliant Mechanisms Using Initially Curved Frame Elements
,”
ASME Design Engineering and Technical Conferences
,
Montreal, Canada
, Aug. 15–18, 2009, Paper No. DETC-29172.
32.
Chandrupatla
,
T. R.
, and
Ashok
,
D. B.
, 1996,
Introduction to Finite Elements in Engineering
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
33.
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
, p.
011003
.
34.
Saxena
,
A.
, and
Ananthasuresh
,
G. K.
, 2000, “
On an Optimal Property of Compliant Topologies
,”
Struct. Multidiscip. Optim.
,
19
, pp.
36
49
.
35.
Hetrick
,
J. A.
, and
Kota
,
S.
, 1999, “
An Energy Formulation for Parametric Size and Shape Optimization of Compliant Mechanisms
,”
ASME J. Mech. Des.
,
121
(
2
), pp.
229
234
.
36.
Chen
,
S.
, and
Wang
,
M. Y.
, 2007, “
Designing Distributed Compliant Mechanisms With Characteristic Stiffness
,”
Proceedings of the ASME 2007 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference
, Paper No. DETC2007–34437.
37.
Rahmatalla
,
S.
, and
Swan
,
C. C.
, 2005, “
Sparse Monolithic Compliant Mechanisms Using Continuum Structural Topology Optimization
,”
Int. J. Numer. Methods Eng.
,
62
, pp.
1579
1605
.
38.
Kobayashi
,
M.
,
Nishiwaki
,
S.
,
Izui
,
K.
, and
Yoshimura
,
M.
, 2009, “
An Innovative Design Method for Compliant Mechanisms Combining Structural Optimisations and Designer Creativity
,”
J. Eng. Design
,
20
(
2
), pp.
125
154
.
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