This study developed a discrete topology optimization procedure for the simultaneous design of ply orientation and thickness for carbon fiber reinforced plastic (CFRP)-laminated structures. A gradient-based discrete material and thickness optimization (DMTO) algorithm was developed by using casting-based explicit parameterization to suppress the intermediate void across the thickness of the laminate. A benchmark problem was first studied to compare the DMTO approach with the sequential three-phase design method using the free size, ply thickness, and stacking sequence of the laminates. Following this, the DMTO approach was applied to a practical design problem featuring a CFRP-laminated engine hood by minimizing overall compliance subject to volume-related and functional constraints under multiple load cases. To verify the optimized design, a prototype of the CFRP engine hood was created for experimental tests. The results showed that the simultaneous discrete topology optimization of ply orientation and thickness was an effective approach for the design of CFRP-laminated structures.

References

References
1.
Patel
,
S.
, and
Ahmad
,
S.
,
2017
, “
Probabilistic Failure of Graphite Epoxy Composite Plates Due to Low Velocity Impact
,”
ASME J. Mech. Des.
,
139
(
4
), p.
044501
.
2.
Beer
,
M.
,
Gloy
,
Y.-S.
,
Raina
,
M.
, and
Gries
,
T.
,
2014
, “
Construction of a Carbon Fiber Reinforced Weft Guide Bar for a Crochet Knitting Machine
,”
ASME J. Mech. Des.
,
136
(
6
), p.
064501
.
3.
Peel
,
L. D.
,
Mejia
,
J.
,
Narvaez
,
B.
,
Thompson
,
K.
, and
Lingala
,
M.
,
2009
, “
Development of a Simple Morphing Wing Using Elastomeric Composites as Skins and Actuators
,”
ASME J. Mech. Des.
,
131
(
9
), p.
091003
.
4.
Lee
,
J.-M.
,
Lee
,
K.-H.
,
Kim
,
B.-M.
, and
Ko
,
D.-C.
,
2016
, “
Design of Roof Panel With Required Bending Stiffness Using CFRP Laminates
,”
Int. J. Precis. Eng. Manuf.
,
17
(
4
), pp.
479
485
.
5.
Sadagopan
,
D.
, and
Pitchumani
,
R.
,
1997
, “
A Combinatorial Optimization Approach to Composite Materials Tailoring
,”
ASME J. Mech. Des.
,
119
(
4
), pp.
494
503
.
6.
Ghiasi
,
H.
,
Fayazbakhsh
,
K.
,
Pasini
,
D.
, and
Lessard
,
L.
,
2010
, “
Optimum Stacking Sequence Design of Composite Materials—Part II: Variable Stiffness Design
,”
Compos. Struct.
,
93
(
1
), pp.
1
13
.
7.
Huang
,
G.
,
Wang
,
H.
, and
Li
,
G.
,
2016
, “
An Efficient Reanalysis Assisted Optimization for Variable-Stiffness Composite Design by Using Path Functions
,”
Compos. Struct.
,
153
, pp.
409
420
.
8.
Adams
,
D. B.
,
Watson
,
L. T.
,
Gürdal
,
Z.
, and
Anderson-Cook
,
C. M.
,
2004
, “
Genetic Algorithm Optimization and Blending of Composite Laminates by Locally Reducing Laminate Thickness
,”
Adv. Eng. Software
,
35
(
1
), pp.
35
43
.
9.
Coburn
,
B. H.
, and
Weaver
,
P. M.
,
2016
, “
Buckling Analysis, Design and Optimisation of Variable-Stiffness Sandwich Panels
,”
Int. J. Solids Struct.
,
96
, pp.
217
228
.
10.
Schläpfer
,
B.
, and
Kress
,
G.
,
2014
, “
Optimal Design and Testing of Laminated Light-Weight Composite Structures With Local Reinforcements Considering Strength Constraints—Part I: Design
,”
Composites, Part A
,
61
, pp.
268
278
.
11.
Zhou
,
M.
,
Fleury
,
R.
, and
Kemp
,
M.
,
2010
, “
Optimization of Composite—Recent Advances and Application
,”
AIAA
Paper No. 2010-9272.
12.
Allaire
,
G.
, and
Delgado
,
G.
,
2016
, “
Stacking Sequence and Shape Optimization of Laminated Composite Plates Via a Level-Set Method
,”
J. Mech. Phys. Solids
,
97
, pp.
168
196
.
13.
Peeters
,
D.
,
van Baalen
,
D.
, and
Abdallah
,
M.
,
2015
, “
Combining Topology and Lamination Parameter Optimisation
,”
Struct. Multidiscip. Optim.
,
52
(
1
), pp.
105
120
.
14.
Lund
,
E.
, and
Stegmann
,
J.
,
2005
, “
On Structural Optimization of Composite Shell Structures Using a Discrete Constitutive Parametrization
,”
Wind Energy
,
8
(
1
), pp.
109
124
.
15.
Stolpe
,
M.
, and
Svanberg
,
K.
,
2001
, “
An Alternative Interpolation Scheme for Minimum Compliance Topology Optimization
,”
Struct. Multidiscip. Optim.
,
22
(
2
), pp.
116
124
.
16.
Wu
,
C.
,
Fang
,
J.
, and
Li
,
Q.
,
2018
, “
Multi-Material Topology Optimization for Thermal Buckling Criteria
,”
Comput. Methods Appl. Mech. Eng.
(in press).
17.
Lund
,
E.
,
2017
, “
Discrete Material and Thickness Optimization of Laminated Composite Structures Including Failure Criteria
,”
Struct. Multidiscip. Optim.
,
57
(
6
), pp.
2357
2375
.
18.
Sjølund
,
J. H.
,
Peeters
,
D.
, and
Lund
,
E.
,
2018
, “
A New Thickness Parameterization for Discrete Material and Thickness Optimization
,”
Struct. Multidiscip. Optim.
,
58
(
5
), pp.
1885
1897
.
19.
Niu
,
B.
,
Olhoff
,
N.
,
Lund
,
E.
, and
Cheng
,
G.
,
2010
, “
Discrete Material Optimization of Vibrating Laminated Composite Plates for Minimum Sound Radiation
,”
Int. J. Solids Struct.
,
47
(
16
), pp.
2097
2114
.
20.
Sørensen
,
R.
, and
Lund
,
E.
,
2015
, “
Thickness Filters for Gradient Based Multi-Material and Thickness Optimization of Laminated Composite Structures
,”
Struct. Multidiscip. Optim.
,
52
(
2
), pp.
227
250
.
21.
Wang
,
F.
,
Lazarov
,
B. S.
, and
Sigmund
,
O.
,
2011
, “
On Projection Methods, Convergence and Robust Formulations in Topology Optimization
,”
Struct. Multidiscip. Optim.
,
43
(
6
), pp.
767
784
.
22.
Gersborg
,
A. R.
, and
Andreasen
,
C. S.
,
2011
, “
An Explicit Parameterization for Casting Constraints in Gradient Driven Topology Optimization
,”
Struct. Multidiscip. Optim.
,
44
(
6
), pp.
875
881
.
23.
Bendsoe
,
M. P.
, and
Sigmund
,
O.
,
2013
,
Topology Optimization: Theory, Methods, and Applications
,
Springer Science & Business Media
, Berlin.
24.
Wu
,
C.
,
Gao
,
Y.
,
Fang
,
J.
,
Lund
,
E.
, and
Li
,
Q.
,
2017
, “
Discrete Topology Optimization of Ply Orientation for a Carbon Fiber Reinforced Plastic (CFRP) Laminate Vehicle Door
,”
Mater. Des.
,
128
, pp.
9
19
.
25.
Jorge
,
N.
, and
Stephen
,
J. W.
,
1999
,
Numerical Optimization
,
Springer-Verlag
, New York.
26.
Kulikov
,
G.
, and
Plotnikova
,
S.
,
2005
, “
Equivalent Single-Layer and Layerwise Shell Theories and Rigid-Body Motions—Part I: Foundations
,”
Mech. Adv. Mater. Struct.
,
12
(
4
), pp.
275
283
.
27.
Sigmund
,
O.
,
2007
, “
Morphology-Based Black and White Filters for Topology Optimization
,”
Struct. Multidiscip. Optim.
,
33
(
4–5
), pp.
401
424
.
28.
Youming
,
T.
,
Weipeng
,
H.
, and
Mingyang
,
S.
,
2016
, “
Topology Optimization and Lightweight Design of Engine Hood Material for SUV
,”
Funct. Mater.
,
23
(
4
), p.
631
.http://dspace.nbuv.gov.ua/handle/123456789/121499
You do not currently have access to this content.