TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 12, Decembe
r
2014, pp. 83
4
4
~ 834
8
DOI: 10.115
9
1
/telkomni
ka.
v
12i12.66
72
8344
Re
cei
v
ed Se
ptem
ber 2, 2014; Re
vi
sed
Octob
e
r 18, 2
014; Accepte
d
No
vem
ber
10, 2014
Computing of Post-buckling Simulation in Functionally
Graded Materials - A Review Paper
Elias Randjb
a
ran*
1
, Rizal Zahari
2
, Ram
i
n Vaghei
3
1,2
Aerospace M
anufactur
i
n
g
R
e
searc
h
Centr
e
(AMRC),
Lev
el 7, T
o
w
e
r Blo
ck, F
a
cult
y
of Engi
neer
in
g,
Universiti P
u
tra Mala
ys
ia, 43
400 Ser
d
a
ng, Sela
ngor D
a
ru
l
Ehsan, Mala
ysia,
3
Departme
n
tof Civil En
gi
neer
i
ng, F
a
cult
y
of Engi
neer
in
g, Universiti P
u
tra Mala
ysi
a
, 434
0
0
Serda
ng,
Sela
ngor D
a
ru
l
Ehsan, Mala
ysia
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: Elias@gm
x.c
o
.uk
A
b
st
r
a
ct
A review
o
n
t
he rec
ent
dev
elo
p
m
ent
in th
e n
on-l
i
ne
ar fl
utter an
d ther
ma
l b
u
ckli
n
g
o
f
an F
G
M
pan
el u
nder t
he co
mb
in
ed
effect of elev
ated te
mp
erat
ure con
d
iti
ons
and a
e
rody
n
a
mic lo
adi
ng
is
investi
gate
d
u
s
ing a
fin
i
te ele
m
ent mo
de
l
bas
ed on
th
e thi
n
pl
ate t
heory
an
d vo
n Kar
m
a
n
str
a
in-
displ
a
ce
ment r
e
lati
ons t
o
acc
ount for
mo
der
ately
larg
e
defl
e
ction. It
is fou
nd th
at the
te
mperatur
e i
n
cre
a
s
e
has an
advers
e
effect on the F
G
M panel
flutter charac
te
ristics throug
h
decreas
in
g the critical dy
na
mi
c
pressur
e
. Decr
easi
ng the vo
l
u
me fraction
e
nha
nces flutte
r
characteristics
but this
is li
mi
ted by structural
integr
ity aspec
t. Structural finite e
l
e
m
e
n
t a
nal
ysis
has
be
en e
m
ploy
ed t
o
deter
mine t
he F
G
M pan
el
'
s
ada
ptive r
e
sp
o
n
se w
h
il
e
und
e
r
the i
n
flu
ence
of a u
n
i
a
xia
l
com
p
r
e
ssive load in
exce
ss
of it
s critical buck
l
ing
valu
e. W
i
th the
increas
e i
n
us
e of co
mp
osite
mater
i
al
s w
i
thi
n
aer
ospac
e p
l
atforms, it is e
n
visa
ged th
at th
e
hybri
d
a
d
a
p
tiv
e
FGM pa
ne
l's confi
gur
ation
w
ill
exte
n
d
th
e o
per
ation
a
l
perfor
m
a
n
ce
o
v
er co
nve
n
tion
a
l
mater
i
als
and s
t
ructures, parti
cularly w
h
e
n
the stru
cture is e
x
pose
d
to an
el
evated te
mp
er
ature.
Key
w
ords
:
function
ally gr
ade
d, F
G
M, non-li
ne
ar finite
ele
m
e
n
t formulati
on, ther
mo-mech
anic
a
l, post-
buckling
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Functio
nally
grad
ed m
a
terials (FGM
s)
a
r
e no
n-homo
gene
ou
s co
m
posite
s
cha
r
a
c
teri
zed
by
a smooth
and co
ntinuo
us ch
ang
e
of material
prop
er
ties fro
m
o
ne
surfa
c
e
to
the othe
r. Thi
s
i
s
achi
eved by grad
ually varying the volume fracti
o
n
of the con
s
tituent materi
al
s. Fun
c
tionall
y
grad
ed mat
e
rials a
r
e u
s
u
a
l
l
y compo
s
e
d
of two or
mo
re mate
rial
s
who
s
e volu
m
e
fractio
n
s
are
cha
ngin
g
sm
oothly and co
ntinuou
sly al
ong de
sired
dire
ction
(
s). This
continu
o
u
s chan
ge in
th
e
comp
ositio
ns leads to
a
smooth
ch
ange in t
h
e
mech
ani
cal
prop
ertie
s
, whi
c
h ha
s
many
advantag
es
o
v
er the lami
n
a
ted compo
s
i
t
es, wh
ere th
e delami
natio
n and
cra
c
ks are m
o
st li
kely
to initiate at
the interface
s
due to the abrupt
varia
t
ionin the mecha
n
ical pro
pertie
s
between
lamina
s. One
of the advantages of u
s
in
g these m
a
te
rials i
s
that they can surviv
e environ
men
t
s
with high te
mperature g
r
adient
s, whil
e maintainin
g
structu
r
al int
egrity. Acco
rdingly, one o
f
th
e
most impo
rta
n
t application
s
of functio
n
a
lly grade
d m
a
terial
s is in t
he skin p
anel
s of su
perso
nic
and hype
rson
ic flight vehicl
es, whi
c
h h
a
ve to
survive the harsh the
r
mal and me
chani
cal loadi
n
g
s
[1-3].
Functio
nally
grad
ed
mate
rials (F
GM
s) are
a
ne
w
gene
ration
of
com
p
o
s
ite
material
s
whe
r
ein
the material prop
erties
vary co
ntinuou
sl
y to
yield a p
r
ed
e
t
ermine
d com
positio
n p
r
ofile.
These mate
ri
als have
bee
n introd
uced
to benefit fro
m
the ideal p
e
rform
a
n
c
e o
f
its con
s
titue
n
ts,
e.g. high
heat
/corro
sion
re
sistan
ce
of ce
ramics
o
n
o
n
e
sid
e
, and
la
rge me
ch
ani
cal strength
an
d
toughn
ess of
metals
on the
other
sid
e
. F
G
Ms
have n
o
interfa
c
e
s
an
d are he
nce
advantag
eou
s
over conventi
onal lami
nate
d
com
p
o
s
ites. FGMs al
so
permit tailo
rin
g
of materi
al comp
ositio
n to
optimize
a de
sire
d cha
r
a
c
teristi
c
such a
s
minimi
ze th
e maximum d
e
flection fo
r a
given load
a
n
d
boun
dary
con
d
itions, o
r
ma
ximize the first freq
uen
cy
of free vibration, or mi
nimi
ze the
maxim
u
m
prin
cipal
ten
s
ile stress. As
a re
sult, FG
M
s
have
gai
ne
d potential
ap
plicatio
ns i
n
a
wide
variety
of
engin
eeri
ng
comp
one
nts
or sy
stem
s, whi
c
h in
cl
ud
e arm
our
pla
t
ing, heat en
gine
comp
on
ents
and
h
u
ma
n
i
m
plants. The
variation of material pr
op
erties in a
n
FGM i
s
u
s
ua
lly achieve
d
by
contin
uou
sly
varying volu
me fra
c
tion
s
of the con
s
tituent mate
rial
s. With th
e i
n
crea
sed
u
s
e of
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these
mate
ri
als, it i
s
imp
o
rtant to
und
ersta
nd th
e
nonlin
ear be
haviour of fu
nction
ally gra
ded
plates
und
er
pre
s
sure loa
d
.
Approximat
e sol
u
tion
s of
com
p
lex en
g
i
neeri
ng p
r
o
b
l
e
ms
are
u
s
ua
lly
obtaine
d by a numeri
c
al m
e
thod.
In re
cent years, a new type of
n
u
meri
cal met
hod called m
e
sh
-
free metho
d
(MFM) is b
e
in
g develop
ed i
n
the area of
comp
utationa
l mecha
n
ics [4-8].
Figure 1. Geo
m
etry and co
ordin
a
te syst
em of
a cylindrical sh
ell su
rro
und
ed by an ela
s
tic
medium [27]
2.
Material an
d Metho
d
s
Conve
n
tional
aero
s
p
a
ce comp
osite
s
have
bee
n compo
s
ed
of high-stiffness carbon
fibres to m
a
intaindim
e
n
s
ion
a
l sta
b
ili
ty under
high-p
e
rfo
r
ma
n
c
e a
ppli
c
atio
n. The
stiffness
property is often associ
ated with a parti
cul
a
r susceptibility
to
impact damage and a
corre
s
p
ondin
g
red
u
ction
o
f
mecha
n
ical prop
ertie
s
. Ho
wever,
su
ch st
ru
cture
s
are expe
cte
d
to
only en
co
unt
er fe
w
uninte
n
tional im
pa
cts. Co
mpo
s
it
e st
ru
cture
s
f
o
r milita
r
y g
r
ound
vehi
cle
s
, on
the othe
r h
a
nd, are d
e
si
gned to
ab
sorb
multip
le
high-ene
rgy i
m
pact
s
b
u
t
have mu
ch
less
dimen
s
ion
a
l restri
ction
s
. Since
softer
m
a
terial
s tend
to dissipate
more
ene
rgy
durin
g impa
ct
, a
low mod
u
lu
s/high strengt
h altern
ative would b
e
well suited for ba
cking p
anel compo
s
ites
Effective Material Prope
rties of Fu
nctio
nally Gr
a
ded
Material
s Consi
der
an F
G
M layer tha
t
is
made from a
mixture of cerami
cs and
metals. Assu
me that the compo
s
ition is varied from the
outer to th
e i
nner
su
rfa
c
e,
i.e., the outer surfa
c
e
(Z=-h/2) of the
pa
nel is m
e
tal ri
ch, wherea
s t
h
e
inner su
rface (Z=+h/2
)
is cerami
c
ri
ch, whe
r
e
Z
i
s
in
the dire
ction
of the downward n
o
rm
al to
the
middle
su
rface, and
h is t
he thickn
ess of the
layer.
Thermal p
o
s
t-bu
ckling
b
e
haviour of F
G
M
cylindri
c
al shells su
rrou
nded by
an
elasti
c me
dium
wa
s
pre
s
ente
d
b
e
ca
use of t
w
o
microme
c
ha
n
i
cal m
odel
s and
multi-scale
ap
pro
a
c
h. T
he
su
rroun
ding
ela
s
tic
mediu
m
is
modelle
d a
s
a Pa
sterna
k fou
ndatio
n
.
The
ma
terial prope
rtie
s of
FGM
s
are a
s
sum
ed
temperature
depe
ndent. Nume
ri
cal re
sults
de
mon
s
trate
that b
o
th bu
ckling
temperature
and
thermal
po
st-bucklin
g st
re
ngth of
the
FGM
shell
s
are i
n
crea
se
d with i
n
crea
se in
found
a
t
ion
stiffness, Fig
u
re 2 sho
w
s t
he detail
s
[9-15].
Figure 2. Sch
e
matic of the
imperfe
ct FG
beam with n
o
n
linea
r found
ation [9]
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Vol. 12, No. 12, Decem
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14 : 8344 – 83
48
8346
2.1.
Voigt and M
o
ri-Tan
aka
Model
Therm
a
l Po
st
-bu
ckli
n
g
of
Shear Deformable
FGM
Cylindri
c
al
S
hells Surrou
n
ded
by a
n
Elastic
Mediu
m
presents
a
study o
n
the
therm
a
l
po
st
-bu
ckli
ng re
spon
se
of a shear
defo
r
ma
ble
function
ally g
r
ade
d cylin
dri
c
al
shell
of finite
length
e
m
bedd
ed in
a
large
oute
r
e
l
astic
mediu
m
b
y
Shen in 20
1
3
. The surro
undin
g
ela
s
tic medi
um is
modelle
d a
s
a Paste
r
na
k
foundatio
n. Two
kind
s of microme
c
h
ani
cs models, na
mely
the Voigt model a
nd Mori
-Ta
n
aka mo
del, are
con
s
id
ere
d
. The governin
g
eq
uation
s
are
ba
sed
o
n
a
high
er-o
rde
r
she
a
r d
e
formatio
n
shell
theory that in
clud
es
sh
ell-f
ound
ation int
e
ra
cti
on. Th
e
thermal
effects a
r
e
also
i
n
clu
ded
and
the
material
pro
pertie
s
of f
unctio
nally g
r
ade
d mate
ri
als
(FGM
s) are
assum
ed temp
erat
ure
depe
ndent. The
gove
r
nin
g
equ
ations are solved
b
y
a singul
ar pertu
rbatio
n
techni
que.
The
nume
r
ic
al re
s
u
lt
s s
h
o
w
t
h
a
t
in some
ca
se
s t
he
FG
M
cylindri
c
al
shell with inte
rmediate volu
me
fraction in
de
x does not have interme
d
iate buc
klin
g temperatu
r
e and therm
a
l post-bu
ckli
n
g
stren
g
th. The
result
s reve
al that Voigt
model an
d Mori-T
ana
ka m
odel have th
e same a
c
cu
racy
for p
r
edi
cting
the the
r
mal
bu
ckli
ng a
n
d
po
st-b
uckli
ngbe
haviou
r
of FGM
sh
el
ls. The
resul
t
s
confirm that f
o
r the
ca
se
of heat
cond
uct
i
on, the po
st-bucklin
g eq
uil
i
brium
path fo
r ge
ometri
call
y
perfe
ct FGM
cylindri
c
al shells with
si
mply s
upp
ort
ed boun
da
ry condition
s is no longer of
the
bifurcation type. Thermal
Post bu
cklin
g of Func
tio
nally Grad
ed
Material
s Shells
Con
s
id
er a
circula
r
cylin
drical shell,
whi
c
h i
s
ma
d
e
of
the
com
b
ined
ce
rami
c an
d metalli
c mate
rial
s
with
contin
uou
sly varying mix ratios
comp
rising ce
rami
c
and metal. T
he length, m
ean radiu
s
, a
n
d
total thickne
s
s of the shell
are L, R, and h, resp
e
c
ti
vely. The shell is referred
to a coordin
a
te
system
(X, Y
,
Z) in
whi
c
h
X and
Y are in th
e
axia
l and
Figu
re
1 shows th
e
circu
m
fere
ntial
dire
ction
s
of the sh
ell and
Z is in the directi
on of the i
n
wa
rd no
rmal
to the middle surfa
c
e.
2.2.
Euler-Berno
u
li Beam Theor
y
and Vo
n-Karman G
e
ometric
No
nlinearit
y
Yaghoo
bi an
d Torabi in
2013 i
n
vestig
ated
that b
e
a
ms m
ade
o
f
functionally
gra
ded
material
s
(F
GMs)
re
sting
on
no
nlinea
r ela
s
tic f
oun
dation su
bje
c
ted
to axial
f
o
rce are
stud
ied.
The materi
al prop
ertie
s
of FGMs a
r
e a
s
sume
d to be grad
ed in the
thickn
ess direction a
c
cord
ing
to a simpl
e
power la
w di
stributio
n in t
e
rm
s of
the
volume fra
c
ti
ons
of the constitue
n
ts.
The
assumptio
n
s
of a
small
strain a
nd m
o
d
e
rate
defo
r
m
a
tion a
r
e
use
d
. Base
d o
n
Euler–Be
rn
ou
lli
beam
theo
ry
and vo
n-Ka
rman
geom
etric n
onlin
earit
y,
the integ
r
al
pa
rtial differential e
quatio
n of
motion is
deri
v
ed. Then thi
s
pa
rtial differential
equ
atio
n (PDE
) probl
em, whi
c
h h
a
s
qu
adratic a
nd
cubi
c n
onlin
e
a
rities, i
s
sim
p
lified into
an
ordi
nary
differential
eq
ua
tion (O
DE) problem
by usi
ng
the Gale
rkin
method. Fin
a
l
l
y, the governing e
quati
o
n
is
solved
an
alytically usi
n
g the vari
atio
na
l
iteration meth
od (VIM) [16
-
27].
3. Resul
t
s
and
Discus
s
ion
It is shown that, utilising the
considerabl
e control aut
hority
generated, ev
en for
a small
actuato
r
volu
me fra
c
tion, the out-of-pla
ne displa
cem
ent of the po
st-buckle
d
FG
M panel'
s
ca
n be
signifi
cantly redu
ced. Su
ch displa
ceme
nt alleviat
ion
allows for loa
d
re
distri
butio
n away from t
he
FGM pan
el'
s
unloa
ded ed
g
e
s.
The re
sult
s show that in some ca
se
s th
e FGM cylind
r
ical
shell wit
h
intermedi
ate volume
fraction
ind
e
x doe
s
not ne
ce
ssarily h
a
ve inte
rmediat
e bu
ckling te
mperature
an
d thermal p
o
s
t-
bucklin
g stre
ngth. The re
sults re
veal th
at the differe
nce of the bu
ckli
ng tempe
r
ature
s
betwe
en
Mori-Tan
aka
Model
and
V
o
igt Mo
del
solution
s i
s
ve
ry sm
all, an
d
the
differen
c
e of th
e the
r
mal
post-bu
ckli
n
g
stren
g
th bet
wee
n
Voigt Model solutio
n
s may be n
egligible. Th
e
results confi
r
m
that for the
case
of he
at condu
ction, th
e po
st-b
uckli
ng e
quilib
ri
u
m
path fo
r g
e
ometri
cally p
e
rfect
FGM cylind
r
i
c
al sh
ells
with simply sup
ported b
ou
n
d
a
ry con
d
ition
s
is no long
er of the bifurcation
type [28].
4. Conclu
sion
The gove
r
nin
g
non
-linea
r
equatio
ns a
r
e obtaine
d u
s
ing the p
r
in
cipal of virtu
a
l wo
rk
adoptin
g an approa
ch ba
sed on the t
herm
a
l stra
i
n
being a cu
mulative physical quantity to
accou
n
t
for
tempe
r
ature d
epen
dent ma
terial pro
p
e
r
ties. T
h
is sy
st
em of
non
-lin
ear eq
uation
s
is
solved by Ne
wton–
Ra
ph
so
n nume
r
ical tech
niqu
e.
It is found that the temperature ri
se h
a
s
an
op
po
site
outcome o
n
the FGM pan
el flutter
feature
s
th
ro
ugh
dimini
sh
ing the
critical dynami
c
pre
s
sure. Re
duci
ng the
volume f
r
a
c
tio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
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ISSN:
2302-4
046
Perform
a
n
c
e
Com
pari
s
o
n
of Host Identi
t
y Protoc
ol an
d TCP/IP with Firewall… (A
lfan Presekal)
8347
improve
s
flutter aspe
cts
but this is
controlle
d by
sy
st
emi
c
int
e
grit
y
cha
r
a
c
t
e
rist
i
c
.
S
t
ruct
ural
finite-elem
ent
analysi
s
ha
s been
ca
rrie
d
out to dete
r
mine th
e F
G
M pan
el'
s
adaptive rea
c
tion
while
un
der t
he im
pa
ct of
a uni
axial
co
mpre
ssive lo
ad in
ex
ce
ss
of its
critical
bucklin
g valu
e to
comply the specifi
c
ation
s
.
The p
r
e
s
en
ce of ae
rodyn
a
mic flo
w
re
sults in
po
stpo
ning the
bu
ckling temp
erat
ure
and
in su
ppressin
g
the po
st-b
u
ckli
ng defle
cti
on while
the t
e
mpe
r
ature i
n
crea
se give
s way for hig
her
limit cycle am
plitude.
Referen
ces
[1]
Ibrahim
HH, Y
oo
HH,
Lee
K
S
. Sup
e
rson
ic
flutter of
fu
ncti
ona
ll
y
grate
d
p
ane
ls su
bj
ect to ac
oustic
an
d
thermal l
oads.
Journ
a
l of Aircr
a
ft
. 2009; 46(2)
; 593-60
0.
[2]
Ibrahim
HH, Y
oo H
H
, L
ee K
S
. Aero-therm
o
-mech
ani
c
a
l
character
i
stics
of imp
e
rfect s
hap
e mem
o
r
y
allo
y
h
y
bri
d
co
mposite p
a
n
e
ls
.
Journal of So
und a
nd Vi
brati
o
n
. 200
9;
325
(
3
); 583-5
96.
[3]
Ibrahim HH, Yoo
H
H
,
H T
a
w
f
ik, Lee
KS.
T
he
rmo-acoustic ra
nd
o
m
respo
n
se
of temperat
ur
e-
dep
en
dent fun
c
tiona
ll
y gra
d
e
d
materia
l
pan
els.
Co
mp
utati
ona
l Mecha
n
ic
s
. 2010; 46(
3): 377-
386.
[4]
Ibrahim HH, T
a
w
f
ik M. Li
mit-c
y
cl
e oscil
l
a
tions of
func
tiona
ll
y
gra
d
e
d
material p
l
a
t
es subject to
aero
d
y
nam
ic a
nd therma
l loa
d
s.
Journa
l of Vibrati
on a
nd
Contro
l
. 201
0; 16(1
4
): 214
7-2
166.
[5]
Yu JS, Ju
ng
YC. Micromec
han
ics Mo
del
i
ng
of F
uncti
on
all
y
Gra
d
e
d
M
a
teria
l
s C
ontai
nin
g
Mu
ltipl
e
Heterogeneities.
한국복합재
료학회지
(
복합재료
)
. 2013;
26
(6): 392-3
97.
[6]
Yaghm
aei M, Naei MH. Lar
ge defl
e
ctio
n beh
avior
of si
mpl
y
s
u
p
porte
d F
G
Circular
plates un
de
r
mechanical and thermal
loadings via FSDT
mesh
less method. Proceedings
of the 3rd IASME/WSEAS
Internatio
na
l confere
n
ce
o
n
contin
uu
m
mec
han
ics
. Chica
g
o
.
[7]
Allah MAAA,
SAES Ward,
AA Youss
e
. Ef
fect of Func
tionally
Graded Material
of
Dis
c Spac
er
w
i
t
h
Presenc
e of Multi-Co
ntam
i
n
ating Partic
les
on Electric
F
i
eld i
n
sid
e
Gas Insulate
d
Bus Duct.
Internatio
na
l Journ
a
l of Electr
ical
a
nd Co
mp
uter Engi
ne
erin
g (IJECE)
. 201
3;
3
(6): p. 831-
848.
[8]
T
i
ngjun Y, Z
Li
nna. F
i
nite
Ele
m
ent Mo
del
of
Shap
e Mem
o
r
y
All
o
y Incor
por
ating
Druck
e
r-
Prager
Mod
e
l
.
T
E
LKOMNIKA Indon
esi
an Jou
r
nal of Electric
al Eng
i
ne
eri
n
g
.
2013;
11
(7): p. 3915-
3
[9]
Beli
nha
J, Di
ni
s LMJS. Ana
l
ysis of p
l
ates
a
nd
l
a
mi
nates
usin
g the
el
e
m
ent-free Ga
l
e
rkin m
e
tho
d
.
Co
mp
uters & structures
. 200
6
;
84(22): 15
47-
155
9.
[10]
Ran
d
jb
ara
n
E, Z
ahari R, Ma
ji
d DL, Jal
il NA
A, V
aghe
i R, Ahmad
i
R. An E
x
p
e
rime
ntal In
vestigati
on o
f
the Effects o
f
Stacking Sequ
enc
e on H
y
brid C
o
mp
osite Materi
al
s Respo
n
se to Open-Ho
l
e
Compress
io
n Strength.
MA
T
R
IX Acade
mic Internati
o
n
a
l Onli
ne J
o
urna
l of Eng
i
neer
ing
an
d
T
e
chno
logy
. 2
013; 1(2): 1-6.
[11]
Ran
d
jb
ara
n
E,
Z
ahari
R, Ma
ji
d D
L
, Jal
il
NAA
,
V
agh
ei
R, Ah
madi
R. T
he Effects of Stacki
ng S
e
q
uenc
e
La
yers
of H
y
b
r
id
Comp
osite
Materials
i
n
E
nerg
y
Abs
o
rpti
on
un
der th
e
High
Ve
locit
y
Ballistic
Impact
Con
d
itio
ns: A
n
E
x
p
e
rime
ntal Inv
e
stigati
o
n.
MAT
R
IX Acade
mic Inter
natio
nal
Onli
n
e
Jo
urna
l o
f
Engi
neer
in
g an
d T
e
chno
lo
gy
. 201
3; 1(2): 30-
37.
[12]
Ran
d
jb
ara
n
E, Z
ahari
R, Maji
d DL, Ja
lil
NA
A, V
agh
ei R, A
h
mad
i
R. Effec
t
s of Stacking
Sequ
enc
e
o
n
Compress
io
n
Resp
onse T
e
sting of C
a
rbo
n
F
i
bre a
nd H
y
brids: F
i
bro
u
s-
Glass/Carb
on/
Kevlar/ Ep
o
x
y
Comp
osite P
l
a
t
es.
MAT
R
IX Acade
mic Inter
natio
nal
Onli
ne
Journ
a
l
of En
gin
eeri
ng
an
d
T
e
chno
logy
.
201
3; 2(1): 13-
17.
[13] Ran
d
jb
ara
n
E,
Zahari R, Maji
d DL, Jalil NA
A, Vaghei R, Ahmad
i
R.
T
he effects of stacking se
que
n
c
e
la
yers
of si
x
la
yers
comp
osite
mate
ria
l
s i
n
b
a
llistic
en
erg
y
absor
ption.
Int
e
rnati
ona
l Jo
ur
nal
of Materi
a
l
Scienc
e Innov
ations
. 20
13; 1
(
6): 293-3
05.
[14]
Ran
d
jb
ara
n
E, Z
ahari R, Majid
DL, Jali
l
NAA,
Vagh
ei
R, Ahmadi R.
Exp
e
rime
ntal
Stud
y
of th
e
Influenc
e of Stackin
g
Order o
f
the F
i
brous L
a
y
ers
on L
a
mi
nated H
y
b
r
id
C
o
mpos
ite Plate
s
Subjecte
d to
Compress
io
n L
oad
ing.
Jo
urna
l of Science a
n
d
Engi
ne
erin
g
. 201
4; 4(1): 01-
08.
[15]
Ran
d
jb
ara
n
E,
Z
ahar
i R, A
b
dul
Jal
il, NA,
Aban
g A
bdu
l
Majid
D
L
. H
y
brid
Com
posit
e L
a
min
a
tes
Reinf
o
rced
w
i
t
h
Kevlar/C
arbo
n/Glass Wove
n Fabrics for Ballistic Impact
T
e
sting.
T
he Scientific W
o
r
l
d
Journ
a
l
. 20
14. doi:1
0.11
55/2
0
14/41
37
53.
[16]
Yagh
oo
bi H, T
o
rab
i
M. Post-
buckli
n
g
an
d n
onli
n
e
a
r free
vi
bratio
n a
nal
ys
i
s
of ge
ometric
a
ll
y
imperfec
t
function
all
y
gr
ade
d b
eams r
e
sting
on no
nli
near el
astic
fo
und
atio
n.
App
l
i
ed Math
e
m
atic
al Mo
del
li
ng
.
201
3; 37(1
8
): 8324-
834
0.
[17]
Yagh
oo
bi H,
T
o
rabi M. An
ana
l
y
t
i
cal
ap
pr
oac
h t
o
lar
g
e
ampl
itud
e vib
r
ation
an
d p
o
s
t-buckli
ng
of
function
all
y
gr
ade
d b
eams r
e
st on
no
n-li
n
ear e
l
astic fo
u
ndati
on.
Jo
urn
a
l of T
h
eor
etical a
nd A
p
p
lie
d
Mechanics
. 20
13; 51(1): 3
9
-5
2.
[18]
T
o
rabi M, Yag
hoo
bi H. Accur
a
te sol
u
tion for
accel
e
ratio
n
m
o
tion
of a vertic
all
y
fal
lin
g sp
h
e
rical
particl
e
in inc
o
mpr
e
ssi
ble N
e
w
t
o
n
ia
n
medi
a.
T
he
Can
adi
an J
our
nal
of Che
m
ic
al En
gin
eeri
n
g
. 2013; 9
1
(2):
376-
381.
[19]
Yagh
oo
bi H, T
o
rab
i
M. Exact
solutio
n
for t
hermal b
u
ckli
n
g
of functiona
ll
y grade
d pl
ates
resting o
n
elastic fou
n
d
a
ti
ons
w
i
th v
a
rio
u
s
bou
ndar
y c
o
nditi
ons.
Jour
n
a
l of T
her
ma
l Stresses. 201
3
;
36(9): 869-
894.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 12, Decem
ber 20
14 : 8344 – 83
48
8348
[20]
T
o
rabi M, Yaghoo
bi H,
Boub
aker K. Accurate solutio
n
for motion of a sp
heric
al soli
d pa
rticle in pl
an
e
Cou
e
tte Ne
w
t
oni
an flu
i
d m
e
cha
n
ica
l
flo
w
usin
g HPM–
Padé
ap
pro
x
i
m
ant an
d th
e Bou
bak
e
r
pol
y
n
omi
a
ls e
x
pans
ion sc
hem
e BPES.
Internation
a
l Jo
urna
l
of Heat and M
a
ss T
r
ansfer
. 2013; 5
8
(1)
:
224-
228.
[21]
T
o
rabi M, Yag
hoo
bi
H, Co
la
nt
oni, A
Bio
n
d
i
P, Bo
ubak
er
K. Ana
l
ysis
o
f
Radi
ative
Ra
dial
F
i
n
w
i
t
h
T
e
mperature-D
epe
nd
ent T
hermal Con
ductiv
i
t
y
Usin
g Non
l
i
near Differe
nti
a
l T
r
ansformation Metho
d
s.
Chin
ese Jo
urn
a
l of Engi
ne
eri
n
g
. 201
3.
[22]
T
o
rabi M, Yagho
obi
H. He
at
T
r
ansfer Anal
ysis F
r
om
Rotatin
g
Poro
us Plate W
i
th
T
e
mperature
-
Dep
end
ent T
h
ermal Co
nd
uctivit
y
.
Isi Bili
mi
Ve Teknigi
Dergis
i-Jo
urna
l
Of Thermal
Scienc
e An
d
T
e
chno
logy
. 2
013; 33(
2): 75-
82.
[23]
Yagh
oo
bi H, F
e
rei
doo
n A. M
e
cha
n
ica
l
a
n
d
thermal
buck
l
ing
an
al
ys
is
of
functio
nal
l
y
g
r
ade
d p
l
ates
resting o
n
el
as
tic found
ations:
An assessme
n
t of a
simpl
e
refine
d nth-or
de
r shear d
e
form
ation th
eor
y.
Comp
osites Pa
rt B: Engi
neeri
ng. 201
4; 62: 5
4
-64.
[24]
T
o
rabi M, Ya
gho
obi H. Ser
i
es Sol
u
tion F
o
r
Convectiv
e
-
R
adi
ative Por
ous F
i
n Usin
g
Differentia
l
T
r
ansformation
Method.
Jour
n
a
l of Porous M
edi
a
. 201
3; 16(
4).
[25]
T
o
rabi M, Yag
hoo
bi
H, Bo
ub
ak
er K. T
herm
a
l A
nal
ys
is of
Non-l
i
n
ear
Con
v
ective–
R
ad
iati
ve H
y
p
e
rb
ol
i
c
Lump
ed S
y
ste
m
s
w
i
th Sim
u
lt
ane
ous Vari
ati
on of T
e
mperature-De
pen
de
n
t
Spec
ific Heat
and Surface
Emissivit
y
b
y
MsDT
M
and
B
PES.
Internatio
nal Jo
urna
l of T
hermop
h
ysics
. 2013; 34(
1): 122-1
38.
[26]
T
o
rabi M, Yag
hoo
bi
H, Kia
n
i
MR. T
hermal a
nal
ys
is
of the
c
onvectiv
e
-rad
i
a
t
ive fin
w
i
th
a s
t
ep ch
ang
e
in thickn
ess a
nd temper
atur
e dep
end
ent thermal co
nd
uc
tivit
y
.
Journ
a
l
of T
heoretica
l
and Ap
pli
e
d
Mechanics
. 20
13; 51(3): 5
93-
602.
[27]
Vagh
ei R,
et al.
Eva
l
uat
e P
e
rformanc
e of
Precast
Co
n
c
rete W
a
l
l
to
W
a
ll C
o
n
necti
on.
A
P
C
BEE
Proced
ia
. 20
14
; 9: 285-29
0.
[28]
Shen
HS. T
hermal p
o
stbuck
l
i
ng
of sh
ear
de
formabl
e F
G
M
c
y
l
i
ndr
ical
sh
ell
s
surro
und
ed
b
y
an
el
asti
c
medi
um.
Journ
a
l of Engi
ne
eri
ng Mech
anics
/.
2013; 1
39(8):
979-
991.
Evaluation Warning : The document was created with Spire.PDF for Python.