This paper studies optimal designs for vibrating structures using a moving isosurface threshold method (MIST). In the present study, a combination of strain and kinetic energy densities is selected as a response function of natural frequency and then formulations to maximize a specific frequency, frequency separation, and average-mean are derived. An efficient algorithm is developed to find a moving isosurface threshold level for evolving the design boundary and updating the weighting factor. The present algorithm coupled with commercial finite element analysis (FEA) software is used to study optimal designs for vibrating structures. The obtained optimal designs are fabricated and the experimental tests are conducted to validate the optimal topologies.

References

1.
Bendsoe
,
M. P.
, and
Sigmund
,
O.
,
2003
,
Topology Optimization: Theory, Methods and Applications
,
Springer
,
New York
.
2.
Bendsøe
,
M. P.
,
1989
, “
Optimal Shape Design as a Material Distribution Problem
,”
Struct. Optim.
,
1
(
4
), pp.
193
202
.10.1007/BF01650949
3.
Zhou
,
M.
, and
Rozvany
,
G. I. N.
,
1991
, “
The COC Algorithm—Part II: Topological, Geometrical and Generalized Shape Optimization
,”
Comput. Methods Appl. Mech. Eng.
,
89
(
1–3
), pp.
309
336
.10.1016/0045-7825(91)90046-9
4.
Rozvany
,
G. I. N.
,
Zhou
,
M.
, and
Birker
,
T.
,
1992
, “
Generalized Shape Optimization Without Homogenization
,”
Struct. Optim.
,
4
(
3–4
), pp.
250
252
.10.1007/BF01742754
5.
Xie
,
Y. M.
, and
Steven
,
G. P.
,
1993
, “
A Simple Evolutionary Procedure for Structural Optimization
,”
Comput. Struct.
,
49
(
5
), pp.
885
896
.10.1016/0045-7949(93)90035-C
6.
Huang
,
X.
,
Zuo
,
Z. H.
, and
Xie
,
Y. M.
,
2010
, “
Evolutionary Topological Optimization of Vibrating Continuum Structures for Natural Frequencies
,”
Comput. Struct.
,
88
(
5–6
), pp.
357
64
.10.1016/j.compstruc.2009.11.011
7.
Allaire
,
G.
, and
Jouve
,
F.
,
2005
, “
A Level-Set Method for Vibration and Multiple Loads Structural Optimization
,”
Comput. Methods Appl. Mech. Eng.
,
194
(
30–33
), pp.
3269
3290
.10.1016/j.cma.2004.12.018
8.
Sethian
,
J. A.
,
1999
, “
Fast Marching Methods
,”
SIAM Rev.
,
41
(
2
), pp.
199
235
.10.1137/S0036144598347059
9.
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
10.
Xia
,
Q.
,
Shi
,
T.
, and
Wang
,
M.
,
2011
, “
A Level Set Based Shape and Topology Optimization Method for Maximizing the Simple or Repeated First Eigenvalue of Structure Vibration
,”
Struct. Multidiscip. Optim.
,
43
(
4
), pp.
473
485
.10.1007/s00158-010-0595-6
11.
Wang
,
M. Y.
,
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
12.
Tong
,
L. Y.
, and
Lin
,
J. Z.
,
2011
, “
Structural Topology Optimization With Implicit Design Variable-Optimality and Algorithm
,”
Finite Elem. Anal. Des.
,
47
(
8
), pp.
922
932
.10.1016/j.finel.2011.03.004
13.
Vasista
,
S.
, and
Tong
,
L. Y.
,
2012
, “
Design and Testing of Pressurized Cellular Planar Morphing Structures
,”
AIAA J.
,
50
(
6
), pp.
1328
1338
.10.2514/1.J051427
14.
Tong
,
L.
, and
Luo
,
Q.
,
2014
, “
Selection of Integral Functions for Normal Mode Analysis in Topology Optimization
,”
Appl. Mech. Mater.
,
553
, pp.
795
800
.10.4028/www.scientific.net/AMM.553.795
15.
Vasista
,
S.
, and
Tong
,
L. Y.
,
2014
, “
Isosurface, Stiffness Design, Three Dimensional Topology Optimisation
,”
Adv. Comput. Mech.
,
553
, pp.
801
806
.10.4028/www.scientific.net/AMM.553.801
16.
Lai
,
F. K.
,
Mou
,
J. Q.
,
See
,
I. B. L.
, and
Lin
,
W. Z.
,
2013
, “
Modeling and Analysis of Notebook Computer Chassis Structure for Optimization of Component Mounting
,”
Int. J. Mech. Sci.
,
76
, pp.
60
69
.10.1016/j.ijmecsci.2013.08.012
17.
Vannucci
,
P.
,
2009
, “
Influence of Invariant Material Parameters on the Flexural Optimal Design of Thin Anisotropic Laminates
,”
Int. J. Mech. Sci.
,
51
(
3
), pp.
192
203
.10.1016/j.ijmecsci.2009.01.005
18.
Ma
,
Z.-D.
,
Cheng
,
H.-C.
, and
Kikuchi
,
N.
,
1994
, “
Structural Design for Obtaining Desired Eigenfrequencies by Using the Topology and Shape Optimization Method
,”
Comput. Syst. Eng.
,
5
(
1
), pp.
77
89
.10.1016/0956-0521(94)90039-6
19.
Andkjaer
,
J.
, and
Sigmund
,
O.
,
2013
, “
Topology Optimized Cloak for Airborne Sound
,”
ASME J. Vib. Acoust.
,
135
(
4
), p.
041011
.10.1115/1.4023828
20.
Du
,
J.
, and
Olhoff
,
N.
,
2007
, “
Topological Design of Freely Vibrating Continuum Structures for Maximum Values of Simple and Multiple Eigenfrequencies and Frequency Gaps
,”
Struct. Multidiscip. Optim.
,
34
(
2
), pp.
91
110
.10.1007/s00158-007-0101-y
21.
Ma
,
Z.-D.
,
Kikuchi
,
N.
, and
Cheng
,
H.-C.
,
1995
, “
Topological Design for Vibrating Structures
,”
Comput. Methods Appl. Mech. Eng.
,
121
(
1–4
), pp.
259
280
.10.1016/0045-7825(94)00714-X
22.
Niu
,
B.
,
Yan
,
J.
, and
Cheng
,
G.
,
2009
, “
Optimum Structure With Homogeneous Optimum Cellular Material for Maximum Fundamental Frequency
,”
Struct. Multidiscip. Optim.
,
39
(
2
), pp.
115
132
.10.1007/s00158-008-0334-4
23.
MSC Software
,
2011
, “
MD Nastran 2011 & MSC Nastran 2011 Dynamic Analysis User's Guide
,”
MSC Software Corp.
,
Santa Ana, CA
.
24.
Bathe
,
K.-J.
,
1996
,
Finite Element Procedures
,
Prentice Hall
,
Upper Saddle River, NJ
.
25.
Deaton
,
J.
, and
Grandhi
,
R.
,
2013
, “
A Survey of Structural and Multidisciplinary Continuum Topology Optimization: Post 2000
,”
Struct. Multidiscip. Optim.
,
49
(
1
), pp.
1
38
.10.1007/s00158-013-0956-z
26.
Sigmund
,
O.
, and
Petersson
,
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
27.
Bendsoe
,
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
28.
Huang
,
X.
, and
Xie
,
Y.-M.
,
2010
, “
A Further Review of ESO Type Methods for Topology Optimization
,”
Struct. Multidiscip. Optim.
,
41
(
5
), pp.
671
683
.10.1007/s00158-010-0487-9
29.
Bendsøe
,
M. P.
, and
Triantafyllidis
,
N.
,
1990
, “
Scale Effects in the Optimal Design of a Microstructured Medium Against Buckling
,”
Int. J. Solids Struct.
,
26
(
7
), pp.
725
741
.10.1016/0020-7683(90)90003-E
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