Buckling and postbuckling of cnt-reinforced composite sandwich cylindrical panels subjected to axial compression in thermal environments

e and almost identical postbuckling curves. Subsequently, it is realized 
from Fig. 5 that critical loads and postbuckling paths are significantly reduced when ratio 
is enhanced, especially as increases from 0.1 to 0.15. In addition, the load carrying capability 
of sandwich panels is decreased at elevated temperature ( K) and detrimental effect of 
temperature is more pronounced for smaller values of ratio. 
/fh
/fh T
FG -L
/f h
/fh h
400T =
/fh h
Fig. 5. Effects of h f /h ratio on the postbuck-
ling behavior of sandwich cylindrical panel
with CNTRC face sheets under axial compres-
sion
Figs. 4 and 5 show the effects of CNT distribution patterns, thickness of face sheet-to-
total thickness h f /h r tio a d enviro ment tempe ature T on the postbuckling behavior
of sandwich panels of type A with CNTRC face sheets. It is evident from Fig. 4 that FG-V
d FG-Λ anels have the stronge t and weak st pos buckling streng hs, respectively,
and UD, FG-X and FG-O panels have intermediate and almost identical postbuckling
curves. Subsequently, it is realized from Fig. 5 that critical loads and postbuckling paths
are significantly reduce when h f /h ratio is enhan ed, especially as h f /h increases from
0.1 to 0.15. In addition, the load carrying capability of sandwich panels is decreased at
elevated temperature (T = 400 K) and detrimental effect of temperature is more pro-
nounced for smaller values of h f /h ratio.
Buckling and postbuckling of CNT-reinforced composite sandwich cylindrical panels. . . 227
Fig. 6. Effects of and ratio on the 
postbuckling behavior of sandwich cylindrical 
panel with CNTRC face sheets under axial 
compression. 
Fig. 7. Effects of CNT distribution patterns on the 
postbuckling behavior of sandwich cylindrical 
panel with CNTRC core layer under axial 
compression. 
As a subsequent example, the influences of curvature ratio and CNT volume fraction 
 on the postbuckling behavior of sandwich panels with CNTRC face sheets are examined in 
Fig. 6. Obviously, the critical buckling loads and postbuckling equilibrium paths are considerably 
enhanced when and/or are increased. In other words, more curved and CNT-rich panels 
have higher postbuckling paths. However, more curved panels ( ) experience an unstable 
postbuckling response with relatively intense snap-through instability. 
Next, numerical illustrations on the postbuckling behavior of sandwich panels of type B with 
CNTRC core layer and homogeneous face sheets under axial compression are given in Figs. 7 and 
8. Fig. 7 indicates that distribution patterns of CNTs in the core layer have significant effects on 
the postbuckling response of sandwich panels of type B. Specifically, among five distribution 
types, FG-X and FG-O types give the best and worst postbuckling response, respectively, and UD 
panel has higher postbuckling strength than FG-V panel, especially in the deep region of 
deflection. 
*
CNTV /a R
/a R
*
CNTV
/a R *CNTV
/ 0.2a R =
Fig. 6. Effects of V∗CNT and a/R ratio on the
postbuckling behavior of sandwich cylindri-
cal panel with CNTRC face sheets under axial
compression
i . 6. E fects of and rati on the 
postbuckling behavior of sandwich cylindrical 
panel with CNTRC face sheets under axial 
compression. 
Fig. 7. Effects of CNT distribution patterns on the 
postbuckling behavior of sandwich cylindrical 
panel with CNTRC core layer under axial 
compression. 
As a subsequent example, the influences of curvature ratio and CNT volume fraction 
 on the postbuckling behavior of sandwich panels with CNTRC face sheets are examined in 
Fig. 6. Obviously, the critical buckling loads and postbuckling equilibrium paths are considerably 
enhanced when and/or are increased. In other words, more curved and CNT-rich panels 
have higher postbuckling paths. However, more curved panels ( ) experience an unstable 
postbuckling response with relatively intense snap-through instability. 
Next, numerical illustrations on the postbuckling behavior of sandwich panels of type B with 
CNTRC core layer and homogeneous face sheets under axial compression are given in Figs. 7 and 
8. Fig. 7 indicates that distribution patterns of CNTs in the core layer have significant effects on 
the postbuckling response of sandwich panels of type B. Specifically, among five distribution 
types, FG-X and FG-O types give the best and worst postbuckling response, respectively, and UD 
panel has higher postbuckling strength than FG-V panel, especially in the deep region of 
deflection. 
*
CNTV /a R
/a R
*
CNTV
/a R *CNTV
/ 0.2a R =
i . 7. f t f ti a terns on
the postbuckling behavi r of sandwich cylin-
drical panel with CNTRC core layer er ax-
ial compression
Finally, the interactive effects of 
 ratio and CNT volume fraction 
 on the postbuckling behavior of 
sandwich panels of type B in a thermal 
environment ( K) are considered 
in Fig. 8. It is clear t at buckling loads 
and postbuckling paths are remarkably 
enhanced due to increase in ratio. 
In addition, effects of CNT volume 
fraction are more slight for rg values 
of ratio, i.e. thicker face sheets. 
Fig. 8. Effects of thickness of face sheets on the 
postbuckling behavior of sandwich cylindrical panel 
with CNTRC core layer under axial compression in a 
thermal environment. 
5. Concluding remarks 
An analytical investigation on the buckling and postbuckling behaviors of two models of 
sandwich cylindrical panels comprising CNTRC and homogeneous layers and subjected to 
uniform axial compression in thermal environments has been presented. From the above results, 
the following remarks are reached: 
1. For sandwich panels of type A with CNTRC face sheets, the type of CNT distribution has 
relatively slight effects on the critical loads and postbuckling equilibrium paths of sandwich 
panels. In this configuration of sandwich panels, FG-V and types give the highest and 
lowest postbuckling strengths, respectively, and load carrying capability of the panel is reduced as 
thickness of face sheets is increased. 
2. For sandwich panels of type B with CNTRC core layer, the type of CNT distribution has 
significant effects on the critical loads and postbuckling equilibrium paths of sandwich panels, and 
FG-X and FG-O distributions give the best and worst postbuckling responses of sandwich panels, 
respectively. For this sandwich model, the load carrying capability of the panel is enhanced when 
the thickness of face sheets is increased. 
/fh h
*
CNTV
400T =
/fh h
/fh h
FG -L
Fig. 8. Effects of thickness of face sheets on the postbuckling behavior of sandwich cylindrical
panel with CNTRC core layer under axial compression in a thermal environment
As a subsequent example, the influences of curvature ratio a/R and CNT volume
fraction V∗CNT on the postbuckling be avior of sandwich panels with CNTRC face sheets
re examined in Fig. 6. Obviously, the critical buckling loads and postbuckling equilib-
rium paths are considerably enhanced when a/R and/or V∗CNT are increased. In other
words, more curved and CNT-rich panels have higher postbuckling paths. However,
more curved panels (a/R = 0.2) experience an unstable postbuckling response with rel-
ative y i tense snap-through instability.
Next, numerical illustrations on the postbuckling behavior of sandwich panels of
type B with CNTRC core layer and homogeneous face sheets under axial compression
are given in Figs. 7 and 8. Fig. 7 indicates that distribution patterns of CNTs in the core
228 Hoang Van Tung, Vu Thanh Long
layer have significant effects on the postbuckling response of sandwich panels of type B.
Specifically, among five distribution types, FG-X and FG-O types give the best and worst
postbuckling response, respectively, and UD panel has higher postbuckling strength than
FG-V panel, especially in the deep region of deflection.
Finally, the interactive effects of h f /h ratio and CNT volume fraction V∗CNT on the
postbuckling behavior of sandwich panels of type B in a thermal environment (T = 400
K) are considered in Fig. 8. It is clear that buckling loads and postbuckling paths are
remarkably enhanced due to increase in h f /h ratio. In addition, effects of CNT volume
fraction are more slight for larger values of h f /h ratio, i.e. thicker face sheets.
5. CONCLUDING REMARKS
An analytical investigation on the buckling and postbuckling behaviors of two mod-
els of sandwich cylindrical panels comprising CNTRC and homogeneous layers and sub-
jected to uniform axial compression in thermal environments has been presented. From
the above results, the following remarks are reached:
1. For sandwich panels of type A with CNTRC face sheets, the type of CNT distribu-
tion has relatively slight effects on the critical loads and postbuckling equilibrium paths
of sandwich panels. In this configuration of sandwich panels, FG-V and FG-Λ types give
the highest and lowest postbuckling strengths, respectively, and load carrying capability
of the panel is reduced as thickness of face sheets is increased.
2. For sandwich panels of type B with CNTRC core layer, the type of CNT distri-
bution has significant effects on the critical loads and postbuckling equilibrium paths of
sandwich panels, and FG-X and FG-O distributions give the best and worst postbuckling
responses of sandwich panels, respectively. For this sandwich model, the load carrying
capability of the panel is enhanced when the thickness of face sheets is increased.
3. For both models of sandwich cylindrical panels, postbuckling load-deflection
paths are enhanced and reduced due to increase in the volume fraction of CNTs and
environment temperature, respectively.
ACKNOWLEDGMENT
This research is funded by Vietnam National Foundation for Science and Technology
Development (NAFOSTED) under grant number 107.02-2017.11.
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