The motivation of this paper is to develop a new and straightforward approach to provide a topology optimization solution for the layout design of stiffened plate/shell structures. Inspired by the similarities between the branching patterns in nature and stiffener layout patterns in engineering, a so-called material increasing design concept is first introduced to represent the topology configuration of the stiffened plate/shell structures. In addition, a well-founded mathematical explanation for the principles, properties, and mechanisms of adaptive growth behaviors of branching patterns in nature is derived from the Kuhn–Tucker conditions, leading to a novel optimality criterion which can serve engineering purposes for stiffener layout design. In this criterion, the common growth mechanism is described as an ideal ‘balanced point’ among individual branches in terms of their weight distribution. After characterizing the relationship between the growth behavior and mechanics self-adaptability, the reproduction of branching patterns in nature is implemented by a global coordinative model, which consists of several bottom programming models to find the optimal height distributions of individual branches and a top programming model to play a global coordinative role among them. The benefit and the advantages of the suggested method are illustrated with several 2D examples that are widely used in the recent research of topology optimization.

References

References
1.
Bendsoe
,
M. P.
, and
Kikuchi
,
N.
,
1988
, “
Generating Optimal Topologies in Structural Design Using a Homogenization Method
,”
Comput. Methods Appl. Mech Eng.
,
71
, pp.
197
224
.10.1016/0045-7825(88)90086-2
2.
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
, pp.
309
336
.10.1016/0045-7825(91)90046-9
3.
Yang
,
R. J.
, and
Chuang
,
C. H.
,
1994
, “
Optimal Topology Design Using Linear Programming
,”
Comput. Struct.
,
52
, pp.
265
275
.10.1016/0045-7949(94)90279-8
4.
Luo
,
J. H.
, and
Gea
,
H. C.
,
1998
, “
A Systematic Topology Optimization Approach for Optimal Stiffener Design
,”
Struct. Optim.
,
16
, pp.
280
288
.10.1007/BF01271435
5.
Luo
,
J. H.
, and
Gea
,
H. C.
,
1998
, “
Optimal Bead Orientation of 3D Shell/Plate Structures
,”
Finite. Elem. Anal. Des.
,
31
, pp.
55
71
.10.1016/S0168-874X(98)00048-1
6.
Krog
,
L. A.
, and
Olhoff
,
N.
,
1999
, “
Optimum Topology and Reinforcement Design of Disk and Plate Structures With Multiple Stiffness and Eigenfrequency Objectives
,”
Comput. Struct.
,
72
, pp.
535
563
.10.1016/S0045-7949(98)00326-5
7.
Ansola
,
R.
,
Canales
,
J.
,
Tarrago
,
J. A.
, and
Rasmussen
,
J.
,
2004
, “
Combined Shape and Reinforcement Layout Optimization of Shell Structures
,”
Struct. Multidiscip. Optim.
,
27
, pp.
219
227
.10.1007/s00158-004-0399-7
8.
Cheng
,
H. C.
,
Kikuchi
,
N.
, and
Ma
,
Z. D.
,
1994
, “
An Improved Approach for Determining the Optimal Orientation of Orthotropic Material
,”
Struct. Optim.
,
8
, pp.
101
112
.10.1007/BF01743305
9.
Ha
,
Y.
,
Kim
,
W.
, and
Cho
,
S.
,
2006
, “
Design Sensitivity Analysis and Topology Optimization Method Applied to Stiffener Layout in Hull Structures
,”
J. Ship Res.
,
50
(3)
, pp.
222
230
.
10.
Rais
,
R. M.
, and
Lokits
,
J.
,
2007
, “
Reinforcement Layout and Sizing Optimization of Composite Submarine Sail Structures
,”
Struct. Multidiscip. Optim.
,
34
, pp.
75
90
.10.1007/s00158-006-0066-2
11.
Chang
,
C. J.
,
Zheng
,
B.
, and
Gea
,
H. C.
,
2008
, “
Automated Design of Thin-Walled Packaging Structures
,”
Struct. Multidiscip. Optim.
,
35
, pp.
601
608
.10.1007/s00158-007-0170-y
12.
Wang
,
Q.
,
Liu
,
Z. Z.
, and
Gea
,
H. C.
,
2011
, “
New Topology Optimization Method for Wing Leading-Edge Rib
,”
J. Aircr.
,
48
, pp.
1741
1748
.10.2514/1.C031362
13.
Brown
,
J. H.
, and
West
,
G. B.
,
2000
,
Scaling in Biology
,
Oxford University Press
,
Oxford, New York
.
14.
Yoseph
,
B. C.
,
Liu
,
Z. Z.
, and
Gea
,
H. C.
,
2006
, “
Biomimetics—Using Nature to Inspire Human Innovation
,”
Bioinspir. Biomim.
,
1
, pp.
1
12
.10.1088/1748-3182/1/1/001
15.
Vincent
,
J. F. V.
,
2006
, “
Making a Mechanical Organism Being the Fourth in a Series of Essays on the Materials of Nature
,”
J. Bionic. Eng.
,
3
, pp.
43
58
.10.1016/S1672-6529(06)60006-1
16.
Bhushan
,
B.
,
2006
, “
Biomimetics: Lessons From Nature—an Overview
,”
Philos. Trans. R. Soc. London, Ser. A.
,
367
(1893)
, pp.
1445
1486
.10.1098/rsta.2009.0011
17.
Markus
,
M.
,
Thomas
,
S.
,
Olga
,
S.
, and
Heinrich
,
P.
,
2006
, “
Biomimetics and Technical Textiles: Solving Engineering Problems With the Help of Nature’s Wisdom
,”
Am. J. Bot.
,
93
, pp.
1455
1465
.10.3732/ajb.93.10.1455
18.
Honda
,
H.
,
1971
, “
Description of the Form of Trees by the Parameters of the Tree-LIke Body: Effects of the Branching Angle and the Branch Length on the Shape of Tree-Like Body
,”
J. Theor. Biol.
,
31
, pp.
331
338
.10.1016/0022-5193(71)90191-3
19.
Fisher
,
J. B.
, and
Honda
,
H.
,
1977
, “
Computer Simulation of Branching Pattern and Geometry in Terminalia (Combretaceae), a Tropical Tree
,”
Bot. Gaz.
,
138
, pp.
377
384
.10.1086/336937
20.
Schreiner
,
W.
,
Karch
,
R.
,
Neumann
,
M.
,
Neumann
,
F.
,
Szawlowski
,
P.
, and
Roedler
,
S.
,
2005
, “
Optimized Arterial Trees Supplying Hollow Organs
,”
Med. Eng. Phys.
,
28
, pp.
416
429
.10.1016/j.medengphy.2005.07.019
21.
Wang
,
Z.
,
Zhao
,
M.
, and
Yu
,
Q.
,
2001
, “
Modeling of Branching Structure of Plants
,”
J. Theor. Biol.
,
209
, pp.
383
394
.10.1006/jtbi.2001.2252
22.
Ding
,
X. H.
, and
Yamazaki
,
K.
,
2004
, “
Stiffener Layout Design for Plate Structures by Growing and Branching Tree Model (Application to Vibration-Proof Design)
,”
Struct. Multidiscip. Optim.
,
26
, pp.
99
110
.10.1007/s00158-003-0309-4
23.
Ding
,
X. H.
, and
Yamazaki
,
K.
,
2007
, “
Constructal Design of Cooling Channel in Heat Transfer System by Utilizing Optimality of Branch Systems in Nature
,”
ASME Trans. J. Heat Transfer
,
129
, pp.
245
255
.10.1115/1.2426357
24.
Chen
,
S.
,
1992
,
Some Modern Design Methods of Precise and Complex Structures
,
Beijing University of Aeronautics and Astronautics Press
,
Beijing
.
25.
Chen
,
S.
,
2008
,
Analysis, Synthesis and Optimization of Engineering Structural Systems
,
China Science Culture
,
Hong Kong
.
26.
Ansys, 2005, ANSYS
“10.0 User’s Manual,”
Ansys, Inc.
,
Canonsburg, PA
.
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