I
nte
rna
t
io
na
l J
o
urna
l o
f
Adv
a
nces in Applie
d Science
s
(
I
J
AAS)
Vo
l.
14
,
No
.
2
,
J
u
n
e
2
0
2
5
,
p
p
.
502
~
5
1
2
I
SS
N:
2252
-
8
8
1
4
,
DOI
:
1
0
.
1
1
5
9
1
/ijaas
.
v
14
.
i
2
.
pp
502
-
5
1
2
502
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
a
a
s
.
ia
esco
r
e.
co
m
Study o
f
a
mo
del
o
f
a
sa
tellit
e
struc
ture
that m
eets
th
e nece
ss
a
ry
crite
ria
for stab
ili
ty a
nd rota
tion in
spa
ce
M
a
hm
o
ud
F
a
dh
el
I
da
n,
O
s
a
m
a
h M
a
hm
o
o
d H
us
s
ein
D
e
p
a
r
t
me
n
t
o
f
C
i
v
i
l
En
g
i
n
e
e
r
i
n
g
,
U
n
i
v
e
r
si
t
y
o
f
A
l
M
a
a
r
i
f
,
A
l
-
R
a
ma
d
i
,
I
r
a
q
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
No
v
11
,
2
0
2
4
R
ev
is
ed
Ap
r
25
,
2
0
2
5
Acc
ep
ted
May
10
,
2
0
2
5
Th
e
stu
d
y
a
ime
d
to
c
re
a
te
a
m
o
d
e
l
o
f
a
sa
telli
te
str
u
c
tu
re
t
h
a
t
m
e
e
ts
th
e
n
e
c
e
ss
a
ry
c
rit
e
ria
fo
r
sta
b
il
it
y
a
n
d
ro
tatio
n
in
sp
a
c
e
.
Th
e
sa
tell
it
e
b
e
in
g
a
n
a
ly
z
e
d
h
a
s
a
n
o
c
tag
o
n
a
l
sh
a
p
e
,
with
a
d
iam
e
ter
o
f
1
1
0
c
m
a
n
d
a
h
e
ig
h
t
o
f
8
5
c
m
.
A
d
y
n
a
m
ic
m
o
d
e
li
n
g
a
p
p
ro
a
c
h
wa
s
u
se
d
to
a
n
a
ly
z
e
th
e
stru
c
tu
ra
l
p
ro
p
e
rti
e
s,
a
n
d
t
h
e
fi
n
it
e
e
le
m
e
n
t
m
e
th
o
d
(F
EM
)
wa
s
e
m
p
lo
y
e
d
f
o
r
c
o
m
p
u
tati
o
n
a
l
a
n
a
ly
sis.
Th
is
m
e
th
o
d
a
ll
o
we
d
fo
r
a
c
o
m
p
re
h
e
n
siv
e
e
v
a
lu
a
ti
o
n
o
f
stre
ss
,
d
is
p
lac
e
m
e
n
t,
a
n
d
v
i
b
ra
ti
o
n
d
istri
b
u
ti
o
n
t
h
ro
u
g
h
o
u
t
th
e
stru
c
tu
re
,
p
ro
v
id
in
g
i
n
sig
h
t
in
t
o
t
h
e
b
e
h
a
v
io
r
o
f
th
e
c
o
m
m
u
n
ica
ti
o
n
s
sa
tel
li
te
in
sp
a
c
e
.
Th
e
tes
t
m
o
d
e
l
fra
m
e
c
o
n
sists
o
f
p
late
s
a
n
d
b
a
rs
a
rra
n
g
e
d
in
a
n
o
c
tag
o
n
a
l
sh
a
p
e
.
Th
e
a
n
a
ly
sis
u
ti
li
z
e
d
t
h
e
v
o
n
M
ise
s
stre
ss
(
σ
v
M
)
c
rit
e
rio
n
to
a
ss
e
ss
th
e
y
ield
stre
n
g
t
h
o
r
b
rit
tl
e
n
e
ss
o
f
t
h
e
c
h
o
se
n
m
a
teria
l,
7
,
0
5
7
a
lu
m
in
u
m
a
ll
o
y
.
Th
e
stu
d
y
r
e
v
e
a
led
th
a
t
t
h
e
stru
c
t
u
re
d
e
m
o
n
stra
te
s
sta
b
il
it
y
in
si
x
d
iffere
n
t
m
o
d
e
s
b
u
t
a
lso
e
x
h
i
b
it
s
d
e
fo
rm
a
ti
o
n
due
to
m
o
d
if
ica
ti
o
n
s
i
n
th
e
b
a
sic
a
rra
n
g
e
m
e
n
t.
Ad
d
it
i
o
n
a
ll
y
,
tran
sie
n
t
flu
c
t
u
a
ti
o
n
s
in
th
e
s
p
a
c
e
c
ra
ft'
s
p
o
siti
o
n
o
v
e
r
a
2
4
-
h
o
u
r
c
y
c
le
re
su
lt
in
c
h
a
n
g
e
s
i
n
to
r
q
u
e
.
T
h
e
stru
c
tu
r
e
re
m
a
in
s
sta
b
le
with
in
a
sp
e
c
ifi
e
d
fre
q
u
e
n
c
y
ra
n
g
e
sta
rti
n
g
a
t
1
5
0
Hz
wh
e
n
su
b
jec
ted
to
v
i
b
ra
ti
o
n
stim
u
li
,
a
n
d
n
o
e
x
tern
a
l
i
n
sta
b
il
i
ty
wa
s
d
e
te
c
ted
with
i
n
th
is r
a
n
g
e
.
K
ey
w
o
r
d
s
:
Dev
elo
p
m
en
t
Geo
s
y
n
ch
r
o
n
o
u
s
o
r
b
it
Hex
ag
o
n
al
s
tr
u
ctu
r
al
Satellite s
tr
u
ctu
r
e
Stab
ilit
y
o
f
s
atellite
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Ma
h
m
o
u
d
Fad
h
el
I
d
a
n
Dep
ar
tm
en
t o
f
C
iv
il E
n
g
in
ee
r
i
n
g
,
Un
iv
e
r
s
ity
o
f
Al
Ma
ar
if
Al
-
R
am
ad
i
,
An
b
ar
Pro
v
i
n
ce
,
I
r
aq
E
m
ail:
d
r
.
m
af
a5
7
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
d
e
v
elo
p
m
e
n
t
o
f
a
s
p
ac
e
s
y
s
tem
en
tails
a
th
o
r
o
u
g
h
ev
alu
atio
n
o
f
its
o
p
e
r
atin
g
en
v
i
r
o
n
m
en
t
to
en
s
u
r
e
o
p
tim
al
p
e
r
f
o
r
m
an
ce
,
d
u
r
ab
ilit
y
,
an
d
lo
n
g
ev
ity
o
f
t
h
e
s
atellite
[
1
]
.
Natu
r
al
alig
n
m
en
t
is
esp
ec
ially
cr
itical
in
s
p
ac
e
b
ec
au
s
e
o
f
th
e
atten
d
an
t
ch
allen
g
es
an
d
ex
p
en
s
es
ass
o
ciate
d
with
th
e
r
ep
air
.
Fo
r
th
e
cu
r
r
e
n
t
in
v
esti
g
atio
n
,
th
e
s
p
atial
en
v
ir
o
n
m
en
t
u
n
d
er
s
tu
d
y
r
elate
s
to
th
e
n
ea
r
-
ea
r
t
h
ex
ten
s
io
n
,
wh
ic
h
in
clu
d
es
a
r
a
n
g
e
o
f
altitu
d
es
r
an
g
in
g
f
r
o
m
l
o
w
-
ea
r
th
o
r
b
it
to
g
e
o
s
y
n
ch
r
o
n
o
u
s
o
r
b
it
an
d
b
ey
o
n
d
,
in
cl
u
d
in
g
all
p
o
s
s
ib
le
in
clin
atio
n
s
[
2
]
,
[
3
]
.
T
h
e
c
o
m
p
lex
an
d
ev
er
-
ch
an
g
in
g
n
at
u
r
al
s
p
ac
e
en
v
i
r
o
n
m
e
n
t
(
SE)
n
ea
r
ea
r
th
ca
n
b
e
d
escr
ib
ed
as
a
d
y
n
a
m
ic
p
h
en
o
m
en
o
n
.
T
h
e
o
u
tlin
e
an
d
ch
a
r
ac
ter
izatio
n
o
f
ea
r
th
'
s
f
ea
tu
r
e
s
ar
e
in
f
lu
e
n
ce
d
b
y
s
ev
er
al
co
m
p
o
n
e
n
ts
,
in
clu
d
in
g
th
e
ea
r
th
'
s
n
atu
r
al
g
eo
ch
em
ical
p
r
o
p
er
ties
,
ac
tiv
e
in
tellig
en
ce
b
etwe
en
th
e
ea
r
th
an
d
th
e
s
u
n
,
an
d
m
u
lt
ip
le
ev
en
ts
in
th
e
i
n
ter
s
tellar
an
d
p
lan
etar
y
s
p
ac
e
f
ield
[
4
]
.
T
h
e
d
if
f
er
en
t
in
ter
ac
tio
n
s
with
s
p
ac
e
s
y
s
tem
s
r
esu
lt in
a
wid
e
r
an
g
e
o
f
ef
f
e
cts
[
5
]
.
T
h
ese
ef
f
ec
ts
ar
e
d
iv
id
ed
in
to
n
atu
r
al
a
n
d
ar
tific
ial
ca
teg
o
r
ies
an
d
ar
e
cl
ass
if
ied
b
ased
o
n
th
e
v
ar
ia
b
les
o
f
th
e
SE
[
6
]
.
W
h
en
f
o
l
lo
win
g
th
e
p
r
esen
tatio
n
s
tr
ateg
y
,
a
s
et
o
f
n
atu
r
al
f
ac
to
r
s
an
d
th
eir
ef
f
ec
ts
o
n
n
ea
r
-
ea
r
th
s
p
ac
e
ar
e
p
r
esen
ted
in
T
ab
le
1
[
7
]
.
I
n
ad
d
itio
n
,
g
u
id
an
ce
s
y
s
tem
s
ar
e
u
s
ed
wi
th
in
th
e
s
atellite
o
r
s
h
u
ttle
to
co
r
r
ec
t
its
o
r
ien
tatio
n
,
as
m
en
tio
n
ed
in
[
8
]
–
[
1
0
]
.
Th
e
m
o
tio
n
o
f
th
e
s
atellite,
a
f
f
ec
ted
b
y
g
r
a
v
ity
an
d
o
th
er
f
o
r
ce
s
,
is
co
m
p
lex
.
I
t
is
im
p
o
r
tan
t
to
d
ev
elo
p
a
d
iag
r
am
o
f
th
e
tr
an
s
ien
t
b
eh
a
v
io
r
o
f
th
e
r
elev
an
t
f
o
r
ce
s
[
5
]
–
[
1
9
]
.
I
n
2
0
1
0
,
h
e
b
r
ief
ly
p
r
esen
ted
a
v
alu
ab
le
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ad
v
Ap
p
l Sci
I
SS
N:
2252
-
8
8
1
4
S
tu
d
y
o
f
a
mo
d
el
o
f a
s
a
tellite str
u
ctu
r
e
th
a
t m
ee
ts
th
e
n
ec
ess
a
r
y
crit
eria
fo
r
…
(
Ma
h
mo
u
d
F
a
d
h
el
I
d
a
n
)
503
r
ef
lectio
n
o
n
th
e
ef
f
ec
t
o
f
n
o
r
m
al
to
r
q
u
e
o
n
th
e
im
p
lem
e
n
tatio
n
o
f
n
o
d
e
n
u
m
b
e
r
(
N
)
-
1
0
t
h
r
u
s
t
tire
s
in
o
r
b
ital
elem
en
ts
[
2
0
]
.
R
ef
er
en
ce
s
f
o
r
m
o
d
elin
g
ac
cu
r
ate
g
r
av
itatio
n
al
r
ev
er
s
al
an
d
r
ad
iativ
e
weig
h
t
b
ased
o
n
th
e
s
u
n
ca
n
b
e
o
b
tain
ed
f
r
o
m
s
o
u
r
ce
s
3
,
4
,
an
d
5
.
A
s
atellite
i
s
n
o
t
a
n
in
s
ig
n
if
ican
t
co
n
ce
n
tr
atio
n
o
f
m
ass
in
s
tu
d
y
in
g
th
e
ex
p
lo
r
atio
n
o
f
a
p
lan
etar
y
b
o
d
y
,
as
alr
ea
d
y
ac
ce
p
te
d
b
y
Kep
ler
[
2
1
]
.
N
o
r
m
ally
,
th
e
s
h
u
ttle
is
s
u
b
jecte
d
to
ch
ar
ac
ter
is
tic
to
r
q
u
es
th
at
af
f
e
ct
its
o
p
er
atio
n
[
2
2
]
–
[
2
4
]
:
g
r
a
v
ity
r
am
p
to
r
q
u
e,
s
u
n
b
e
am
weig
h
t
to
r
q
u
e,
g
r
av
ity
to
r
q
u
e,
air
f
lo
w,
h
ea
t
p
r
o
b
e,
an
d
p
u
ls
e
th
r
u
s
t
to
r
q
u
e.
L
o
w
ea
r
th
o
r
b
it
(
L
E
O)
is
a
SE
th
at
p
o
s
es
v
ar
i
o
u
s
h
az
ar
d
o
u
s
elem
en
ts
,
in
clu
d
in
g
b
u
t
n
o
t
lim
ited
t
o
ato
m
ic
o
x
y
g
en
,
u
ltra
v
io
let
r
ad
iatio
n
,
an
d
io
n
izin
g
r
a
d
iatio
n
co
n
s
is
tin
g
o
f
elec
tr
o
n
s
an
d
p
r
o
to
n
s
,
h
ig
h
v
ac
u
u
m
,
p
lasma
,
m
icr
o
m
eteo
r
ites
,
d
eb
r
is
,
an
d
f
lu
ctu
atio
n
s
in
d
eg
r
ee
s
o
f
h
ea
t
[
2
5
]
–
[
3
0
]
.
Sp
ac
ec
r
af
t
ex
ter
io
r
s
u
r
f
ac
es
ar
e
s
u
b
ject
to
v
ar
io
u
s
en
v
ir
o
n
m
e
n
tal
s
tr
es
s
es
th
at
ca
n
d
eg
r
ad
e
th
eir
b
u
ild
in
g
m
ate
r
ials
.
On
e
to
p
ic
o
f
cu
r
r
en
t
in
te
r
est
is
th
e
im
p
ac
t
o
f
th
e
n
atu
r
al
s
p
atial
en
v
ir
o
n
m
en
t
o
n
s
p
ac
ec
r
af
t
d
esig
n
,
d
e
v
elo
p
m
en
t,
an
d
o
p
er
atio
n
s
.
I
n
2
0
1
8
,
Nak
k
a
et
a
l
.
s
tu
d
ied
a
r
o
b
o
tic
s
p
ac
ec
r
af
t
s
im
u
latio
n
p
latf
o
r
m
ca
lled
M
-
STAR
to
ev
alu
ate
c
o
n
f
ig
u
r
at
io
n
o
r
ien
tatio
n
,
r
elativ
e
n
av
ig
atio
n
,
an
d
c
o
n
tr
o
l
alg
o
r
ith
m
s
[
1
8
]
.
T
h
e
s
im
u
lat
io
n
f
u
n
ctio
n
s
with
f
r
ictio
n
less
tr
an
s
latio
n
al
an
d
r
o
tatio
n
al
m
o
tio
n
,
alo
n
g
s
id
e
g
r
av
ity
-
d
r
iv
en
f
lig
h
t
-
lik
e
en
g
i
n
es
[
3
1
]
–
[
3
3
]
.
A
2
0
1
9
s
tu
d
y
p
r
esen
ted
a
th
eo
r
etica
l
f
r
am
e
wo
r
k
f
o
r
a
n
aly
zin
g
th
e
d
y
n
am
ics
o
f
a
teth
e
r
ed
s
atellite
s
y
s
tem
.
I
t
in
clu
d
es
s
y
m
m
etr
ical
r
ig
id
s
tr
u
ctu
r
es
,
b
ala
n
ce
d
an
ch
o
r
p
o
in
ts
,
an
d
teth
er
in
g
to
m
i
n
im
ize
weig
h
t
[
3
4
]
.
Satellites
ap
p
r
o
ac
h
in
g
th
e
en
d
o
f
th
eir
s
er
v
ice
life
ca
n
b
e
r
e
f
u
r
b
is
h
ed
with
im
m
in
en
t
ca
p
ab
ilit
ies
[
3
5
]
.
T
h
e
r
ev
iv
al
o
f
an
u
n
u
s
ed
s
atellite
wa
s
en
ab
led
b
y
No
r
th
r
o
p
Gr
u
m
m
an
’
s
m
is
s
io
n
ex
ten
s
io
n
v
eh
icle
-
1
(
MEV
-
1
)
,
m
ar
k
in
g
a
n
ew
e
r
a
o
f
s
u
s
tain
ab
le
o
r
b
ital
u
tili
za
tio
n
an
d
a
d
v
an
ci
n
g
r
esear
ch
in
co
m
p
u
ter
s
im
u
latio
n
o
f
s
atellite
in
f
r
astru
ctu
r
e,
en
v
is
io
n
in
g
it
in
a
SE
.
T
h
e
s
y
s
tem
'
s
s
tr
u
ctu
r
al
in
teg
r
ity
is
in
f
lu
en
ce
d
b
y
v
a
r
y
in
g
m
o
m
en
ts
f
r
o
m
d
if
f
er
e
n
t
d
ir
ec
tio
n
s
.
T
h
is
s
tu
d
y
aim
s
to
im
p
r
o
v
e
th
e
g
eo
m
etr
ic
p
r
o
p
er
ties
an
d
m
o
m
en
t o
f
in
e
r
tia
f
o
r
e
n
h
an
ce
d
s
tab
ilit
y
an
d
r
o
tatio
n
d
u
r
in
g
s
p
ac
e
tr
an
s
it.
T
ab
le
1
.
SE
an
d
its
im
p
ac
t o
n
th
e
s
p
ac
e
s
y
s
tem
[
7
]
En
v
i
r
o
n
m
e
n
t
a
l
f
a
c
t
o
r
Ef
f
e
c
t
s
Ea
r
t
h
sh
i
n
e
a
n
d
s
u
n
l
i
g
h
t
P
o
w
e
r
,
p
h
o
t
o
-
m
i
ssi
o
n
,
t
o
r
q
u
e
,
d
r
a
g
,
mat
e
r
i
a
l
d
a
m
a
g
e
,
t
h
e
r
ma
l
c
y
c
l
i
n
g
,
a
n
d
h
e
a
t
i
n
g
G
r
a
v
i
t
y
To
r
q
u
e
s a
n
d
a
c
c
e
l
e
r
a
t
i
o
n
N
e
u
t
r
a
l
a
t
m
o
s
p
h
e
r
e
D
r
a
g
,
t
o
r
q
u
e
s,
h
i
g
h
v
a
c
u
u
m
,
v
a
c
u
u
m
c
o
n
t
a
mi
n
a
t
i
o
n
,
d
r
a
g
,
a
n
d
ma
t
e
r
i
a
l
d
e
g
r
a
d
a
t
i
o
n
S
y
st
e
m
g
e
n
e
r
a
t
e
d
S
y
st
e
m
d
e
p
e
n
d
e
n
t
:
p
l
a
s
ma,
n
e
u
t
r
a
l
s,
p
l
a
sma
,
f
o
r
c
e
s
,
f
i
e
l
d
s,
p
a
r
t
i
c
l
e
s,
r
a
d
i
a
t
i
o
n
,
a
n
d
t
o
r
q
u
e
s
T
h
e
s
tu
d
y
aim
ed
t
o
d
ev
el
o
p
a
s
tab
le
o
ctag
o
n
al
s
atellite
s
tr
u
ctu
r
e
u
s
in
g
d
y
n
am
ic
m
o
d
el
in
g
an
d
f
in
ite
elem
en
t
an
aly
s
is
an
d
ev
alu
ate
s
tr
ess
,
d
is
p
lace
m
en
t,
an
d
v
ib
r
atio
n
th
r
o
u
g
h
o
u
t
th
e
d
esig
n
p
r
o
ce
s
s
.
I
n
ad
d
itio
n
,
it
s
o
u
g
h
t
to
o
p
tim
ize
th
e
g
eo
m
etr
ic
p
r
o
p
e
r
ties
an
d
m
o
m
en
t
o
f
in
er
tia
to
en
s
u
r
e
th
at
th
e
s
atellite
m
ee
t
s
th
e
n
ec
ess
ar
y
cr
iter
ia
f
o
r
s
tab
ilit
y
an
d
r
o
tatio
n
d
u
r
in
g
s
p
ac
e
tr
av
el.
T
h
e
r
esear
ch
q
u
esti
o
n
in
th
is
s
tu
d
y
is
“
Ho
w
ca
n
a
s
tab
le
o
cta
g
o
n
al
s
atellite
s
tr
u
ctu
r
e
b
e
d
ev
el
o
p
ed
u
s
in
g
d
y
n
am
ic
m
o
d
elin
g
an
d
f
in
ite
e
lem
en
t
an
aly
s
is
b
y
ev
alu
atin
g
s
tr
ess
,
d
is
p
lace
m
en
t
,
an
d
v
ib
r
atio
n
th
r
o
u
g
h
o
u
t
t
h
e
d
esig
n
p
r
o
ce
s
s
?
”.
T
h
e
r
esear
ch
in
n
o
v
atio
n
s
in
th
is
s
tu
d
y
ar
e
s
atellite
d
esig
n
s
th
at
h
av
e
f
o
c
u
s
ed
p
r
im
ar
ily
o
n
cy
lin
d
r
ical
an
d
cu
b
ic
s
h
a
p
es.
W
e
s
tu
d
ied
th
e
o
ctag
o
n
t
o
ex
p
l
o
r
e
th
e
p
o
ten
ti
al
o
f
th
e
o
cta
g
o
n
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
Sa
t
ellit
e
s
t
ruct
ure
re
presenta
t
io
n
T
o
s
im
u
late
a
co
m
m
u
n
icatio
n
s
s
atell
ite
o
p
er
atin
g
in
a
cir
cu
lar
lo
w
ea
r
th
o
r
b
it
u
n
d
er
SE
c
o
n
d
itio
n
s
,
we
u
s
ed
a
co
m
p
u
tatio
n
al
an
al
y
s
is
tech
n
iq
u
e
ca
lled
th
e
f
i
n
ite
elem
en
t
m
eth
o
d
(
FEM
)
to
t
h
o
r
o
u
g
h
ly
ex
am
in
e
s
tr
ess
,
s
tr
ain
,
an
d
v
ib
r
atio
n
th
r
o
u
g
h
o
u
t
th
e
en
tire
s
atellite
s
tr
u
ctu
r
e.
T
h
e
f
r
am
e
s
u
b
s
t
r
u
ctu
r
e
in
th
e
SE
u
n
d
er
g
o
es
v
ar
y
i
n
g
d
e
g
r
ee
s
o
f
to
r
q
u
e
s
tr
ess
f
r
o
m
m
u
ltid
ir
ec
ti
o
n
al
f
o
r
ce
s
d
u
r
in
g
th
e
co
m
p
u
t
atio
n
al
s
im
u
latio
n
.
T
o
ac
co
m
p
lis
h
th
is
,
we
d
esig
n
ed
a
test
m
o
d
el
in
th
e
s
h
ap
e
o
f
an
o
ctag
o
n
with
a
d
iam
et
er
o
f
1
1
0
cm
an
d
a
h
eig
h
t
o
f
8
5
cm
,
as
s
h
o
wn
in
Fig
u
r
e
1
.
Fig
u
r
e
2
,
c
o
n
tain
s
a
leg
en
d
th
at
illu
s
tr
ates
th
e
n
u
m
b
er
o
f
elem
e
n
ts
an
d
n
o
d
es
in
th
e
p
r
o
p
o
s
ed
s
atellite
s
tr
u
ctu
r
e,
in
clu
d
in
g
t
h
e
co
n
n
ec
tio
n
p
o
in
ts
b
etwe
en
th
em
.
W
e
an
aly
ze
d
th
e
s
tr
u
ctu
r
al
p
r
o
p
e
r
ties
b
y
em
p
lo
y
in
g
a
d
y
n
a
m
ic
m
o
d
elin
g
a
p
p
r
o
ac
h
,
u
s
in
g
FEM
as
th
e
co
m
p
u
tatio
n
al
an
aly
s
is
m
eth
o
d
.
MSC
Nastra
n
s
o
f
twar
e
was
u
s
ed
f
o
r
s
tatic
an
d
d
y
n
am
ic
an
aly
s
es,
an
d
a
n
al
y
s
es
f
o
r
s
tr
u
ctu
r
al
o
p
tim
izatio
n
,
f
atig
u
e,
an
d
v
ib
r
atio
n
u
s
in
g
FEM
s
.
T
h
is
ap
p
r
o
ac
h
en
ab
led
a
c
o
m
p
r
e
h
en
s
iv
e
in
v
esti
g
atio
n
o
f
th
e
allo
ca
tio
n
o
f
s
tr
ess
,
f
atig
u
e,
a
n
d
v
i
b
r
atio
n
t
h
r
o
u
g
h
o
u
t
t
h
e
s
tr
u
ctu
r
e.
T
h
e
test
m
o
d
el
f
r
a
m
e
is
r
ep
r
esen
ted
as
a
r
ig
h
t
o
ctag
o
n
o
f
p
lates
an
d
b
a
r
s
,
with
th
e
p
late
b
ein
g
r
e
p
r
esen
ted
b
y
a
f
o
u
r
-
n
o
d
e
q
u
a
d
r
ila
ter
al
elem
en
t.
T
h
e
s
tr
u
ctu
r
e
co
n
s
is
ts
o
f
th
r
ee
b
a
s
es:
u
p
p
er
,
m
id
d
le,
an
d
lo
wer
.
E
ac
h
b
ase
in
clu
d
es
f
o
u
r
p
l
ate
e
lem
en
ts
,
eig
h
t
p
er
ip
h
er
al
n
o
d
es,
an
d
o
n
e
ce
n
tr
al
n
o
d
e
.
Ad
d
itio
n
ally
,
ea
ch
r
o
d
is
r
ep
r
esen
ted
b
y
a
two
-
n
o
d
e
elem
en
t.
T
h
e
u
p
p
er
a
n
d
lo
wer
b
ases
ea
ch
co
n
s
is
t
o
f
eig
h
t
elem
en
ts
,
wh
ile
th
e
m
id
d
le
b
ase
is
r
ein
f
o
r
ce
d
with
two
ad
d
itio
n
al
b
ar
s
.
T
h
e
r
e
ar
e
two
r
o
d
s
a
t
t
h
e
m
id
d
le
b
ase,
with
th
e
f
ir
s
t
co
n
n
ec
tin
g
k
n
o
t
1
1
to
ce
n
tr
al
k
n
o
t
2
5
an
d
th
e
s
ec
o
n
d
co
n
n
ec
tin
g
k
n
o
t
1
5
to
ce
n
tr
al
k
n
o
t
2
5
.
E
ig
h
t
r
o
d
s
co
n
n
ec
t
th
e
u
p
p
er
b
ase
to
th
e
m
id
d
le
b
ase,
an
d
an
o
th
er
ei
g
h
t
co
n
n
ec
t
th
e
l
o
wer
b
ase
to
th
e
m
id
d
le
b
ase.
T
h
e
f
ir
s
t
r
o
d
a
t
t
h
e
m
id
d
le
b
ase
co
n
n
ec
ts
k
n
o
t
2
7
to
k
n
o
t
2
5
,
a
n
d
th
e
s
ec
o
n
d
c
r
o
s
s
b
ar
co
n
n
ec
ts
k
n
o
t
2
5
to
k
n
o
t
2
6
.
A
p
late
is
a
f
o
u
r
-
s
id
ed
p
lan
e
with
u
n
if
o
r
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
1
4
I
n
t J Ad
v
Ap
p
l Sci
,
Vo
l.
14
,
No
.
2
,
J
u
n
e
2
0
2
5
:
5
0
2
-
512
504
th
ick
n
ess
.
All
elem
en
ts
,
f
r
o
m
p
lates
to
b
ar
s
,
h
a
v
e
th
e
s
am
e
p
h
y
s
ical
p
r
o
p
er
ties
.
E
ac
h
n
o
d
e
h
as
s
ix
d
eg
r
ee
s
o
f
fre
ed
o
m
,
th
r
ee
tr
an
s
latio
n
al
a
n
d
th
r
ee
r
o
tatio
n
al.
T
h
e
o
r
ig
i
n
is
lo
ca
ted
in
th
e
m
id
d
le
o
f
th
e
b
o
d
y
at
n
o
d
e
2
5
.
T
h
is
g
iv
es
th
e
am
o
u
n
t
o
f
2
7
n
o
d
es
(
N)
an
d
5
4
elem
e
n
ts
(
NE
)
,
with
1
2
elem
en
ts
r
ep
r
e
s
en
tin
g
p
lates
an
d
4
2
elem
en
ts
r
ep
r
esen
tin
g
r
o
d
s
.
Fig
u
r
e
1
illu
s
t
r
ates
th
e
d
is
tr
ib
u
tio
n
o
f
p
an
els,
b
ar
s
,
an
d
n
o
d
es
o
n
th
e
f
r
am
e
.
T
o
ad
eq
u
ately
m
ee
t
th
e
r
e
q
u
ir
e
m
en
ts
o
f
th
ese
lo
a
d
s
,
it
is
r
e
co
m
m
en
d
e
d
to
u
s
e
th
e
v
o
n
M
is
es
s
tr
e
s
s
(
σ
v
M
)
cr
iter
io
n
to
ass
ess
th
e
y
ield
ca
p
ac
ity
o
r
b
r
ittl
en
ess
o
f
th
e
m
ater
ial.
T
h
e
e
x
p
er
im
e
n
tal
p
r
o
to
ty
p
e
will
b
e
f
ab
r
icate
d
u
s
in
g
7
,
0
5
7
alu
m
i
n
u
m
allo
y
,
ch
o
s
en
f
or
its
n
o
te
wo
r
th
y
m
ec
h
an
ical
p
r
o
p
er
ties
,
in
clu
d
in
g
a
te
n
s
ile
s
tr
en
g
th
o
f
5
7
2
MPa
an
d
y
ield
s
tr
en
g
th
o
f
5
0
3
MPa.
Fig
u
r
e
1
.
Satellite a
r
ch
itectu
r
e
with
m
o
d
elin
g
an
aly
s
is
Fig
u
r
e
2
.
A
l
eg
e
n
d
th
at
d
is
p
lay
s
th
e
n
u
m
b
er
o
f
elem
en
ts
an
d
n
o
d
es in
th
e
p
r
o
p
o
s
ed
s
atellite
s
tr
u
ctu
r
e
an
d
th
e
co
n
n
ec
tio
n
p
o
in
ts
b
etwe
en
t
h
e
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ad
v
Ap
p
l Sci
I
SS
N:
2252
-
8
8
1
4
S
tu
d
y
o
f
a
mo
d
el
o
f a
s
a
tellite str
u
ctu
r
e
th
a
t m
ee
ts
th
e
n
ec
ess
a
r
y
crit
eria
fo
r
…
(
Ma
h
mo
u
d
F
a
d
h
el
I
d
a
n
)
505
2
.
2
.
Repre
s
ent
a
t
io
n o
f
lo
a
ds
o
n t
he
s
a
t
ellit
e
s
t
ruct
ure
T
h
e
p
r
o
to
t
y
p
e'
s
s
teer
in
g
an
d
h
an
d
lin
g
will
b
e
co
n
tr
o
lled
u
s
in
g
1
0
N
m
o
to
r
s
,
k
n
o
wn
f
o
r
th
eir
lo
w
lev
els
o
f
th
r
u
s
t.
T
h
e
p
u
ls
e
d
u
r
atio
n
is
ty
p
ically
s
h
o
r
t,
with
a
m
in
im
u
m
o
f
0
.
3
s
ec
o
n
d
s
.
T
o
a
n
aly
ze
th
e
s
tr
ess
es
an
d
d
ef
o
r
m
atio
n
s
o
f
t
h
e
s
tr
u
ctu
r
e,
we
d
eter
m
in
e
d
an
d
cl
ass
if
ied
th
e
lo
ad
s
as
in
ter
n
al
an
d
ex
ter
n
al.
T
h
e
in
ter
n
al
lo
ad
s
r
e
p
r
esen
t
th
e
p
ay
lo
a
d
s
,
s
u
ch
as
th
e
co
m
m
u
n
icatio
n
an
ten
n
a
in
s
talled
at
n
o
d
e
2
7
,
t
h
e
co
m
p
r
ess
ed
air
ta
n
k
t
o
s
u
p
p
ly
th
e
th
r
u
s
ter
s
in
th
e
air
,
a
n
d
th
e
en
er
g
y
s
to
r
ag
e
b
atter
y
in
s
talled
b
etw
ee
n
p
o
in
ts
2
5
an
d
2
7
to
s
u
p
p
ly
elec
tr
ica
l
p
o
wer
t
o
th
e
s
atellite
in
th
e
d
ar
k
ar
ea
.
Fu
r
th
er
m
o
r
e,
t
h
e
co
n
tr
o
l
s
y
s
tem
s
ar
e
r
ep
r
esen
ted
b
y
two
t
h
r
u
s
t
m
o
to
r
s
(
1
0
N)
in
s
talled
in
n
o
d
es
1
4
an
d
1
8
in
th
e
x
d
ir
ec
t
io
n
,
an
d
two
m
o
r
e
in
s
talled
in
n
o
d
es
2
a
n
d
6
in
th
e
y
d
ir
ec
tio
n
,
t
o
h
an
d
le
in
te
r
n
al
lo
a
d
s
an
d
f
o
r
m
o
v
e
m
en
t
an
d
m
an
eu
v
er
in
g
.
E
x
ter
n
al
lo
ad
s
in
clu
d
e
g
r
av
it
atio
n
al
f
o
r
ce
s
f
r
o
m
th
e
ea
r
th
,
s
u
n
,
an
d
o
th
e
r
p
lan
ets,
as
well
as
air
p
r
ess
u
r
e.
T
h
ese
ex
ter
n
al
l
o
ad
s
ca
n
b
e
r
e
p
r
esen
ted
b
y
a
to
r
q
u
e
th
at
af
f
e
cts
all
n
o
d
es
eq
u
ally
,
with
a
to
r
q
u
e
o
f
1
Nm
.
T
h
e
to
tal
to
r
q
u
e
o
f
th
e
ex
ter
n
al
l
o
a
d
g
r
o
u
p
is
less
th
an
1
Nm
.
T
o
ass
ess
th
e
s
tr
e
s
s
an
d
d
ef
o
r
m
a
tio
n
ca
p
ab
ilit
ies
o
f
th
e
in
ten
d
e
d
s
atellite
co
n
s
tr
u
c
tio
n
,
an
in
v
esti
g
atio
n
was
co
n
d
u
cted
o
n
d
if
f
er
e
n
t
class
es
o
f
lo
ad
s
to
wh
ic
h
t
h
e
p
r
o
to
ty
p
e
is
s
u
b
jecte
d
to
SE
t
esti
n
g
.
C
o
n
v
en
tio
n
al
an
aly
s
is
was
ca
r
r
ied
o
u
t
to
d
eter
m
in
e
th
e
f
r
eq
u
e
n
cies
an
d
m
o
d
es
co
r
r
esp
o
n
d
in
g
t
o
th
e
s
tr
u
ctu
r
e,
al
o
n
g
with
th
eir
co
r
r
esp
o
n
d
in
g
m
o
d
es.
I
n
th
e
f
ield
o
f
s
tatic
an
aly
s
is
,
th
e
o
b
s
er
v
ed
d
is
p
lace
m
en
t
ca
u
s
ed
b
y
th
e
ap
p
lied
lo
a
d
was c
alcu
lated
.
Fu
r
th
er
m
o
r
e,
th
e
m
et
h
o
d
u
s
ed
f
o
r
s
tatic
an
aly
s
is
in
clu
d
ed
th
e
ca
lcu
latio
n
o
f
co
m
p
o
n
en
t
f
o
r
ce
s
,
s
tr
ess
es,
an
d
in
ter
ac
tio
n
f
o
r
ce
s
.
An
ex
am
in
atio
n
was
co
n
d
u
cte
d
to
s
tu
d
y
th
e
ef
f
ec
t
o
f
an
ap
p
lied
to
r
q
u
e
o
f
1
N
m
o
n
th
e
d
is
tr
ib
u
tio
n
o
f
σ
v
M
alo
n
g
th
e
X
an
d
Y
co
o
r
d
in
ates
o
f
th
e
s
tr
u
ctu
r
e
to
co
p
e
with
th
e
e
x
ter
n
al
lo
ad
s
.
Fu
r
th
er
m
o
r
e
,
th
e
ef
f
ec
ts
o
f
th
e
ap
p
lied
to
r
q
u
e
o
f
1
0
N
o
n
th
e
d
is
tr
ib
u
tio
n
o
f
σ
v
M
alo
n
g
th
e
X
a
n
d
Y
co
o
r
d
in
ates
o
f
th
e
s
tr
u
ctu
r
e
wer
e
s
tu
d
ied
to
ad
d
r
ess
in
ter
n
al
lo
ad
s
,
m
a
n
eu
v
er
,
an
d
co
m
p
lete
th
e
task
s
ass
ig
n
ed
to
th
e
p
r
o
p
o
s
ed
s
atellite.
2
.
3
.
P
r
o
pert
ies o
f
7
,
0
7
5
a
lum
inu
m
a
llo
y
Alu
m
in
u
m
ty
p
e
7
,
0
7
5
is
o
n
e
o
f
th
e
s
tr
o
n
g
est
alu
m
in
u
m
allo
y
s
[
3
6
]
–
[
3
8
]
.
I
ts
h
ig
h
y
ield
s
tr
en
g
th
an
d
lo
w
d
en
s
ity
m
ak
e
th
e
m
ater
i
al
s
u
itab
le
f
o
r
ap
p
licatio
n
s
s
u
ch
as
air
cr
af
t
p
ar
ts
o
r
p
ar
ts
s
u
b
ject
to
h
ea
v
y
co
r
r
o
s
io
n
air
cr
af
t
f
itti
n
g
s
.
T
h
e
co
m
p
o
s
itio
n
o
f
7
,
0
7
5
al
u
m
in
u
m
allo
y
r
o
u
g
h
l
y
in
cl
u
d
es
5
.
6
-
6
.
1
%
zin
c,
2
.
1
-
2
.
5
%
m
ag
n
esiu
m
,
1
.
2
-
1
.
6
%
co
p
p
er
,
an
d
less
th
an
h
alf
a
p
er
ce
n
t
s
ilico
n
,
ir
o
n
,
m
an
g
an
ese,
titan
iu
m
,
ch
r
o
m
iu
m
,
a
n
d
o
th
er
m
etals
[
3
7
]
.
I
ts
d
en
s
ity
is
2
.
8
1
g
/c
m
3
,
wh
ich
is
r
elativ
ely
lig
h
t
f
o
r
a
m
etal.
7
,
0
7
5
alu
m
in
u
m
is
o
n
e
o
f
th
e
s
tr
o
n
g
est
alu
m
in
u
m
allo
y
s
av
ailab
le,
m
ak
in
g
it
v
al
u
ab
le
in
h
ig
h
-
s
tr
ess
s
itu
atio
n
s
.
T
h
e
co
p
p
er
c
o
n
ten
t
in
7
,
0
7
5
alu
m
in
u
m
in
cr
ea
s
es
its
s
u
s
ce
p
tib
ilit
y
to
co
r
r
o
s
io
n
.
A
m
ate
r
ial's
r
esis
tan
ce
to
d
ef
o
r
m
atio
n
is
d
eter
m
in
ed
b
y
its
m
o
d
u
lu
s
o
f
elasticity
a
n
d
s
h
ea
r
m
o
d
u
lu
s
.
T
h
e
m
o
d
u
lu
s
o
f
elasticity
f
o
r
7
,
0
7
5
alu
m
in
u
m
is
7
1
.
7
GPa,
an
d
th
e
s
h
ea
r
m
o
d
u
lu
s
is
2
6
.
9
GPa
(
s
ee
T
ab
le
2
)
[
3
8
]
,
[
3
9
]
.
On
e
o
f
th
e
m
o
s
t
im
p
o
r
tan
t
m
ea
s
u
r
es
is
its
y
iel
d
s
tr
en
g
th
.
T
h
e
y
ield
s
tr
en
g
th
o
f
a
m
ater
ial
is
d
ef
in
ed
as
th
e
m
ax
im
u
m
am
o
u
n
t
o
f
s
tr
ess
(
o
r
f
o
r
ce
o
v
e
r
a
n
a
r
e
a)
th
at
will
n
o
t
p
er
m
an
en
tly
d
ef
o
r
m
th
e
m
ater
ial.
T
h
e
y
iel
d
s
tr
en
g
th
o
f
7
,
0
7
5
alu
m
in
u
m
is
5
0
3
GPa
[
3
6
]
.
T
ab
le
2
.
Me
ch
a
n
ical
p
r
o
p
er
tie
s
o
f
7
,
0
7
5
alu
m
i
n
u
m
allo
y
[
3
6
]
M
e
c
h
a
n
i
c
a
l
p
r
o
p
e
r
t
i
e
s
M
e
a
su
r
e
me
n
t
(
M
P
a
)
Te
n
s
i
l
e
s
t
r
e
n
g
t
h
5
7
2
Y
i
e
l
d
t
e
n
si
l
e
st
r
e
n
g
t
h
5
0
3
S
h
e
a
r
st
r
e
n
g
t
h
3
3
1
F
a
t
i
g
u
e
s
t
r
e
n
g
t
h
1
5
9
M
o
d
u
l
u
s
o
f
e
l
a
s
t
i
c
i
t
y
7
1
.
7
S
h
e
a
r
mo
d
u
l
u
s
2
6
.
9
2
.
4
.
Vo
n
M
is
es
cr
it
er
io
n
T
h
e
σ
v
M
s
tr
ess
cr
iter
io
n
s
im
p
lifie
s
s
tr
ess
an
aly
s
is
b
y
p
r
o
v
id
in
g
a
s
in
g
le
v
alu
e
th
at
s
u
m
m
ar
izes
th
e
to
tal
s
tr
es
s
in
ten
s
ity
,
r
eg
ar
d
les
s
o
f
d
ir
ec
tio
n
.
Fo
r
ev
alu
atin
g
m
ater
ials
u
n
d
er
m
u
lti
-
ax
ial
s
tr
ess
,
th
is
ef
f
ec
tiv
ely
ca
p
tu
r
es
th
e
co
m
b
in
ed
ef
f
ec
ts
o
f
m
u
ltip
le
s
tr
ess
es
at
a
s
in
g
le
p
o
in
t.
T
h
is
ca
p
ab
il
ity
e
n
h
a
n
ce
s
th
e
s
af
ety
an
d
r
eliab
ilit
y
o
f
s
tr
u
ctu
r
es a
n
d
p
r
o
d
u
cts,
m
ak
in
g
it e
s
s
en
tial f
o
r
s
tr
ess
an
aly
s
i
s
in
s
atellite
s
tr
u
ctu
r
es.
T
h
e
σ
v
M
is
ca
lcu
lated
u
s
in
g
th
e
(
1
)
.
=
√
(
−
)
2
+
(
−
)
2
+
(
−
)
2
+
6
(
2
+
2
+
2
)
(
1
)
I
n
th
is
co
n
te
x
t,
σ
x
,
σ
y
,
an
d
σ
z
r
ep
r
esen
t
th
e
n
o
r
m
al
s
tr
ess
es
in
th
e
x
,
y
,
an
d
z
d
ir
ec
tio
n
s
,
wh
ile
τ
x
,
τ
y
,
an
d
τ
z
d
en
o
te
th
e
s
h
ea
r
s
tr
ess
es in
th
e
r
esp
ec
tiv
e
x
,
y
,
an
d
z
p
lan
es.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
1
4
I
n
t J Ad
v
Ap
p
l Sci
,
Vo
l.
14
,
No
.
2
,
J
u
n
e
2
0
2
5
:
5
0
2
-
512
506
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
r
esu
lts
o
b
tain
ed
f
r
o
m
th
e
an
aly
s
is
ar
e
s
h
o
wn
in
T
ab
le
3
an
d
Fi
g
u
r
es
3
-
2
4
.
T
ab
le
3
s
h
o
ws
th
e
eig
en
v
ec
to
r
s
an
d
th
eir
co
r
r
esp
o
n
d
in
g
m
o
d
es,
wh
ich
ar
e
s
im
ilar
to
th
e
f
ix
ed
d
is
p
lace
d
f
ea
tu
r
es
in
Fig
u
r
e
3
.
T
h
e
h
ig
h
est
d
is
to
r
tio
n
v
alu
es
ar
e
f
o
u
n
d
in
m
o
d
es
6
an
d
5
,
with
d
is
to
r
tio
n
v
alu
es
o
f
0
.
0
5
4
4
an
d
0
.
0
4
8
8
m
,
r
esp
ec
tiv
ely
,
at
eig
e
n
v
ec
to
r
s
o
f
1
8
7
.
8
5
9
0
4
a
n
d
1
7
8
.
6
3
5
7
Hz.
I
n
s
tab
ilit
y
a
n
aly
s
is
,
o
b
s
er
v
ed
d
is
p
lace
m
en
t
r
ef
er
s
to
th
e
p
h
y
s
ical
d
is
p
lace
m
en
t
r
esu
ltin
g
f
r
o
m
an
ap
p
lied
lo
ad
.
T
h
is
s
tu
d
y
ex
p
lo
r
e
s
th
e
ef
f
ec
t
o
f
an
ap
p
lied
to
r
q
u
e
o
f
1
N
o
n
th
e
d
is
p
er
s
io
n
o
f
σ
v
M
ac
r
o
s
s
th
e
X
an
d
Y
a
x
es.
Fig
u
r
es
4
-
6
ill
u
s
tr
ate
th
e
v
alu
es
o
f
σ
v
M
with
in
d
if
f
e
r
en
t
s
tr
u
ct
u
r
al
co
m
p
o
n
e
n
ts
,
ex
am
i
n
in
g
th
e
s
tr
ess
d
is
tr
ib
u
tio
n
d
u
e
to
th
e
t
o
r
q
u
e.
T
h
e
o
b
s
er
v
ed
d
is
p
lace
m
en
t
v
al
u
es
at
th
e
ch
a
r
ac
ter
is
tic
n
o
d
es
o
f
th
e
s
tr
u
ctu
r
e,
alo
n
g
with
th
ei
r
c
o
r
r
esp
o
n
d
in
g
X
an
d
Y
co
o
r
d
in
ates
u
n
d
e
r
a
1
N
to
r
q
u
e,
ar
e
s
h
o
w
n
in
Fig
u
r
es
7
-
9
.
Fu
r
th
e
r
m
o
r
e,
Fig
u
r
es
10
-
1
5
d
is
p
lay
th
e
cu
r
r
en
t
v
alu
es
o
f
σ
v
M
with
in
d
if
f
er
en
t
s
tr
u
ctu
r
al
co
m
p
o
n
e
n
ts
o
f
th
e
s
y
s
tem
,
alo
n
g
with
th
eir
co
r
r
esp
o
n
d
in
g
d
is
tr
ib
u
tio
n
s
.
T
h
ese
s
tr
ess
v
al
u
es
wer
e
o
b
tain
ed
wh
ile
th
e
s
y
s
tem
was
s
u
b
jecte
d
to
a
th
r
u
s
t
lo
ad
o
f
1
0
N
i
n
b
o
th
th
e
X
an
d
Y
d
ir
ec
tio
n
s
.
Fig
u
r
es
1
6
-
2
1
d
is
p
lay
th
e
d
is
p
lace
m
en
t
m
ag
n
itu
d
es
o
f
v
ar
i
o
u
s
n
o
d
es
at
th
e
X
an
d
Y
co
o
r
d
in
ates
o
f
th
e
s
tr
u
c
tu
r
e.
T
h
ese
m
ea
s
u
r
em
e
n
ts
wer
e
tak
en
wh
ile
s
u
b
jectin
g
th
e
s
t
r
u
ctu
r
e
to
a
t
h
r
u
s
t
lo
ad
o
f
1
0
N
in
b
o
th
d
ir
ec
tio
n
s
.
B
ased
o
n
th
e
ex
p
er
im
en
tal
f
in
d
in
g
s
,
it
is
ev
id
en
t
th
at
s
tr
e
s
s
d
if
f
u
s
io
n
r
esu
lts
in
a
s
ig
n
if
ican
t
in
cr
ea
s
e
in
s
tr
ess
lev
els
o
n
th
e
b
o
tto
m
p
late
o
f
elem
en
t
3
4
c
o
m
p
ar
e
d
to
o
th
er
p
late
an
d
r
o
d
elem
en
ts
.
T
h
e
h
in
g
e
p
o
s
itio
n
s
ar
e
o
f
p
ar
ticu
lar
in
ter
est,
wit
h
a
r
ec
o
r
d
ed
σ
v
M
o
f
3
1
4
.
7
1
4
N/m
2
.
Ad
d
itio
n
ally
,
b
o
th
th
e
h
in
g
es
an
d
th
e
b
o
d
y
p
an
el
ex
p
er
ien
ce
d
ex
tr
em
e
s
tr
ess
lev
els
o
f
4
,
4
2
3
N/m
².
W
h
en
a
s
p
ec
if
ic
ar
ch
itectu
r
al
s
tr
u
ctu
r
e
is
s
u
b
jecte
d
to
a
d
r
iv
i
n
g
f
o
r
ce
in
th
e
x
-
ax
is
,
th
e
co
m
p
o
n
e
n
t e
x
h
ib
itin
g
th
e
h
ig
h
est s
tr
es
s
lev
el
is
co
m
p
o
n
en
t
4
9
,
wh
ile
t
h
e
s
tr
ess
lev
el
is
lo
wer
in
ele
m
en
t
3
8
d
u
e
to
its
p
late
-
ty
p
e
n
atu
r
e,
in
c
o
n
tr
ast
to
th
e
s
tr
ip
elem
en
t
n
u
m
b
er
(
N
E
)
4
9
.
T
h
e
r
esu
lts
ab
o
v
e
d
e
m
o
n
s
tr
ate
h
o
w
ex
ter
n
al
f
o
r
ce
s
in
ter
ac
t
with
th
e
s
tr
u
ctu
r
e,
g
u
id
in
g
d
esig
n
an
d
tech
n
o
lo
g
ical
ap
p
licatio
n
s
.
W
h
en
th
e
th
r
u
s
t
lo
ad
is
ap
p
lied
in
th
e
y
d
ir
ec
tio
n
,
elem
en
t 4
2
ex
p
e
r
ien
ce
s
th
e
h
i
g
h
est s
tr
ess
,
wh
ile
elem
en
t 4
9
ex
p
er
ien
ce
s
th
e
lo
west st
r
ess
with
in
th
e
s
tr
u
ctu
r
e.
Ad
d
iti
o
n
ally
,
th
e
m
a
x
im
u
m
d
is
p
lace
m
en
t
o
cc
u
r
s
at
n
o
d
e
4
in
two
d
if
f
er
e
n
t
d
ir
ec
tio
n
s
.
T
h
er
e
is
a
n
o
ticea
b
le
d
if
f
er
en
ce
in
s
tr
ess
lev
els b
et
wee
n
item
s
1
-
3
2
an
d
3
3
-
5
4
,
w
h
ich
is
attr
ib
u
ted
to
th
eir
s
tr
u
ctu
r
al
ch
ar
ac
ter
is
tics
-
th
e
f
o
r
m
er
co
n
s
is
ts
o
f
r
o
d
s
,
a
n
d
th
e
latt
er
co
n
s
is
ts
o
f
s
h
ee
t
s
tr
u
ctu
r
es.
T
h
is
r
esu
lt
em
p
h
as
izes
th
e
cr
itical
r
o
le
th
at
th
e
in
h
e
r
en
t
s
tr
u
ctu
r
al
p
r
o
p
er
ties
o
f
m
ater
ials
p
lay
in
d
eter
m
in
in
g
th
eir
s
tr
ess
r
esp
o
n
s
e.
T
h
e
p
r
o
p
o
s
ed
s
atellite
i
s
s
u
b
jecte
d
to
en
v
ir
o
n
m
e
n
tal
lo
ad
s
f
r
o
m
ac
c
eler
atio
n
in
a
s
p
ac
e
f
ield
.
T
o
d
eter
m
in
e
th
e
d
is
p
lace
m
en
ts
an
d
s
tr
ess
es
e
x
p
er
ien
ce
d
b
y
th
e
n
o
d
es
an
d
ch
ar
ac
ter
is
tic
elem
en
ts
u
n
d
er
v
ar
iab
le
lo
a
d
s
,
tr
an
s
ien
t
r
esp
o
n
s
e
a
n
aly
s
is
u
s
in
g
th
e
FEM
co
n
f
ig
u
r
atio
n
m
o
d
el
f
o
llo
wed
b
y
lo
a
d
a
p
p
lic
atio
n
is
n
ec
ess
ar
y
.
Fig
u
r
e
2
2
v
is
u
ally
r
e
p
r
esen
ts
th
e
r
elatio
n
s
h
ip
b
etwe
en
d
is
p
l
ac
em
en
t
an
d
tim
e,
wh
ile
th
e
s
tr
ess
d
is
tr
ib
u
tio
n
is
in
v
esti
g
ated
.
T
h
e
in
v
esti
g
atio
n
illu
s
tr
ates
th
e
σ
v
M
in
v
ar
i
o
u
s
co
m
p
o
n
en
ts
,
as
s
h
o
wn
i
n
Fig
u
r
e
2
3
.
T
h
e
s
tr
u
ctu
r
e
was
s
u
b
jecte
d
to
a
f
r
eq
u
e
n
cy
r
an
g
e
o
f
0
to
2
0
0
Hz,
with
an
ad
d
itio
n
al
s
tep
o
f
1
Hz.
Fig
u
r
e
2
4
p
r
o
v
id
es a
g
r
ap
h
ical
r
ep
r
esen
t
atio
n
o
f
th
e
r
elatio
n
s
h
ip
b
etwe
en
d
is
p
lace
m
en
t a
n
d
f
r
e
q
u
en
c
y
.
T
ab
le
3
O
u
tp
u
t su
m
s
f
o
r
ea
c
h
ca
s
e,
th
e
m
o
d
al
v
al
u
e
in
h
er
tz,
an
d
th
e
t
o
tal
d
is
to
r
tio
n
at
th
at
f
r
eq
u
e
n
cy
C
a
se
n
u
m
b
e
r
Ei
g
e
n
v
e
c
t
o
r
s (H
z
)
To
t
a
l
d
i
st
o
r
t
i
o
n
(
c
m)
1
1
.
9
3
5
5
9
0
.
0
4
0
5
2
3
.
4
9
0
0
3
0
.
0
4
0
7
3
4
6
.
6
2
0
1
5
0
.
0
5
9
1
4
4
9
.
2
8
5
2
1
0
.
0
6
2
5
5
1
7
8
.
6
3
5
7
0
.
0
4
8
8
6
1
8
7
.
8
5
9
0
4
0
.
0
5
4
4
3
.
1
.
P
r
a
ct
ica
l i
m
pli
ca
t
io
ns
T
h
e
Nastra
n
s
o
f
twar
e
was
u
s
ed
f
o
r
d
y
n
am
ic
m
o
d
elin
g
a
n
d
f
in
ite
elem
en
t
an
aly
s
is
in
th
is
s
tu
d
y
.
T
h
e
r
esear
ch
f
o
cu
s
ed
o
n
d
e
v
elo
p
i
n
g
a
s
tab
le
o
ctag
o
n
al
s
atellit
e
s
tr
u
ctu
r
e,
with
an
em
p
h
asis
o
n
en
h
an
ci
n
g
its
m
ec
h
an
ical
p
r
o
p
e
r
ties
an
d
t
o
r
q
u
e
ch
a
r
ac
ter
is
tics
.
T
h
is
was
ess
en
tial
to
en
s
u
r
e
s
tr
u
ctu
r
al
s
tab
ilit
y
an
d
p
r
ec
is
e
r
o
tatio
n
al
b
eh
a
v
io
r
i
n
th
e
s
p
a
ce
en
v
ir
o
n
m
en
t.
T
h
e
d
esig
n
p
r
o
ce
s
s
also
co
n
s
id
er
ed
th
e
h
ar
s
h
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
en
c
o
u
n
ter
e
d
in
s
p
a
ce
,
wh
ich
h
elp
e
d
im
p
r
o
v
e
th
e
s
atellite
's r
eliab
ilit
y
an
d
o
p
er
at
io
n
al
p
er
f
o
r
m
an
ce
.
3
.
2
.
T
heo
re
t
ica
l i
m
pli
ca
t
io
ns
T
h
e
an
al
y
s
is
o
f
m
ec
h
an
ical
s
tr
u
ctu
r
es
u
n
d
er
v
a
r
io
u
s
l
o
ad
in
g
co
n
d
itio
n
s
p
r
im
ar
ily
d
e
p
en
d
s
o
n
s
tatic
an
d
d
y
n
a
m
ic
p
r
in
cip
les
to
ev
alu
ate
s
tr
ess
e
s
,
d
is
p
lace
m
en
ts
,
an
d
n
atu
r
al
f
r
e
q
u
en
cies.
W
h
ile
th
is
an
aly
tical
p
r
o
ce
s
s
ca
n
b
e
tim
e
-
co
n
s
u
m
i
n
g
,
th
e
u
s
e
o
f
Nastra
n
s
ig
n
if
i
ca
n
tly
en
h
an
ce
s
b
o
th
co
m
p
u
t
atio
n
al
ac
cu
r
ac
y
a
n
d
ef
f
icien
cy
.
T
h
is
ad
v
an
ce
m
en
t
is
cr
u
cial
f
o
r
m
an
ag
in
g
co
m
p
lex
s
tr
u
ctu
r
es,
s
u
ch
as
s
atel
lites
,
as
it
en
ab
le
s
r
ea
l
-
tim
e
r
esu
lts
th
at
ac
cu
r
atel
y
r
ef
lect
th
eir
b
eh
av
i
o
r
.
Ultim
ately
,
th
is
im
p
r
o
v
e
m
en
t
in
cr
e
ases
th
e
th
eo
r
etica
l
an
d
p
r
ac
tical
s
ig
n
if
ica
n
ce
o
f
t
h
e
an
aly
s
is
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ad
v
Ap
p
l Sci
I
SS
N:
2252
-
8
8
1
4
S
tu
d
y
o
f
a
mo
d
el
o
f a
s
a
tellite str
u
ctu
r
e
th
a
t m
ee
ts
th
e
n
ec
ess
a
r
y
crit
eria
fo
r
…
(
Ma
h
mo
u
d
F
a
d
h
el
I
d
a
n
)
507
3
.
3
.
L
im
it
a
t
io
ns
o
f
t
he
s
t
ud
y
A
s
ig
n
if
ican
t
lim
itatio
n
o
f
th
is
s
tu
d
y
is
th
e
n
ec
es
s
ity
to
ac
cu
r
ately
s
p
ec
if
y
th
e
in
p
u
t
d
at
a
f
o
r
ea
ch
elem
en
t,
n
o
d
e
,
an
d
p
a
n
el
with
in
th
e
Nastra
n
s
o
f
twar
e,
p
ar
tic
u
lar
ly
co
n
ce
r
n
in
g
th
e
l
o
ad
s
an
d
m
o
m
en
ts
ap
p
lied
to
th
e
s
atellite
s
tr
u
ctu
r
e.
W
h
ile
th
e
s
o
f
twar
e
f
ac
ilit
ates
ea
s
y
m
o
d
if
icatio
n
s
o
f
lo
ad
s
a
n
d
d
im
en
s
io
n
s
,
a
n
y
in
ac
cu
r
ac
ies o
r
ass
u
m
p
tio
n
s
in
th
ese
in
p
u
ts
co
u
ld
n
eg
ativ
ely
af
f
ec
t th
e
s
im
u
latio
n
'
s
ac
cu
r
ac
y
.
3
.
4
.
L
im
it
s
o
f
s
cient
i
f
ic
re
s
ea
rc
h
T
h
is
s
tu
d
y
f
o
c
u
s
es
o
n
th
e
d
esig
n
o
f
an
o
ctag
o
n
al
lo
w
-
ea
r
th
o
r
b
it
co
m
m
u
n
icatio
n
s
s
atellite,
u
s
in
g
th
e
Nastra
n
m
o
d
elin
g
s
o
f
twar
e.
I
t
d
o
es
n
o
t
in
clu
d
e
f
ield
test
s
o
r
p
r
ac
tical
ap
p
licatio
n
s
.
T
h
e
ap
p
lied
lo
ad
s
a
n
d
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
a
r
e
b
ased
o
n
th
eo
r
etica
l
p
ar
am
eter
s
an
d
d
o
n
o
t
ad
d
r
ess
lo
n
g
-
ter
m
ef
f
ec
ts
o
r
s
atellite
life
tim
e.
T
h
e
a
n
aly
s
is
is
b
ased
o
n
s
p
ec
if
ic
m
ate
r
ials
,
ass
u
m
in
g
co
n
s
tan
t
m
ec
h
a
n
ical
p
r
o
p
er
ties
,
an
d
e
x
clu
d
es
co
n
s
id
er
atio
n
s
o
f
m
ater
ial
d
ef
ec
ts
,
d
eg
r
a
d
atio
n
,
a
n
d
h
ar
s
h
en
v
ir
o
n
m
en
tal
f
ac
t
o
r
s
th
at
co
u
ld
a
f
f
ec
t
p
er
f
o
r
m
an
ce
an
d
r
eliab
ilit
y
.
Ou
tp
u
t set: c
ase
1
: m
o
d
e
1
.
9
3
5
5
9
Hz.
Def
o
r
m
ed
(
0
.
0
4
0
5
)
: to
tal
tr
a
n
s
l
atio
n
Ou
tp
u
t set: c
ase
2
: m
o
d
e
3
.
4
9
0
0
3
Hz
.
Def
o
r
m
ed
(
0
.
0
4
0
7
)
: to
tal
tr
a
n
s
latio
n
Ou
tp
u
t set: c
ase
3
: m
o
d
e
4
6
.
6
2
0
1
5
Hz
.
Def
o
r
m
e
d
(
0
.
0
5
9
1
)
: to
tal
tr
a
n
s
latio
n
Ou
tp
u
t set: c
ase
4
: m
o
d
e
4
9
.
2
8
5
2
1
Hz.
Def
o
r
m
e
d
(
0
.
0
6
2
5
)
: to
tal
tr
a
n
s
latio
n
Ou
tp
u
t set: c
ase
5
: m
o
d
e
1
7
8
.
6
3
5
7
6
Hz.
Def
o
r
m
ed
(
0
.
0
4
8
8
)
: to
tal
tr
a
n
s
latio
n
Ou
tp
u
t set: c
ase
6
: m
o
d
e
1
8
7
.
8
5
9
0
4
Hz.
Def
o
r
m
ed
(
0
.
0
5
4
4
)
: to
tal
tr
a
n
s
latio
n
Fig
u
r
e
3
.
Stru
ctu
r
e
m
o
d
e
s
h
ap
es
Fig
u
r
e
4.
T
h
e
r
elatio
n
s
h
ip
b
et
wee
n
th
e
v
alu
es σ
v
M
o
f
an
d
its
p
o
s
itio
n
in
th
e
Y
d
ir
ec
tio
n
Fig
u
r
e
5.
T
h
e
r
elatio
n
s
h
ip
b
et
wee
n
th
e
v
alu
es o
f
σ
v
M
an
d
its
p
o
s
itio
n
in
th
e
X
d
ir
ec
tio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
1
4
I
n
t J Ad
v
Ap
p
l Sci
,
Vo
l.
14
,
No
.
2
,
J
u
n
e
2
0
2
5
:
5
0
2
-
512
508
Fig
u
r
e
6.
T
h
e
r
elatio
n
s
h
ip
b
et
wee
n
th
e
v
alu
es o
f
σ
v
M
an
d
its
NE
Fig
u
r
e
7.
T
h
e
r
elatio
n
s
h
ip
b
et
wee
n
d
is
p
lace
m
en
t
v
alu
es a
n
d
its
N
Fig
u
r
e
8.
T
h
e
r
elatio
n
s
h
ip
b
et
wee
n
d
is
p
lace
m
en
t
v
alu
es a
n
d
its
p
o
s
itio
n
in
t
h
e
X
d
ir
ec
tio
n
Fig
u
r
e
9.
T
h
e
r
elatio
n
s
h
ip
b
et
wee
n
d
is
p
lace
m
en
t
v
alu
es a
n
d
its
p
o
s
itio
n
in
t
h
e
Y
d
ir
ec
tio
n
Fig
u
r
e
10
T
h
e
r
elatio
n
s
h
i
p
b
et
wee
n
σ
v
M
v
alu
es a
n
d
its
NE
at
lo
ad
th
r
u
s
ter
lo
ad
i
n
X
–
th
e
d
ir
ec
tio
n
(
TX
)
Fig
u
r
e
1
1.
T
h
e
r
elatio
n
s
h
ip
b
e
twee
n
σ
v
M
v
alu
es a
n
d
its
NE
at
lo
ad
th
r
u
s
ter
lo
ad
i
n
Y
–
th
e
d
ir
ec
tio
n
(
T
Y)
Fig
u
r
e
1
2.
T
h
e
r
elatio
n
s
h
ip
b
e
twee
n
σ
v
M
v
alu
es a
n
d
X
at
lo
ad
T
X
Fig
u
r
e
1
3.
T
h
e
r
elatio
n
s
h
ip
b
e
twee
n
σ
v
M
v
alu
es a
n
d
X
at
lo
ad
T
Y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ad
v
Ap
p
l Sci
I
SS
N:
2252
-
8
8
1
4
S
tu
d
y
o
f
a
mo
d
el
o
f a
s
a
tellite str
u
ctu
r
e
th
a
t m
ee
ts
th
e
n
ec
ess
a
r
y
crit
eria
fo
r
…
(
Ma
h
mo
u
d
F
a
d
h
el
I
d
a
n
)
509
Fig
u
r
e
1
4.
T
h
e
r
elatio
n
s
h
ip
b
e
twee
n
σ
v
M
v
alu
es
an
d
Y
at
lo
ad
T
X
Fig
u
r
e
1
5.
T
h
e
r
elatio
n
s
h
ip
b
e
twee
n
σ
v
M
v
alu
es a
n
d
Y
at
lo
ad
T
Y
Fig
u
r
e
1
6.
T
h
e
r
elatio
n
s
h
ip
b
e
twee
n
d
is
p
lace
m
en
t
v
alu
es a
n
d
N
at
lo
a
d
T
X
Fig
u
r
e
1
7.
T
h
e
r
elatio
n
s
h
ip
b
e
twee
n
d
is
p
lace
m
en
t
v
alu
es a
n
d
X
at
lo
a
d
T
X
Fig
u
r
e
1
8.
T
h
e
r
elatio
n
s
h
ip
b
e
twee
n
d
is
p
lace
m
en
t
v
alu
es a
n
d
Y
at
lo
a
d
T
X
Fig
u
r
e
1
9.
T
h
e
r
elatio
n
s
h
ip
b
e
twee
n
d
is
p
lace
m
en
t
v
alu
es a
n
d
N
at
lo
a
d
T
Y
Fig
u
r
e
20.
T
h
e
r
elatio
n
s
h
ip
b
e
twee
n
d
is
p
lace
m
en
t
v
alu
es a
n
d
X
at
lo
a
d
T
Y
Fig
u
r
e
2
1.
T
h
e
r
elatio
n
s
h
ip
b
e
twee
n
d
is
p
lace
m
en
t
v
alu
es a
n
d
Y
at
lo
a
d
T
X
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
1
4
I
n
t J Ad
v
Ap
p
l Sci
,
Vo
l.
14
,
No
.
2
,
J
u
n
e
2
0
2
5
:
5
0
2
-
512
510
Fig
u
r
e
2
2.
T
h
e
r
elatio
n
s
h
ip
b
e
twee
n
d
is
p
lace
m
en
t
v
alu
es a
n
d
tim
e
Fig
u
r
e
2
3.
T
h
e
r
elatio
n
s
h
ip
b
e
twee
n
th
e
σ
v
M
v
al
u
e
an
d
tim
e
Fig
u
r
e
2
4.
T
h
e
r
elatio
n
s
h
ip
b
e
twee
n
d
is
p
lace
m
en
t v
alu
es a
n
d
f
r
eq
u
en
cy
4.
CO
NCLU
SI
O
N
T
h
e
o
p
er
atio
n
al
p
ar
am
eter
s
h
av
e
b
ee
n
o
b
tain
ed
an
d
a
p
p
r
o
v
ed
f
o
r
u
s
e
in
SE
co
n
d
itio
n
s
.
Pas
s
iv
e
an
d
d
y
n
am
ic
in
v
esti
g
atio
n
s
h
a
v
e
r
ev
ea
led
s
ev
er
al
ad
d
itio
n
al
b
en
ef
its
f
o
r
th
ei
r
u
s
e
i
n
s
tr
u
ctu
r
al
d
esig
n
a
n
d
u
s
ef
u
l
lo
ad
d
is
tr
ib
u
tio
n
.
T
h
e
n
ea
r
-
ea
r
th
en
v
ir
o
n
m
en
t
co
n
s
tan
tl
y
ch
an
g
es
an
d
in
v
o
lv
es
v
ar
io
u
s
co
m
p
o
n
en
ts
s
ig
n
if
ican
tly
af
f
ec
ted
b
y
r
elev
an
t
f
r
am
es.
B
ased
o
n
th
e
f
r
a
m
e
p
o
s
itio
n
v
alu
es,
it
ca
n
b
e
co
n
clu
d
ed
th
at
th
e
s
tr
u
ctu
r
e
m
ain
tain
s
s
tab
ilit
y
in
u
p
to
s
ix
s
p
ec
if
ic
p
o
s
itio
n
s
,
w
h
ich
ex
h
ib
it sl
ig
h
t d
ef
o
r
m
atio
n
d
u
e
to
ch
an
g
es in
th
e
ar
r
a
n
g
em
en
t
o
f
th
e
u
p
p
er
an
d
lo
we
r
b
ases
.
T
h
e
s
ig
n
if
i
ca
n
t
d
is
p
lace
m
en
t
o
f
th
e
lo
wer
p
late
u
n
d
e
r
a
1
0
N
th
r
u
s
t
at
elem
en
t
3
3
,
alo
n
g
wi
th
th
e
co
n
ce
n
tr
ated
th
r
u
s
t
o
n
th
e
d
r
iv
en
co
m
p
o
n
en
t
o
f
elem
e
n
t
4
1
,
m
ak
es
u
s
in
g
a
d
r
iv
en
p
ile
o
n
th
e
u
p
p
er
an
d
lo
wer
p
lates
im
p
r
ac
tical.
T
h
e
σ
v
M
m
ag
n
itu
d
e
is
s
ig
n
if
ican
tly
lo
wer
th
an
th
e
y
ield
s
tr
ess
o
f
7
,
0
7
5
alu
m
in
u
m
allo
y
,
in
d
icatin
g
t
h
at
th
e
s
tr
u
ctu
r
e
is
s
af
e.
T
h
e
s
p
ac
ec
r
af
t
'
s
to
r
q
u
e
u
n
d
er
g
o
es
tr
an
s
ien
t
ch
an
g
es
d
u
e
to
its
p
o
s
itio
n
ch
an
g
es
o
v
er
2
4
h
o
u
r
s
.
T
h
e
s
tr
u
ctu
r
e
is
s
tab
le
d
u
r
in
g
v
ib
r
atio
n
with
in
a
f
r
eq
u
e
n
cy
r
an
g
e
o
f
1
5
0
Hz
,
with
n
o
ex
ter
n
al
in
s
tab
ilit
y
o
b
s
er
v
ed
.
E
x
am
i
n
e
d
if
f
e
r
en
t
s
atellite
s
tr
u
ctu
r
es
-
cir
cu
lar
,
q
u
a
d
r
ilater
al,
p
en
t
ag
o
n
al,
an
d
h
ex
ag
o
n
al
ev
alu
ate
s
tab
ilit
y
,
r
o
tatio
n
,
s
tr
ess
d
is
tr
ib
u
tio
n
,
d
is
p
lace
m
en
t,
an
d
v
ib
r
atio
n
s
o
p
tim
al
d
esig
n
.
ACK
NO
WL
E
DG
M
E
N
T
S
T
h
e
r
esear
c
h
er
s
wo
u
l
d
lik
e
to
th
an
k
th
e
Dea
n
s
h
ip
an
d
p
r
o
f
ess
o
r
s
o
f
th
e
C
o
lleg
e
o
f
E
n
g
i
n
ee
r
in
g
f
o
r
th
e
g
r
ea
t su
p
p
o
r
t a
n
d
en
c
o
u
r
a
g
em
en
t th
ey
p
r
o
v
id
ed
t
o
co
m
p
lete
th
e
r
esear
ch
.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
Au
th
o
r
s
s
tate
n
o
f
u
n
d
in
g
in
v
o
lv
ed
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ad
v
Ap
p
l Sci
I
SS
N:
2252
-
8
8
1
4
S
tu
d
y
o
f
a
mo
d
el
o
f a
s
a
tellite str
u
ctu
r
e
th
a
t m
ee
ts
th
e
n
ec
ess
a
r
y
crit
eria
fo
r
…
(
Ma
h
mo
u
d
F
a
d
h
el
I
d
a
n
)
511
AUTHO
R
CO
NT
RI
B
UT
I
O
NS ST
A
T
E
M
E
N
T
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
o
n
tr
ib
u
to
r
R
o
les
T
ax
o
n
o
m
y
(
C
R
ed
iT)
to
r
ec
o
g
n
ize
in
d
iv
id
u
al
au
th
o
r
co
n
tr
ib
u
tio
n
s
,
r
ed
u
ce
au
th
o
r
s
h
ip
d
is
p
u
tes,
an
d
f
ac
ilit
ate
co
llab
o
r
atio
n
.
Na
m
e
o
f
Aut
ho
r
C
M
So
Va
Fo
I
R
D
O
E
Vi
Su
P
Fu
Ma
h
m
o
u
d
Fad
h
el
I
d
a
n
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Osam
ah
Ma
h
m
o
o
d
Hu
s
s
ein
✓
✓
✓
✓
✓
✓
C
:
C
o
n
c
e
p
t
u
a
l
i
z
a
t
i
o
n
M
:
M
e
t
h
o
d
o
l
o
g
y
So
:
So
f
t
w
a
r
e
Va
:
Va
l
i
d
a
t
i
o
n
Fo
:
Fo
r
mal
a
n
a
l
y
s
i
s
I
:
I
n
v
e
s
t
i
g
a
t
i
o
n
R
:
R
e
so
u
r
c
e
s
D
:
D
a
t
a
C
u
r
a
t
i
o
n
O
:
W
r
i
t
i
n
g
-
O
r
i
g
i
n
a
l
D
r
a
f
t
E
:
W
r
i
t
i
n
g
-
R
e
v
i
e
w
&
E
d
i
t
i
n
g
Vi
:
Vi
su
a
l
i
z
a
t
i
o
n
Su
:
Su
p
e
r
v
i
s
i
o
n
P
:
P
r
o
j
e
c
t
a
d
mi
n
i
st
r
a
t
i
o
n
Fu
:
Fu
n
d
i
n
g
a
c
q
u
i
si
t
i
o
n
CO
NF
L
I
C
T
O
F
I
N
T
E
R
E
S
T
ST
A
T
E
M
E
NT
Au
th
o
r
s
s
tate
n
o
co
n
f
lict o
f
in
t
er
est.
DATA AV
AI
L
AB
I
L
I
T
Y
T
h
e
d
ata
th
at
s
u
p
p
o
r
t
th
e
f
in
d
in
g
s
o
f
th
is
s
tu
d
y
ar
e
av
ailab
l
e
f
r
o
m
th
e
co
r
r
esp
o
n
d
in
g
au
t
h
o
r
,
[
MFI
]
,
u
p
o
n
r
ea
s
o
n
ab
le
r
eq
u
est.
RE
F
E
R
E
NC
E
S
[
1
]
J.
E.
La
v
í
n
-
D
e
l
g
a
d
o
,
S
.
C
h
á
v
e
z
-
V
á
z
q
u
e
z
,
J.
F
.
G
ó
m
e
z
-
A
g
u
i
l
a
r
,
M
.
O
.
A
l
a
ssaf
i
,
F
.
E.
A
l
sa
a
d
i
,
a
n
d
A
.
M
.
A
h
mad
,
“
I
n
t
e
l
l
i
g
e
n
t
n
e
u
r
a
l
i
n
t
e
g
r
a
l
sl
i
d
i
n
g
-
m
o
d
e
c
o
n
t
r
o
l
l
e
r
f
o
r
a
sp
a
c
e
r
o
b
o
t
i
c
m
a
n
i
p
u
l
a
t
o
r
m
o
u
n
t
e
d
o
n
a
f
r
e
e
-
f
l
o
a
t
i
n
g
sa
t
e
l
l
i
t
e
,
”
A
d
v
a
n
c
e
s
i
n
S
p
a
c
e
Re
se
a
rc
h
,
v
o
l
.
7
1
,
n
o
.
9
,
p
p
.
3
7
3
4
–
3
7
4
7
,
M
a
y
2
0
2
3
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
a
sr
.
2
0
2
2
.
0
8
.
0
5
3
.
[
2
]
M
.
D
e
v
e
c
i
,
D
.
P
a
mu
c
a
r
,
I
.
G
o
k
a
s
a
r
,
a
n
d
M
.
Ta
v
a
n
a
,
“
S
p
a
c
e
c
r
a
f
t
t
r
a
c
k
i
n
g
c
o
n
t
r
o
l
a
n
d
s
y
n
c
h
r
o
n
i
z
a
t
i
o
n
:
a
n
a
ssessm
e
n
t
o
f
c
o
n
v
e
n
t
i
o
n
a
l
,
u
n
c
o
n
v
e
n
t
i
o
n
a
l
,
a
n
d
c
o
mb
i
n
e
d
me
t
h
o
d
s,”
A
d
v
a
n
c
e
s
i
n
S
p
a
c
e
R
e
se
a
rc
h
,
v
o
l
.
7
1
,
n
o
.
9
,
p
p
.
3
5
3
4
–
3
5
5
1
,
M
a
y
2
0
2
3
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
a
sr
.
2
0
2
2
.
0
7
.
0
5
6
.
[
3
]
K
.
K
.
d
e
G
r
o
h
,
B
.
A
.
B
a
n
k
s,
S
.
K
.
R
.
M
i
l
l
e
r
,
a
n
d
J
.
A
.
D
e
v
e
r
,
“
D
e
g
r
a
d
a
t
i
o
n
o
f
s
p
a
c
e
c
r
a
f
t
m
a
t
e
r
i
a
l
s,
”
i
n
H
a
n
d
b
o
o
k
o
f
En
v
i
r
o
n
m
e
n
t
a
l
D
e
g
r
a
d
a
t
i
o
n
o
f
Ma
t
e
r
i
a
l
s
,
E
l
se
v
i
e
r
,
p
p
.
6
0
1
–
645
,
2
0
1
8
,
d
o
i
:
1
0
.
1
0
1
6
/
B
9
7
8
-
0
-
323
-
5
2
4
7
2
-
8
.
0
0
0
2
9
-
0.
[
4
]
Y
.
Lu
,
Q
.
S
h
a
o
,
H
.
Y
u
e
,
a
n
d
F
.
Y
a
n
g
,
“
A
r
e
v
i
e
w
o
f
t
h
e
sp
a
c
e
e
n
v
i
r
o
n
m
e
n
t
e
f
f
e
c
t
s o
n
s
p
a
c
e
c
r
a
f
t
i
n
d
i
f
f
e
r
e
n
t
o
r
b
i
t
s,”
I
EE
E
Ac
c
e
ss
,
v
o
l
.
7
,
p
p
.
9
3
4
7
3
–
9
3
4
8
8
,
2
0
1
9
,
d
o
i
:
1
0
.
1
1
0
9
/
A
C
C
ESS
.
2
0
1
9
.
2
9
2
7
8
1
1
.
[
5
]
J.
L.
R
a
m
ó
n
,
J.
P
o
m
a
r
e
s,
a
n
d
L
.
F
e
l
i
c
e
t
t
i
,
“
D
i
r
e
c
t
v
i
s
u
a
l
ser
v
o
i
n
g
a
n
d
i
n
t
e
r
a
c
t
i
o
n
c
o
n
t
r
o
l
f
o
r
a
t
w
o
-
a
r
ms
o
n
-
o
r
b
i
t
serv
i
c
i
n
g
sp
a
c
e
c
r
a
f
t
,
”
A
c
t
a
As
t
r
o
n
a
u
t
i
c
a
,
v
o
l
.
1
9
2
,
p
p
.
3
6
8
–
3
7
8
,
M
a
r
.
2
0
2
2
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
a
c
t
a
a
s
t
r
o
.
2
0
2
1
.
1
2
.
0
4
5
.
[
6
]
B
.
F
.
J
a
mes
,
O
.
W
.
N
o
r
t
o
n
,
a
n
d
M
.
B
.
A
l
e
x
a
n
d
e
r
,
“
T
h
e
n
a
t
u
r
a
l
s
p
a
c
e
e
n
v
i
r
o
n
m
e
n
t
:
e
f
f
e
c
t
s
o
n
sp
a
c
e
c
r
a
f
t
,
”
1
9
9
4
.
[
O
n
l
i
n
e
]
.
A
v
a
i
l
a
b
l
e
:
h
t
t
p
s:
/
/
n
t
r
s.n
a
sa
.
g
o
v
/
a
p
i
/
c
i
t
a
t
i
o
n
s/
1
9
9
5
0
0
1
9
4
5
5
/
d
o
w
n
l
o
a
d
s
/
1
9
9
5
0
0
1
9
4
5
5
.
p
d
f
[
7
]
I
.
K
o
l
m
a
n
o
v
sk
y
a
n
d
M
.
I
l
i
ć
,
“
C
o
n
t
r
o
l
o
f
a
e
r
o
s
p
a
c
e
s
y
s
t
e
ms,
”
A
n
n
u
a
l
Re
v
i
e
w
s
i
n
C
o
n
t
r
o
l
,
v
o
l
.
5
2
,
p
p
.
2
8
0
–
2
8
1
,
2
0
2
1
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
a
r
c
o
n
t
r
o
l
.
2
0
2
1
.
1
0
.
0
1
1
.
[
8
]
A
.
C
.
B
o
l
e
y
a
n
d
M
.
B
y
e
r
s,
“
S
a
t
e
l
l
i
t
e
meg
a
-
c
o
n
s
t
e
l
l
a
t
i
o
n
s
c
r
e
a
t
e
r
i
s
k
s
i
n
l
o
w
e
a
r
t
h
o
r
b
i
t
,
t
h
e
a
t
m
o
s
p
h
e
r
e
a
n
d
o
n
e
a
r
t
h
,
”
S
c
i
e
n
t
i
f
i
c
Re
p
o
r
t
s
,
v
o
l
.
1
1
,
n
o
.
1
,
M
a
y
2
0
2
1
,
d
o
i
:
1
0
.
1
0
3
8
/
s4
1
5
9
8
-
021
-
8
9
9
0
9
-
7.
[
9
]
N
.
T
.
R
e
d
d
,
“
B
r
i
n
g
i
n
g
sa
t
e
l
l
i
t
e
s
b
a
c
k
f
r
o
m
t
h
e
d
e
a
d
:
m
i
ssi
o
n
e
x
t
e
n
si
o
n
v
e
h
i
c
l
e
s
g
i
v
e
d
e
f
u
n
c
t
s
p
a
c
e
c
r
a
f
t
a
n
e
w
l
e
a
se
o
n
l
i
f
e
-
[
n
e
w
s]
,
”
I
EEE
S
p
e
c
t
r
u
m
,
v
o
l
.
5
7
,
n
o
.
8
,
p
p
.
6
–
7
,
A
u
g
.
2
0
2
0
,
d
o
i
:
1
0
.
1
1
0
9
/
M
S
P
EC
.
2
0
2
0
.
9
1
5
0
5
4
0
.
[
1
0
]
M
.
N
.
R
o
ss
a
n
d
K
.
L.
J
o
n
e
s,
“
I
mp
l
i
c
a
t
i
o
n
s
o
f
a
g
r
o
w
i
n
g
s
p
a
c
e
f
l
i
g
h
t
i
n
d
u
s
t
r
y
:
c
l
i
ma
t
e
c
h
a
n
g
e
,
”
J
o
u
r
n
a
l
o
f
S
p
a
c
e
S
a
f
e
t
y
En
g
i
n
e
e
ri
n
g
,
v
o
l
.
9
,
n
o
.
3
,
p
p
.
4
6
9
–
4
7
7
,
S
e
p
.
2
0
2
2
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
j
ss
e
.
2
0
2
2
.
0
4
.
0
0
4
.
[
1
1
]
R
.
X
u
,
J.
L
u
o
,
a
n
d
M
.
W
a
n
g
,
“
K
i
n
e
mat
i
c
a
n
d
d
y
n
a
m
i
c
ma
n
i
p
u
l
a
b
i
l
i
t
y
a
n
a
l
y
si
s
f
o
r
f
r
e
e
-
f
l
o
a
t
i
n
g
s
p
a
c
e
r
o
b
o
t
s
w
i
t
h
c
l
o
se
d
c
h
a
i
n
c
o
n
st
r
a
i
n
t
s,
”
R
o
b
o
t
i
c
s
a
n
d
Au
t
o
n
o
m
o
u
s
S
y
s
t
e
m
s
,
v
o
l
.
1
3
0
,
A
u
g
.
2
0
2
0
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
r
o
b
o
t
.
2
0
2
0
.
1
0
3
5
4
8
.
[
1
2
]
Z.
W
a
n
g
,
R
.
M
.
Ju
n
g
e
r
s,
M
.
P
e
t
r
e
c
z
k
y
,
B
.
C
h
e
n
,
a
n
d
L.
Y
u
,
“
Le
a
r
n
i
n
g
st
a
b
i
l
i
t
y
o
f
p
a
r
t
i
a
l
l
y
o
b
s
e
r
v
e
d
sw
i
t
c
h
e
d
l
i
n
e
a
r
s
y
st
e
ms,
”
Au
t
o
m
a
t
i
c
a
,
v
o
l
.
1
6
4
,
J
u
n
.
2
0
2
4
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
a
u
t
o
ma
t
i
c
a
.
2
0
2
4
.
1
1
1
6
4
3
.
[
1
3
]
B
.
M
.
M
o
g
h
a
d
d
a
m
a
n
d
R
.
C
h
h
a
b
r
a
,
“
O
n
t
h
e
g
u
i
d
a
n
c
e
,
n
a
v
i
g
a
t
i
o
n
a
n
d
c
o
n
t
r
o
l
o
f
i
n
-
o
r
b
i
t
s
p
a
c
e
r
o
b
o
t
i
c
m
i
ssi
o
n
s:
a
su
r
v
e
y
a
n
d
p
r
o
s
p
e
c
t
i
v
e
v
i
s
i
o
n
,
”
A
c
t
a
Ast
r
o
n
a
u
t
i
c
a
,
v
o
l
.
1
8
4
,
p
p
.
7
0
–
1
0
0
,
J
u
l
.
2
0
2
1
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
a
c
t
a
a
st
r
o
.
2
0
2
1
.
0
3
.
0
2
9
.
[
1
4
]
H
.
Tsu
k
a
m
o
t
o
,
S
.
-
J.
C
h
u
n
g
,
a
n
d
J.
-
J
.
E.
S
l
o
t
i
n
e
,
“
C
o
n
t
r
a
c
t
i
o
n
t
h
e
o
r
y
f
o
r
n
o
n
l
i
n
e
a
r
st
a
b
i
l
i
t
y
a
n
a
l
y
si
s
a
n
d
l
e
a
r
n
i
n
g
-
b
a
se
d
c
o
n
t
r
o
l
:
a
t
u
t
o
r
i
a
l
o
v
e
r
v
i
e
w
,
”
A
n
n
u
a
l
Re
v
i
e
w
s
i
n
C
o
n
t
ro
l
,
v
o
l
.
5
2
,
p
p
.
1
3
5
–
1
6
9
,
2
0
2
1
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
a
r
c
o
n
t
r
o
l
.
2
0
2
1
.
1
0
.
0
0
1
.
[
1
5
]
X
.
Z
h
a
n
g
,
Y
.
G
e
n
g
,
a
n
d
B
.
W
u
,
“
A
p
p
r
o
a
c
h
i
n
g
a
n
d
p
o
i
n
t
i
n
g
t
r
a
c
k
i
n
g
c
o
n
t
r
o
l
f
o
r
t
u
m
b
l
i
n
g
t
a
r
g
e
t
u
n
d
e
r
m
o
t
i
o
n
c
o
n
s
t
r
a
i
n
t
s,”
A
c
t
a
Ast
r
o
n
a
u
t
i
c
a
,
v
o
l
.
2
0
9
,
p
p
.
6
–
2
0
,
A
u
g
.
2
0
2
3
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
a
c
t
a
a
s
t
r
o
.
2
0
2
3
.
0
4
.
0
2
5
.
[
1
6
]
R
.
J
i
n
,
P
.
R
o
c
c
o
,
a
n
d
Y
.
G
e
n
g
,
“
O
b
s
e
r
v
e
r
-
b
a
se
d
f
i
x
e
d
-
t
i
me
t
r
a
c
k
i
n
g
c
o
n
t
r
o
l
f
o
r
sp
a
c
e
r
o
b
o
t
s
i
n
t
a
sk
s
p
a
c
e
,
”
A
c
t
a
As
t
r
o
n
a
u
t
i
c
a
,
v
o
l
.
1
8
4
,
p
p
.
35
–
4
5
,
J
u
l
.
2
0
2
1
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
a
c
t
a
a
s
t
r
o
.
2
0
2
1
.
0
4
.
0
0
2
.
[
1
7
]
C
.
N
i
e
t
o
-
P
e
r
o
y
,
M
.
S
a
b
a
t
i
n
i
,
G
.
P
a
l
m
e
r
i
n
i
,
a
n
d
É
.
Jero
n
i
mo
d
e
O
l
i
v
e
i
r
a
,
“
A
c
o
n
c
u
r
r
e
n
t
t
e
s
t
i
n
g
f
a
c
i
l
i
t
y
a
p
p
r
o
a
c
h
t
o
v
a
l
i
d
a
t
e
sm
a
l
l
sat
e
l
l
i
t
e
c
o
m
b
i
n
e
d
o
p
e
r
a
t
i
o
n
s,”
Ae
r
o
s
p
a
c
e
,
v
o
l
.
8
,
n
o
.
1
2
,
p
.
3
6
1
,
N
o
v
.
2
0
2
1
,
d
o
i
:
1
0
.
3
3
9
0
/
a
e
r
o
s
p
a
c
e
8
1
2
0
3
6
1
.
[
1
8
]
Y
.
K
.
N
a
k
k
a
e
t
a
l
.
,
“
A
s
i
x
d
e
g
r
e
e
-
of
-
f
r
e
e
d
o
m
s
p
a
c
e
c
r
a
f
t
d
y
n
a
mi
c
s
si
m
u
l
a
t
o
r
f
o
r
f
o
r
mat
i
o
n
c
o
n
t
r
o
l
r
e
se
a
r
c
h
,
”
i
n
2
0
1
8
A
AS
/
AI
AA
Ast
r
o
d
y
n
a
m
i
c
s
S
p
e
c
i
a
l
i
st
C
o
n
f
e
r
e
n
c
e
,
A
I
A
A
,
2
0
1
8
.
[
O
n
l
i
n
e
]
.
A
v
a
i
l
a
b
l
e
:
h
t
t
p
s
:
/
/
a
u
t
h
o
r
s.l
i
b
r
a
r
y
.
c
a
l
t
e
c
h
.
e
d
u
/
r
e
c
o
r
d
s/
r
1
4
2
4
-
x
mc
6
4
/
f
i
l
e
s
/
2
0
1
8
_
A
A
S
_
A
I
A
A
.
p
d
f
?
d
o
w
n
l
o
a
d
=
1
[
1
9
]
W
.
Z
h
a
n
g
a
n
d
H
.
W
e
n
,
“
M
o
t
i
o
n
p
l
a
n
n
i
n
g
o
f
a
f
r
e
e
-
f
l
y
i
n
g
s
p
a
c
e
r
o
b
o
t
sy
s
t
e
m
u
n
d
e
r
e
n
d
e
f
f
e
c
t
o
r
t
a
s
k
c
o
n
s
t
r
a
i
n
t
s,”
Ac
t
a
Ast
r
o
n
a
u
t
i
c
a
,
v
o
l
.
1
9
9
,
p
p
.
1
9
5
–
2
0
5
,
O
c
t
.
2
0
2
2
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
a
c
t
a
a
s
t
r
o
.
2
0
2
2
.
0
7
.
0
0
5
.
[
2
0
]
M
.
Y
u
,
J.
L
u
o
,
M
.
W
a
n
g
,
J.
L
i
,
C
.
Li
u
,
a
n
d
J
.
S
u
n
,
“
D
i
r
e
c
t
l
y
s
k
i
l
l
-
t
r
a
n
s
f
e
r
r
e
d
D
M
P
-
b
a
s
e
d
t
r
a
j
e
c
t
o
r
y
p
l
a
n
n
i
n
g
f
o
r
r
o
b
o
t
s
o
f
t
-
c
a
p
t
u
r
e
o
f
s
p
a
c
e
t
u
mb
l
i
n
g
t
a
r
g
e
t
s,
”
A
c
t
a
Ast
r
o
n
a
u
t
i
c
a
,
v
o
l
.
2
0
4
,
p
p
.
6
1
1
–
6
2
9
,
M
a
r
.
2
0
2
3
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
a
c
t
a
a
st
r
o
.
2
0
2
2
.
1
1
.
0
4
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.