ANALYSIS OF FUNCTIONALLY GRADED CNT REINFORCED COMPOSITE CYLINDRICAL PANEL.pptx

A
Presentation
on
“ANALYSIS OF FUNCTIONALLY GRADED CNT REINFORCED
COMPOSITE CYLINDRICAL PANEL”
By
SHASHI BHUSHAN KUMAR
Roll no. 2134006
Programme- M.Tech.( Design Engineering )
Under the guidance
of
Dr. Saroj Kumar Sarangi
Associate Professor
Department of Mechanical Engineering
NIT Patna

OUTLINE OF PRESENTATION
• Introduction
• Motivation
• Literature Review
• Objective
• Materials and Methodology
• Result and discussion
• Conclusion
• References
November 23
ANALYSIS OF FG MWCNTCs PANEL 2

INTRODUCTION
Composite material:
Material system which consist of a mixture or a combination of two or more distinctly
differing material which are not soluble in each other and differ in or chemical
composition, or it consist of two or more phases on a microscopic scale and the
properties of composite material are designed to be superior to those of the constituent
material considered independently.
November 23 3
Fig.1 Composite Material
ANALYSIS OF FG MWCNTCs PANEL

November 23
Composites
Particulate
Random
Orientation
Preferred
orientation
Fibrous
Single layered
Continuous
long fiber
Unidirectional Bidirectional
Discontinuous
Short fiber
Unidirectional Bidirectional
Multi layered
Laminated
Hybrid
Laminated
Functionally
Graded
Classification of Composites

Functionally Graded Composite Materials:
Functionally graded composite materials (FGCMs) are inhomogeneous
materials, consisting of two (or more) different materials, engineered to have
a continuously varying spatial composition profile , or (FGMs) are
multifunctional materials, which contain a spatial variation in composition
and/or microstructure for the specific purpose of controlling variations in
thermal, structural or functional properties.
November 23
Fig.2 Various forms of gradation, including changes in (a) Volume fraction, (b) shape, (c) Orientation, and
(d) Constituent materials size

NEED OF STUDY
The aircraft, automobile and marine curved structural components such as curved
panels, open shells, conical shells and circular cylindrical shells structures are
predominantly subjected to dynamic forces, which may lead to bending or
resonance failure specifically in light weight structures made of matrix composites.
Therefore, the bending and free vibration analysis of composite elements is very
important field of research to predict the flexural strength and natural frequency,
both analytically and experimentally to avoid sudden failure.
CNT Composite polymer
Recently carbon nanotubes (CNTs) have attracted huge attention in many research
areas of science and engineering because of their high specific strength, stiffness at
very low density.
November 23

November 23
Fig.3- Applications of CNT composite [1]
Applications
Of
FGCNTCs
Panel
Aeronautical
Aerospace
Civel
Nuclear
Mechanical
Pipeline

LITERATURE REVIEW
Paper
Details
Objective Methodology
Result and
Discussion
Gap in
Literature
Vibration
analysis of
multiwalled
carbon
nanotube-
reinforced
composite
shell.
Subramani
and Ramam
oorthy. 2020
To investigate
the
enhancement
in natural
frequencies
and damping
of a
multiwalled
carbon
nanotubes
(MWCNTs)-
reinforced
composite
shell structure.
•Fabricated by
Traditional hand layup
method with vacuum
bagging and the
ultrasonication method
was deployed for the
proper dispersion of
MWCNT in the matrix
phase.
• Vibration analysis
Natural frequencies
and damping factor
are determined with
the assistance of the
DEWESoft 7.1.1®
software.
•Fundamental
natural frequencies
were increased by
20% at 1 wt% of
the MWCNT.
•Maximum
damping factor
value of 33%
attained at 2 wt%
of MWCNT.
• They were
concluded that
damping enhanced
by the
reinforcement of
MWCNT.
They did not
studied about
variation in
edge to
thickness
ratio,
boundary
condition, and
also not of
functionally
graded of
MWCNT in
composite
shell.
November 23

LITERATURE REVIEW(Contin…)
Paper Details Objective Methodology
Result and
Discussion
Gap in
Literature
Experimental
Investigation of
Mechanical
Properties on
Multiwalled
Carbon
Nanotube
Reinforced
Composites
S. Dinesh et al.
2017
Determine
mechanical
properties such
as: tensile
strength ,
compressive
strength and
flexural strength
variation with
different weight
percentage of
multiwalled
carbon nanotube
.
Samples were
fabricated by
adopting simple
hand layup
technique with
four different
composition as
per ASTM
standards,
And mechanical
properties are
evaluated using
computerized
universal testing
machine .
Tensile
properties and
flexural
properties are
increased with
increase in
percentage of
Multiwalled
carbon
nanotubes while
the compressive
property does
not vary with the
carbon nanotube
fibers.
They neither
performed
flexural strength
test nor vibration
analysis.
November 23

Paper
Details
Result and
Discussion
Gap in
Literature
Free and
forced
vibration
analysis of
laminated
functionall
y graded
CNT-
reinforced
composite
cylindrical
panels.
Arani et al.
2021.
Aims to
investigate
the effect of
volume
fraction,
distribution
types,
orientation of
CNT and
geometrical
parameters on
the natural
frequencies of
the panel for
different
boundary
conditions.
The set of
governing
equations and
boundary
conditions is
derived using
Hamilton’s
principle and is
solved numerically
using generalized
differential
quadrature method
and Newmark beta
method.
FG-X has the
maximum and
FG-O has the
minimum
Natural
frequencies and
it rise as value of
the volume
fraction of CNTs
increases, and
increase in
thickness.
They didn’t
studied
experimentally
and also not
about flexural
strength.
November 23

Paper
Details
Result and
Discussion
Gap in
Literature
Static and
dynamic of
carbon
nanotube
reinforced
functionall
y graded
cylindrical
panels.
Zhang et al.
2019
To revealed the
influences of
volume fraction,
types of
distributions of
CNT, different
boundary
conditions,
edge-to-radius
ratio and
thickness on
flexural strength
and free
vibration
responses of the
panels.
1. Material
properties
of nanocomposite
panels are
estimated by
employing an
equivalent continu
um model based
on the Eshelby–
Mori–Tanaka
approach.
2. The mesh-free kp-
Ritz is employed
for analysis of
flexural strength
and free vibration
of FG-CNTRC
cylindrical panels.
They reveal that
volume fractions
of carbon
nanotubes, edge-
to-radius ratios,
thickness,
boundary
conditions and
distribution type
of CNTs have
significant
influences on the
flexural strength
and free vibration
responses of the
panels
They didn’t
investigated
experimentally
and also not
performed any
comparison
study with
published
literature.
November 23
11

OBJECTIVES OF WORK
To the best of our knowledge currently there is no existing literature that
provides both numerical and experimental analyses of the free
vibration and bending characteristics of FG-MWCNTs cylindrical
panels, encompassing both material characterization and structural
modeling. To fill up the lacunae of existing literature, the aim of current study
is to:
1. Fabrication of Panel by centrifugal Casting method.
2. Design panel in ANSYS software and estimate material properties of
different layer by a micromechanical model.
3. Explore the bending and free vibration characteristics of the FG-
MWCNTs cylindrical panel through experimentations and numerical
method considering the different parameters like weight percentage of
CNT, aspect ratio, edge to thickness ratio and boundary conditions.
4. Establish the accuracy of present experimental and numerical solution by
comparison studies with published literature.
November 23

MATRIX
Epoxy:
Lapox L-12 is a liquid, unmodified epoxy resin of medium viscosity.
Hardener:
Lapox K-6 is a light-yellow aliphatic polyamine hardener.
Fig.4 Epoxy And Hardener
November 23
ANALYSIS OF FG MWCNTCs
PANEL
13
Materials of our Composites

Carbon nanotube: Carbon nanotubes (CNTs) are cylinder-shaped allotropic forms of
carbon, most widely produced under chemical vapor deposition. They possess astounding
chemical, electronic, mechanical, and optical properties in nanotechnology.
Single-wall carbon nanotubes (SWCNTs): SWCNTs one of the allotropes of carbon,
intermediate between fullerene cages and flat graphene, with diameters in the range of a
nanometer. SWCNTs are known for high strength but high production cost and chemical
instability.
Multi-wall carbon nanotubes (MWCNTs): consisting of nested single-wall carbon
nanotubes weakly bound together by van der Waals interactions in a tree ring-like structure.
MWCNTs are chemically stable and owing to low production cost, largely used in scientific
research works and industries.
Fig. 5 Schematic representation of SWCNT & MWCNT
November 23
SWCNT MWCNT
0.5 to 1.5nm >100nm
FIBER
14

November 23
Fig.6 MWCNT with their specification

November 23
Model for Experiment
The horizontal centrifugal casting
method was used to fabricate the test
samples. A hollow steel cylindrical
mould was created and assembled for
the purpose.
Design of the set up
Mould Making
Mixture of material
Pouring
Solidification and
Cooling
Removal of Mold
Finishing Casting
Cleaning and Inspection
Fig.8 Flow chart of casting process for FGM
hollow cylinder
Fig.7 Presents Isometric view of the hollow cylinder used in
centrifugal casting
METHODOLOGY

November 23 ANALYSIS OF FG MWCNTCs PANEL 17
Part name Specification
Cylinder Diameter (Internal) 10cm
Diameter (External) 15cm
Mould length 10cm
Motor Speed 350rpm
Supply 240V , 50HZ
Input Voltage AC 220
Bearing Internal diameter 10cm
External diameter 15cm
Mould length 10cm
Table 1 Specification of mould
 The matrix Lapox L-12 and K-6 hardener are mixed in a 1: 10 ratio with various weight
proportions of MWCNT.
 The composites are made using horizontal centrifugal casting Method.
 To provide a good surface finish and facilitate the removal of the composite from the
mould, a Mylar sheet {Electric motor winding insulating white paper; Density (kg/m³ ):.
160 ;Thermal Conductivity: 0.055~0.180W/m.k ; Shrinkage (1800℉, 3h)} should be
placed on the inside portion of the mould.
 The MWCNT fibres have a purity of more than 98%, an average length of 10 m, and an
outside and inside diameter of 15-10 nm.

November 23
Fig.9 Workshop Image of Centrifugal Casting Setup
Pouring basin
Mould Cavity
Runner

November 23
Fig.10 Laboratory image of molding equipment
Weighting machine
Measuring scale
Flask

November 23
Fig. 11 Cylindrical Shell molding box ( made up of steel and wood )
Fig. 12 Cylindrical shell specimen of FG-CNTRC and Pure Epoxy

November 23
Fig. 13 Cylindrical panel after finishing and at 90degree angle (a)
Pure Epoxy (b) FG-CNT Composite
(a) (b)

November 23
Free vibration test for determination of natural frequency
The vibration tests are performed using FFT Analyzer (DAQ , OROS), modal impact
hammer and accelerometer. The specimen were excited with the help of modal impact hammer
and subsequent vibration is received by the accelerometer (B&K 4507). The signals are supplied
to the FFT Analyzer and frequency spectrums were obtained with the help of PULSE software.
Both frequency response function (FRF) and auto spectrum (amplitude-frequency) spectrum are
observed along with coherence plots.
Fig.14 Block diagram of experimental vibration test
FG Composite
Specimen Accelerometer
DAQ(OROS)
Model
hammer
Signal Processing in
NV Gate software

November 23
CPU
(DAQ) OROS
Modal Hammer
Accelerometer FG Panel
PC for Signal Processing
Fig. 15 Experimental setup of vibration analyzer

November 23
(c) Accelerometer (d) Modal Impact Hammer
(a) Display unit (b) OROS FFT Analyzer
Fig. 16 Vibration measurement test setup unit (a, b, c and d)

November 23
Fig.17 Vibration response of panel (pure epoxy)

November 23
Fig.18 Vibration response of FGCNT Panel

November 23
Development of Simulation Model
Functionally graded composite cylindrical panel is developed taking various layers in
ANSYS software. To develop the model in ANSYS, following the steps below:-
Geometry Design/Modelling
Define material used
END
Define support condition
Define Meshing Method
START
Open ANSYS Workbench 17.2
Use Modal analysis System
Fig. 19 Procedure
adopted in ANSYS for
static analysis and modal
analysis

November 23
Simulation Model OF ANSYS
 The ANSYS software has been utilized to model a panel with an inner
diameter of 100mm and height of 100mm, consisting of 5 distinct cylindrical
strips, each with a thickness of 0.5mm.
 These strips have been modeled separately, but with perfect matching
achieved through the application of tie constraints within the ANSYS
software.
 In order to ensure accurate simulation of the panel's behavior, a suitable
material comprising MWCNT, epoxy (Lapox L-12), and hardener (K-6) has
been selected and identified as solid 186 element type.
Fig.20 Composite Cylindrical panel Fig.21 Model of Composite cylindrical panel with made
of different strip

November 23
 Model divided into several elements/divisions
 Meshing(Quadrilateral) applied to each element
 Mesh fineness determines analysis precision/efficiency
 Numerical analysis used in finite element simulations
 Optimum mesh size determined
 Fine mesh [1x1] used for accurate results (Fig. 22)
 Each end of cylindrical panel examined
 Three different boundary conditions: Clamped (C), Pin (P), Free (F).
Fig.22 Meshed model of composite cylindrical panel Fig.23 C-F boundary condition.

November 23
First, a convergence analysis is performed in order to optimize modeling, and
presented in Table 2 and 3.
No. of
Layers
Non-dimensional deflection at its
maximum (w’=w/h)
C-C C-F H-H
6 0.2986 0.66232 0.3726
8 0.3092 0.74561 0.3846
10 0.3156 0.82344 0.3945
12 0.3160 0.82380 0.3949
Mesh
size
Non-dimensional deflection at
its maximum (w’=w/h)
C-C C-F H-H
0.5x0.5 0.2986 0.6623 0.3826
1x1 0.2992 0.6656 0.3846
5x5 0.3156 0.7234 0.3945
10x10 0.3260 0.8238 0.4049
Table 2: Convergence study for
different layers for UD
Table 3: Convergence study for
discretization of model for UD

November 23
Material properties
The material properties of the composite cylindrical shells are explained in Table
4-5. The other required properties are calculated using extended rule of mixture.
Table:-4 Table:-5
S.No. Properties[8] CNT Matrix
1. 2100 1190
2. 5646.6 2.5
3 . 7080 2.5
4. 0.175 0.3
5. 1944.5 0.7267
CNT
Efficiency
Parameter[8] 0.12 0.17 0.28
0.137 0.142 0.141
1.022 1.626 1.585
0.715 1.138 1.109

November 23
Three types of grading pattern of CNT were investigated as uniformly distributed,
Type-X distribution and Type-Δ.
Distributed Uniformly Type-X Type-Δ
Fig. 24 Schematic diagram of grading pattern of FGCNTRC material
The fraction of volume is defined as follows :
For the UD-CNT,
For the FG-XCNT,
For the UD-CNT,
This variation is explained by mathematical equation as:

November 23
r
θ
L
h
Fig. 25 FG-CNTRC cylindrical Panel
Dimensional parameter such as inner radius (r), Thickness (h), Length (L) and angle
between the arc length (Ɵ) are taken for numerical analysis for present study as
depicted with the help of schematic diagram of cylindrical panel.

November 23
Result and Discussion;
Bending Analysis
• Now performing bending analysis by applying different boundary condition for
UD-CNT and FG-CNT Cylindrical panel and comparison studies have been
performed against published result to validate the computational result used in this
study.
• It should be pointed out that the overall CNT volume percentage in the analysis is
indicated by the variable Vtcnt. The panel has a boundary condition in which four
of its edges are clamped while the other four are simply supported.
Table 6 Maximum deflections using present model and available results [5]
Boundary
Condition
Vtcnt
0.11 0.17
ANSYS Exp. Ref.[5] ANSYS Exp. Ref.[5]
SSSS UD 1.1153 1.2458 1.1279 0.7125 0.7896 0.7270
FG-Δ 1.5542 1.5964 1.6002 1.0145 1.0952 1.0486
FG-X 0.7698 0.7936 0.7765 0.5124 0.5654 0.5059
CCCC UD 0.2432 0.2635 0.2500 0.1624 0.1987 0.1625
FG-Δ 0.3371 0.3654 0.3482 0.2147 0.2545 0.2281
FG-X 0.1723 0.2541 0.1800 0.1154 0.1547 0.1165

November 23
Ansys Exp. Ref.[5]
Fig.26 Non-dimensional deflection for FGCNTRC cylindrical panel for SSSS boundary
condition
Result and Discussion(contie…)

November 23
VCNT
0.11 0.17 0.28
SSSS UD 1.1153 0.7125 0.5246
FG-Δ 1.5542 1.0145 0.7231
FG-X 0.7698 0.5124 0.3216
CCCC UD 0.2432 0.1624 0.1245
FG-Δ 0.3371 0.2147 0.1758
FG-X 0.1723 0.1154 0.1015
• When subjected to a load that is evenly distributed and has a pressure of -0.1 MPa.
• The following values have been determined for the size of the panels: = 0.1 rad, h =
0.002 m, h/R = 0.002, and L/R = 0.1.
Table 7 Non dimensional deflection w/h
of FGCNTRC cylindrical Panels with
different volume fraction of CNTs .
L/R
0.1 0.15 0.2 0.25 0.3
SSSS UD 1.1153 40.6523 10.4590 18.9196 24.9542
FG-Δ 1.5542 6.0124 12.4256 19.6625 24.7250
FG-X 0.7698 3.4526 8.83325 14.1450 21.1456
CCCC UD 0.2432 0.9542 2.3456 3.7524 4.7265
FG-Δ 0.3371 1.3325 2.9654 4.2250 4.9562
FG-X 0.0987 0.7825 1.8542 3.11245 4.1123
Table 8 Deflection w/h of FGCNTRC cylindrical
Panels for edge-to-thickness ratio (L/R) at of
CNTs

November 23
L/R
0.1 0.15 0.2 0.25 0.3
SSSS UD 0.07530 0.3214 0.7724 1.2841 1.7254
FG-Δ 0.1126 0.4216 0.9124 1.4125 1.8001
FG-X 0.0559 0.2474 0.6212 1.0245 1.4521
CCCC UD 0.0234 0.0874 0.1725 0.2965 0.3584
FG-Δ 0.0321 0.1125 0.2241 0.3241 0.3838
FG-X 0.0189 0.0645 0.1542 0.2475 0.3214
Table 9 Nondimensional deflection w/h of FGCNTRC cylindrical Panels
for edge to thickness ratio (L/R) and thickness h=4mm

November 23
Fig. 27 Deflection (w/h) of FGCNTRC panels along the centreline for (a)
Different grading patterns, (b) different volume fraction

November 23
Vibration Analysis
• Now performing vibration analysis by applying different boundary condition
for UD-CNT and FG-CNT Cylindrical panel and comparison studies have
been performed against published result to validate the computational result
used in this study.
• First, a comparison analysis for a clamped cylindrical panel is performed.
Table 5.6 and Fig 5.8show comparison of the present mesh-free results and
solutions of Au and Cheung for first six frequencies, using isoparametric
spline finite strip method. It can be seen that a good agreement is obtained.
Boundary Condition
Mode CCCC SSSS
Present Exp. Ref.[6] Present Exp. Ref.[6]
1 35.8459 35.6452 36.849 17.6401 16.8754 17.850
2 40.6523 39.5481 40.924 22.1543 21.4586 22.073
3 50.3541 49.5786 51.825 33.1756 32.5459 33.285
4 69.8454 68.4567 70.638 50.3489 49.8654 51.778
5 91.2254 90.3547 91.445 64.1573 63.5481 65.121
6 93.6547 92.4651 93.611 66.7892 65.8749 67.264
Table 10 Comparison for nondimensional first six frequencies for a cylindrical panel

November 23
Fig.28 Non-dimensional frequency for FGCNTRC cylindrical panel for CCCC
boundary condition
Non-dimensional frequency parameters ( ) of various FG-CNTRC
panels with four edges simply supported and four edges clamped boundary
conditions are shown
Ansys Exp. Ref.[6]

November 23
Mode CNT Distributuion
UD FG-Δ FG-X
SSSS 1 17.6401 14.2789 21.1576
2 22.1543 19.1254 24.0579
3 33.1756 31.2547 34.6523
4 50.3489 50.4211 53.2587
5 64.1573 54.2546 75.6849
6 66.7892 57.2489 77.4448
CCCC 1 35.8459 30.4594 41.3691
2 40.6523 35.4869 45.6336
3 50.3541 47.9865 55.4789
4 69.8454 67.2354 74.6895
5 91.2254 78.9456 101.2571
6 93.6547 81.5456 103.4785
Mode CNT Distribution
UD FG-Δ FG-X
SSSS 1 19.6589 13.5841 22.6691
2 23.6548 18.9654 28.8454
3 33.6985 31.2591 44.6359
4 47.1236 47.1159 67.8543
5 47.3214 47.6584 67.4591
6 51.2469 47.9653 70.8549
CCCC 1 14.6681 12.6325 27.5421
2 18.6674 17.6986 37.3025
3 23.5456 23.2356 47.1251
4 23.0589 23.5456 46.3219
5 29.1456 26.9854 57.8631
6 38.4569 32.6987 74.2291
Table 12 Nondimensional frequency of various
FGCNTRC cylindrical Panels with thickness h= 4mm
Table 11 Nondimensional frequency of various FG-
CNTRC Cylindrical Panel with thickness h= 2.5mm.
 The convergence and comparison studies verified the correctness and accuracy of
the current solution approach which will be applied to generate the solution for
FG∆-CNT and FGX-CNT.

November 23
Fig.29 Effect of volume fraction of CNTs on frequency
parameters of FG-CNTRC panels with four edges clamped
boundary conditions.
Fig.30 Effect of edge-to-thickness ratio (L/h) on frequency
parameters of FG-CNTRC panels with four edges simply
supported boundary conditions.

November 23
Fig.31 Effect of edge-to-thickness ratio (L/h) on frequency
parameters of FG-CNTRC panels with four edges clamped
boundary conditions
Fig.32 Effect of volume fraction of CNTs on frequency
parameters of FG-CNTRC panels with four edges simply
supported boundary conditions.

November 23
The bending and vibration of FG-CNTRC cylindrical panels under mechanical loading
involves examining the effects of various factors on the material's performance. The
following factors are considered in the analysis:-
 Volume fraction of carbon nanotubes: The higher the volume fraction of CNTs, the
greater the material's flexural strength and vibration characteristic.
 Edge-to-radius ratio: Panels with a larger edge-to-radius ratio tend to exhibit higher
bending and lower natural frequency.
 Thickness: Thicker panels tend to be the greater the material's flexural strength and
vibration characteristic than thinner ones.
 Boundary conditions: Panels with simply supported four edges exhibit higher bending
and lower natural frequency while vice versa with four clamped edges.
 Distribution types of CNTs: The cylindrical panels of the FG-Δ variety exhibited the
lowest frequency parameters and the greatest central deflection, while the FG-X type
panels had the highest frequency parameters and the least central deflection.
Conclusions

November 23
List Of Publications
1) Shashi Bhushan Kumar, Manish Kumar and Saroj Kumar Sarangi. "Bending
Analysis of Multiwall Carbon Nanotube Reinforced Functionally Graded
Composite Cylindrical Shells" International Conference on Mechanical Design
and Manufacturing (ICMDM 2023) held at IIEST Shibpur, India during 27th –
28th April 2023.
2) Manish Kumar, Shashi Bhushan Kumar and Saroj Kumar Sarangi. "Free
Vibration of Carbon Nanotube Reinforced Functionally Graded Shells."
International Conference on Mechanical Design and Manufacturing (ICMDM
2023) held at IIEST Shibpur, India during 27th – 28th April 2023.

References
1) Anand Joy, Susy Varughese, Sankaran Shanmugam, and Prathap Haridoss ,
Multiwalled Carbon Nanotube Reinforced Epoxy Nanocomposites for Vibration
Damping , Department of Metallurgical and Materials Engineering, IIT Madras,
2019.
2) Asha Patel, Rahul Das and Shishir Kumar Sahu, Experimental and Numerical Study
on Free Vibration of Multiwall Carbon Nanotube Reinforced Composite Plates ,
National Institute of Technology, Rourkela, 2020.
3) Arash Montazeri, Jafar Javadpour, Alizera Khavandi, Abbas Tcharkhtchi, Ali
Mohajeri, Mechanical properties of multi-walled carbon nanotube/epoxy composites
, Materials and Design, Elsevier, 2010.
4) Subramani, M., & Ramamoorthy, M. (2020). Vibration analysis of the multi-walled
carbon nanotube reinforced doubly curved laminated composite shallow shell
panels: An experimental and numerical study. Journal of Sandwich Structures &
Materials, 109963621990048..
5) J. Gou , B. Minaie , B. Wang ,J. Liang ,C. Zhang , Computational and experimental
study of interfacial bonding of single-walled nanotube reinforced composites,
Computational Material. Science 31(2004) 225-236.
6) S.H. Shen, Nonlinear bending of functionally graded carbon nanotube reinforced
composite plates in thermal environments, Compos Struct 91(2009) 9–19.
November 23

November 23
References (contie…)
7) Zhang, L. W., Z. X. Lei, K. M. Liew, and J. L. Yu. "Static and dynamic of carbon
nanotube reinforced functionally graded cylindrical panels." Composite
Structures 111 (2014): 205-212.
8) Kumar, Manish, and Saroj Kumar Sarangi. "Finite Element Analysis of Carbon
Nanotubes Reinforced Smart Functionally Graded Beam." In Key Engineering
Materials, vol. 928, pp. 127-135. Trans Tech Publications Ltd, 2022.
9) Arani, Ali Ghorbanpour, FarhadKiani, and Hassan Afshari. "Free and forced
vibration analysis of laminated functionally graded CNT-reinforced composite
cylindrical panels." Journal of Sandwich Structures & Materials 23, no. 1 (2021):
255-278

Thank you!
November 23

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