I
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l J
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f
Adv
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d Science
s
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I
J
AAS)
Vo
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10
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.
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2
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2
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M
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M
IR)
h
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s
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th
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f
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teria
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K
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w
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s
:
C
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m
et
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Mu
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No
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P
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T
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s
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rticle
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CC B
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SA
li
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se
.
C
o
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r
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s
p
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A
uth
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r
:
Ma
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m
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Fad
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an
Dep
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C
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1.
I
NT
RO
D
UCT
I
O
N
Af
ter
p
o
l
y
m
er
s
h
a
v
e
b
ee
n
w
id
el
y
u
s
ed
in
v
ar
io
u
s
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n
d
u
s
tr
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d
co
m
m
o
d
it
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f
ield
s
,
p
o
ly
m
er
ic
m
ater
ials
ar
e
n
o
w
w
id
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y
u
s
ed
in
s
tr
u
ct
u
r
al
a
n
d
co
n
s
tr
u
c
t
io
n
ap
p
licatio
n
s
,
as
its
p
er
f
o
r
m
a
n
ce
m
ee
ts
t
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es
s
ar
y
m
a
x
i
m
u
m
m
ec
h
an
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r
eq
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ir
e
m
e
n
t
s
,
h
e
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ce
t
h
e
i
m
p
o
r
tan
ce
o
f
r
esear
ch
an
d
s
tu
d
y
.
An
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t
h
er
p
ar
am
eter
o
f
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ar
a
m
o
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n
t
i
m
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th
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v
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.
C
h
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a
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d
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to
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eq
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ca
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v
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f
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m
ater
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[
1
]
-
[
4
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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A
d
v
A
p
p
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N:
2
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2
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teg
r
a
l
(
Ma
h
mo
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F
a
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I
d
a
n
)
289
B
r
in
s
o
n
an
d
B
r
in
s
o
n
[
5
]
,
T
o
r
r
en
s
an
d
C
as
tella
n
o
[
6
]
u
s
ed
a
o
n
e
-
d
i
m
e
n
s
io
n
al
eq
u
atio
n
co
n
tain
i
n
g
f
ir
s
t
an
d
th
ir
d
o
r
d
er
in
teg
r
als
to
d
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e
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m
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eh
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ch
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,
f
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ly
p
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p
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e
(
PP
)
m
ater
ial
[
7
]
-
[
1
0
]
.
T
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ati
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d
C
ed
er
b
au
m
[
1
1
]
,
L
ai
a
n
d
Fin
d
le
y
[
1
2
]
id
en
ti
f
ied
n
in
e
k
er
n
el
f
u
n
ctio
n
s
to
d
escr
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th
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r
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f
p
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l
y
v
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n
y
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c
h
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(
P
VC
)
u
n
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in
f
lu
e
n
ce
o
f
b
o
t
h
ten
s
ile
a
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d
t
w
i
s
ti
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s
.
Fo
r
f
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,
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d
t
h
ir
d
o
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d
er
o
f
p
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r
e
t
w
i
s
t
[
1
3
]
-
[
17
]
.
W
h
en
s
t
u
d
y
i
n
g
t
h
e
p
r
o
p
er
ties
o
f
p
o
lietilen
a
(
PE
)
,
"
th
e
s
ec
o
n
d
k
er
n
el
ar
r
an
g
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m
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n
t
s
u
f
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to
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p
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tr
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th
"
[
1
8
]
-
[
24
]
.
O
th
er
s
r
esear
ch
e
s
u
s
e
m
u
ltip
le
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n
te
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r
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r
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tatio
n
(
MI
R
)
a
n
d
p
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la
w
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cr
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th
e
lar
g
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d
is
to
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tio
n
o
cc
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r
r
in
g
in
n
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lo
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-
6
,
i
n
w
h
ic
h
th
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m
ec
h
a
n
ical
b
eh
a
v
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r
ch
an
g
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s
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m
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e
m
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to
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o
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an
d
in
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ch
m
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th
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m
ec
h
a
n
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l
b
eh
av
io
r
r
e
m
ai
n
s
s
u
b
j
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t to
th
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p
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w
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d
f
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r
all
k
i
n
d
s
o
f
d
if
f
er
en
t lo
ad
s
[
2
5
]
-
[
36
]
.
T
h
e
g
o
al
o
f
all
o
f
t
h
i
s
is
to
th
i
n
k
u
s
in
g
a
co
m
b
i
n
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n
o
f
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R
a
n
d
p
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w
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la
w
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i
n
v
esti
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ate
h
o
w
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m
p
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at
u
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e
af
f
ec
ts
th
e
m
ec
h
an
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b
eh
av
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r
o
f
v
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s
co
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s
m
ater
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ls
(
0
.
9
0
9
g
/c
m
3
at
2
0
°
C
)
u
n
d
er
t
h
e
in
f
l
u
e
n
ce
o
f
u
n
ia
x
ial
lo
ad
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
Fo
r
th
e
p
u
r
p
o
s
e
o
f
d
ev
elo
p
in
g
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s
u
i
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ch
ar
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ter
izatio
n
o
f
n
o
n
li
n
ea
r
b
eh
a
v
io
r
,
it
is
ass
u
m
ed
th
a
t
th
e
m
ater
ial
elo
n
g
atio
n
r
ate
with
r
e
s
p
ec
t
to
t
i
m
e
(
t)
d
ep
en
d
s
m
ai
n
l
y
o
n
t
h
e
v
al
u
es
o
f
t
h
e
l
o
ad
r
ate
p
r
ev
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u
s
l
y
p
lace
d
o
n
th
e
m
ater
ial
o
r
s
a
m
p
le.
I
n
o
th
er
w
o
r
d
s
,
th
e
elo
n
g
atio
n
th
at
o
cc
u
r
s
in
t
h
e
s
a
m
p
l
e
is
a
f
u
n
ctio
n
o
f
th
e
r
ated
lo
ad
s
[
1
]
.
=
[
(
)
]
−
∞
(
1
)
W
h
er
e
F
IJ
is
r
ep
r
esen
t
th
e
c
o
n
tin
u
o
u
s
n
o
n
l
in
ea
r
f
u
n
ctio
n
.
T
h
e
F
f
u
n
ctio
n
ca
n
b
e
r
ep
r
esen
ted
as
in
d
icati
n
g
t
h
e
d
eg
r
ee
o
f
p
r
ec
is
io
n
w
ith
in
t
h
e
m
u
l
tip
le
in
te
g
r
a
tio
n
eq
u
atio
n
[
5
]
,
[
6
]
.
(
)
=
∫
(
−
ξ
1
)
ξ
1
ξ
1
+
∫
∫
(
−
ξ
1
.
−
ξ
2
)
ξ
1
−
∞
−
∞
−
∞
ξ
2
ξ
1
ξ
2
+
∫
∫
∫
(
−
ξ
1
,
−
−
∞
−
∞
−
∞
ξ
2
,
−
ξ
3
)
ξ
1
ξ
2
ξ
3
ξ
1
ξ
2
ξ
3
(
2
)
A
cc
o
r
d
in
g
to
(
2
)
,
th
e
ti
m
e
d
ep
en
d
en
t e
lo
n
g
at
io
n
p
r
o
d
u
ce
d
b
y
u
n
ia
x
ial
te
n
s
i
le
lo
ad
in
g
ap
p
lied
at
ti
m
e
ξ
1
= ξ
2
=
ξ
3
=
0
is
g
iv
e
n
b
y
t
h
e
ex
p
r
es
s
i
o
n
(
3
)
.
(
)
=
1
(
)
+
2
(
)
2
+
3
(
)
3
(
3
)
B
y
s
u
b
s
t
itu
tin
g
t
h
e
r
esp
o
n
s
e
s
o
b
tain
ed
f
r
o
m
th
r
ee
te
n
s
i
le
t
ests
at
d
if
f
er
e
n
t
lev
e
ls
o
f
s
tr
e
s
s
,
(
3
)
b
ec
o
m
es
a
s
y
s
te
m
o
f
s
i
m
u
ltan
eo
u
s
al
g
eb
r
aic
eq
u
atio
n
s
w
it
h
t
h
e
t
h
r
ee
u
n
k
n
o
w
n
s
,
F
1
,
F
2
,
an
d
F
3
.
T
h
ese
eq
u
atio
n
s
h
av
e
b
ee
n
s
o
lv
ed
f
o
r
ea
ch
s
tep
t
i
m
e
u
s
i
n
g
"
Gau
s
s
ia
n
eli
m
i
n
atio
n
"
to
f
i
n
d
th
e
s
e
k
er
n
el
s
i
n
t
h
e
f
o
r
m
o
f
Fin
d
la
y
’
s
p
o
w
er
[
8
]
as (
4a
)
,
(
4
b
)
,
an
d
(
4
c)
.
1
=
01
+
1
(
4
a)
2
=
02
+
2
(
4
b
)
3
=
03
+
3
(
4
c)
T
h
e
eq
u
atio
n
o
f
ten
s
ile
s
tr
ai
n
ca
n
b
e
o
b
tain
ed
b
y
s
u
b
s
ti
tu
t
in
g
(
4
)
in
to
(
3
)
.
(
)
=
(
01
+
1
)
+
(
02
+
2
)
2
+
(
03
+
3
)
3
=
0
+
0
(
5
)
W
h
er
e
e
o
a
n
d
m
o
ar
e
ti
m
e
i
n
d
ep
en
d
en
t
s
tr
ai
n
a
n
d
ti
m
e
d
ep
en
d
en
t
co
ef
f
icie
n
t
r
e
s
p
ec
tiv
el
y
,
an
d
b
o
th
ar
e
f
u
n
ctio
n
s
o
f
s
tr
e
s
s
a
n
d
m
ater
ial
co
n
s
ta
n
t
s
.
N
i
s
co
n
s
tan
t
(
5
)
em
p
h
asize
s
t
h
at
cr
ee
p
r
ea
ctio
n
o
f
n
o
n
-
li
n
ea
r
v
is
co
elas
ticit
y
m
a
ter
ials
ca
n
b
e
p
ar
titi
o
n
ed
in
to
ti
m
e,
s
tr
etch
,
an
d
te
m
p
er
atu
r
e
r
elian
ce
co
m
p
o
n
en
ts
.
A
"
cr
ee
p
test
"
is
p
er
f
o
r
m
ed
o
n
a
s
a
m
p
le
u
s
in
g
a
cr
ee
p
m
ete
r
(
n
o
te
th
e
d
ev
ice
i
n
Fi
g
u
r
e
1
)
.
I
n
s
i
m
p
l
e
ter
m
s
,
t
h
e
s
a
m
p
le
i
s
h
ea
ted
t
o
a
tem
p
er
atu
r
e.
O
n
ce
th
e
te
m
p
er
at
u
r
e
s
et
p
o
in
t
i
s
r
ea
ch
e
d
,
a
co
n
s
tan
t
lo
ad
is
ap
p
lied
to
ex
er
t
a
lo
n
g
itu
d
i
n
al
f
o
r
ce
o
n
th
e
m
ater
ial
'
s
g
r
ain
s
tr
u
c
tu
r
e.
P
r
eg
n
an
c
y
is
m
ai
n
tai
n
ed
f
o
r
th
e
d
u
r
atio
n
o
f
th
e
test
o
r
u
n
til
th
e
s
a
m
p
le
i
s
r
u
p
tu
r
ed
.
Du
r
i
n
g
test
i
n
g
,
d
ata
is
co
n
ti
n
u
o
u
s
l
y
m
o
n
ito
r
ed
an
d
r
ec
o
r
d
e
d
to
q
u
alif
y
f
o
r
te
m
p
er
atu
r
e
s
tab
ilit
y
,
lo
ad
,
an
d
s
a
m
p
l
e
elo
n
g
atio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
2
5
2
-
8814
I
n
t J
A
d
v
A
p
p
l Sci
,
Vo
l.
10
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
288
–
2
9
6
290
Fig
u
r
e
1
.
SM1
0
0
6
c
r
ee
p
test
d
ev
ice
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
d
ef
o
r
m
a
tio
n
b
e
h
av
io
r
av
a
ilab
le
at
2
0
°
C
a
n
d
6
0
°
C
o
n
l
y
a
n
d
li
n
ea
r
in
ter
p
o
latio
n
b
etw
ee
n
t
h
e
m
ca
n
b
e
m
ad
e
to
o
b
tain
th
e
d
ef
o
r
m
atio
n
at
3
0
,
4
0
,
an
d
5
0
°
C
[
8
]
.
Ker
n
el
f
u
n
ctio
n
s
h
a
v
e
b
ee
n
d
eter
m
in
ed
at
ea
ch
te
m
p
er
atu
r
e
u
s
in
g
t
h
r
ee
d
if
f
er
e
n
t
s
tr
ess
le
v
els
(
σ
=
1
.
3
7
8
,
4
.
1
3
6
,
an
d
6
.
8
9
7
M
P
A
)
in
th
e
f
o
r
m
o
f
p
o
w
e
r
la
w
,
i
n
w
h
ich
t
h
e
v
alu
e
o
f
ti
m
e
ex
p
o
n
en
t
i
s
v
al
id
f
o
r
all
lev
els
o
f
lo
ad
in
g
.
Fro
m
T
ab
le
1
i
t
ca
n
b
e
n
o
ted
th
at
th
e
ti
m
e
e
x
p
o
n
en
t
i
n
cr
ea
s
es
as
te
m
p
er
at
u
r
e
in
cr
ea
s
es.
Ke
r
n
el
f
u
n
ctio
n
s
g
iv
e
n
i
n
T
ab
les
2
,
3
,
an
d
4
ar
e
p
r
esen
ted
in
Fi
g
u
r
es
2
,
3
,
an
d
4
.
T
h
ese
f
ig
u
r
es
s
h
o
w
t
h
at,
f
ir
s
t
an
d
th
ir
d
k
er
n
el
s
in
cr
ea
s
e
n
o
n
-
lin
ea
r
l
y
w
it
h
ti
m
e,
w
h
er
ea
s
t
h
e
s
ec
o
n
d
k
er
n
el
d
ec
r
ea
s
es
n
o
n
-
li
n
ea
r
l
y
.
T
h
is
r
esu
l
t is
e
m
p
h
as
ized
b
y
t
h
e
p
r
esen
ce
o
f
n
e
g
ati
v
e
v
alu
e
s
o
f
ti
m
e
d
ep
en
d
en
t
co
ef
f
icien
ts
in
T
ab
le
1
.
T
h
is
b
eh
av
io
r
w
as
o
b
s
er
v
ed
at
ea
ch
tem
p
er
at
u
r
e.
Als
o
,
it
w
a
s
f
o
u
n
d
t
h
at
te
m
p
er
atu
r
e
i
n
cr
ea
s
in
g
ca
u
s
ed
a
s
h
i
f
t
i
n
v
al
u
es
o
f
all
k
er
n
e
ls
.
I
t
is
cr
it
ical
h
er
e
to
s
p
ec
if
y
t
h
at
n
o
n
-
li
n
ea
r
v
is
co
ela
s
ticit
y
ca
n
b
e
r
elate
d
to
th
e
ti
m
e
d
ep
en
d
en
t
o
n
ter
m
s
o
f
t
h
ese
p
ar
ts
,
s
in
ce
t
h
e
ti
m
e
au
to
n
o
m
o
u
s
ter
m
s
al
lu
d
e
to
s
t
ar
tin
g
r
ea
ctio
n
s
.
T
ab
le
1
.
Var
iatio
n
o
f
ti
m
e
ex
p
o
n
en
t
w
it
h
te
m
p
er
atu
r
e
T
e
mp
.
°
C
N
20
0
.
0
7
0
30
0
.
0
7
6
5
40
0
.
0
8
1
7
50
0
.
0
8
6
60
0
.
0
9
0
T
ab
le
2
.
First k
er
n
el
at
d
if
f
er
e
n
t
te
m
p
er
at
u
r
e
T
e
mp
.
°
C
F
1
(
M
P
a
-
1
)
20
-
0
.
0
1
4
1
2
4
1
+
0
.
1
3
2
2
5
4
t
N
30
-
0
.
0
1
2
8
4
6
8
1
+
0
.
1
6
2
7
7
1
t
N
40
-
0
.
0
0
7
5
5
3
0
1
4
+
0
.
1
8
8
6
0
0
7
t
N
50
-
0
.
0
0
8
7
6
3
1
2
6
+
0
.
2
2
1
9
7
2
5
t
N
60
-
0
.
1
1
8
4
2
8
5
+
0
.
2
5
1
4
4
2
5
t
N
T
ab
le
3
.
Seco
n
d
k
er
n
el
at
d
if
f
er
en
t te
m
p
er
at
u
r
e
T
e
mp
.
°
C
F
2
X
10
-
3
(
M
P
a
-
2
)
20
2
.
3
2
0
2
2
7
–
9
.
0
3
4
0
7
6
t
N
30
1
.
9
9
2
6
8
5
–
6
.
1
3
0
7
3
2
t
N
40
1
.
2
6
9
9
8
2
–
2
.
5
6
3
6
2
3
t
N
50
2
.
1
9
3
6
7
0
0
–
1
.
0
5
2
8
2
t
N
60
5
.
2
9
0
4
0
1
–
0
.
3
8
6
7
6
7
4
t
N
T
ab
le
4
.
T
h
ir
d
k
er
n
el
at
d
if
f
er
en
t te
m
p
er
at
u
r
e
T
e
mp
.
°
C
F
3
X
1
0
-
3
(
M
P
a
-
3
)
20
-
0
.
5
1
8
9
4
5
1
+
1
.
5
4
0
5
6
5
t
N
30
-
0
.
4
4
7
1
4
0
7
+
1
.
6
0
8
1
1
3
t
N
40
-
0
.
2
7
7
4
5
9
5
+
1
.
6
1
3
8
6
2
t
N
50
-
0
.
3
5
1
9
8
9
8
+
1
.
8
8
4
0
7
6
1
t
N
60
-
0
.
3
6
3
7
0
9
2
+
2
.
0
7
7
7
9
8
t
N
No
n
-
l
in
ea
r
it
y
d
eg
r
ee
ca
n
b
e
r
elate
d
to
th
e
te
m
p
er
at
u
r
e
in
cr
ea
s
e
s
i
n
ce
ti
m
e
s
u
b
o
r
d
in
ate
co
ef
f
icie
n
t
s
ar
e
s
h
if
ted
w
i
th
te
m
p
er
atu
r
e.
Fro
m
T
ab
les
2
,
3
,
an
d
4
,
tim
e
d
ep
en
d
en
t
co
ef
f
icie
n
t
s
o
f
f
ir
s
t
an
d
th
ir
d
k
er
n
el
s
ar
e
in
cr
ea
s
ed
as
te
m
p
er
at
u
r
e
i
n
cr
ea
s
es,
w
h
er
ea
s
d
ec
r
ea
s
ed
f
o
r
s
ec
o
n
d
k
er
n
el.
T
h
u
s
,
th
e
n
o
n
-
li
n
ea
r
it
y
d
eg
r
ee
in
cr
ea
s
es
f
o
r
f
ir
s
t a
n
d
th
ir
d
k
e
r
n
els,
an
d
d
ec
r
ea
s
es
f
o
r
s
ec
o
n
d
k
e
r
n
el
s
h
o
w
n
i
n
Fi
g
u
r
es 2
,
3
,
an
d
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
d
v
A
p
p
l Sci
I
SS
N:
2
2
5
2
-
8814
N
o
n
-
lin
ea
r
creep
o
f
p
o
lyp
r
o
p
y
len
e
u
tili
z
in
g
mu
ltip
le
in
teg
r
a
l
(
Ma
h
mo
u
d
F
a
d
h
el
I
d
a
n
)
291
Fig
u
r
e
2
.
First k
er
n
el
f
u
n
ctio
n
o
f
P
P
f
o
r
ax
ial
ten
s
ile
lo
ad
in
g
at
d
if
f
er
e
n
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u
r
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r
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ile
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t te
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er
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r
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g
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r
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e
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ted
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ts
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d
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e
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ite
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u
p
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C
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ey
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er
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Fig
u
r
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3
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37
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See
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u
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en
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ile
co
m
p
o
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e
n
t
o
f
ti
m
e
i
n
d
ep
en
d
en
t
s
tr
ain
e
o
%
v
s
s
tr
ess
at
d
i
f
f
er
e
n
t te
m
p
er
at
u
r
e
Fig
u
r
e
1
6
.
C
o
ef
f
icie
n
t o
f
ti
m
e
d
ep
en
d
en
t stra
in
m
o
%
vs
s
tr
ess
at
d
i
f
f
er
e
n
t te
m
p
er
at
u
r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
2
5
2
-
8814
I
n
t J
A
d
v
A
p
p
l Sci
,
Vo
l.
10
,
No
.
4
,
Dec
em
b
er
2
0
2
1
:
288
–
2
9
6
294
Fig
u
r
e
1
7
.
T
en
s
ile
co
m
p
o
n
e
n
t
o
f
ti
m
e
i
n
d
ep
en
d
en
t
s
tr
ain
e
o
%
v
s
te
m
p
er
atu
r
e
at
d
i
f
f
er
en
t te
n
s
ile
s
tr
ess
e
s
Fig
u
r
e
1
8
.
C
o
ef
f
ici
e
n
t o
f
ti
m
e
d
ep
en
d
en
t stra
in
m
o
%
vs
te
m
p
er
atu
r
e
at
d
if
f
er
en
t te
n
s
ile
s
tr
es
s
es
Fig
u
r
e
1
9
.
T
im
e
e
x
p
o
n
en
t (
N)
v
s
t
e
m
p
er
atu
r
e
4.
CO
NCLU
SI
O
N
Fro
m
th
e
ab
o
v
e
d
is
cu
s
s
io
n
,
we
ca
n
d
r
aw
:
a)
T
he
n
o
n
-
l
in
ea
r
b
eh
av
io
r
o
f
PP
is
ad
e
q
u
atel
y
d
escr
ib
ed
b
y
p
o
w
er
la
w
,
w
h
ic
h
t
h
e
ti
m
e
ex
p
o
n
en
t
is
v
alid
f
o
r
all
s
tr
ess
le
v
els;
b
)
N
on
-
lin
ea
r
cr
ee
p
o
f
P
P
is
en
o
u
g
h
s
p
o
k
en
to
b
y
t
h
e
f
ir
s
t,
s
ec
o
n
d
,
a
n
d
t
h
ir
d
ar
r
an
g
e
s
tr
etc
h
o
f
MI
R
;
c)
T
i
m
e
ex
p
o
n
e
n
t
n
i
n
cr
ea
s
e
as
te
m
p
er
at
u
r
e
in
cr
ea
s
es
;
d)
F
ir
s
t
an
d
t
h
ir
d
k
e
r
n
els
i
n
cr
ea
s
e
n
o
n
-
l
in
ea
r
l
y
w
i
t
h
ti
m
e
w
h
er
ea
s
F2
d
ec
r
ea
s
es
n
o
n
-
li
n
ea
r
l
y
;
e)
A
l
l
k
er
n
el
s
i
n
cr
ea
s
e
n
o
n
-
lin
ea
r
l
y
a
s
te
m
p
er
atu
r
e
in
cr
ea
s
e
s;
f)
F
ir
s
t
a
n
d
t
h
ir
d
k
er
n
els
ca
n
r
ep
r
esen
t
th
e
d
ef
o
r
m
atio
n
o
f
n
o
n
-
cr
y
s
tal
lin
e
p
h
ase,
w
h
er
ea
s
s
ec
o
n
d
r
ep
r
esen
t
t
h
at
o
f
cr
y
s
ta
lli
n
e
p
h
ase
,
w
h
ich
b
o
t
h
o
cc
u
r
b
ey
o
n
d
4
0
°
C;
g)
Stre
s
s
i
n
c
r
ea
s
in
g
ca
u
s
ed
n
o
n
-
li
n
ea
r
l
y
i
n
cr
ea
s
es
i
n
ti
m
e
i
n
d
ep
en
d
en
t
s
tr
ain
s
an
d
ti
m
e
d
ep
en
d
en
t
co
ef
f
icie
n
t
s
;
h)
T
e
m
p
er
at
u
r
e
in
cr
ea
s
e
s
ca
u
s
e
n
o
n
-
lin
ea
r
l
y
d
ec
r
ea
s
e
s
in
ti
m
e
in
d
ep
en
d
en
t
s
tr
ai
n
s
an
d
lin
ea
r
l
y
in
cr
ea
s
e
s
i
n
ti
m
e
d
ep
en
d
en
t
co
ef
f
ic
ien
t
;
an
d
h)
T
h
e
ti
m
e
e
x
p
o
n
en
t
(
N)
i
n
cr
ea
s
es
n
o
n
-
lin
ea
r
l
y
w
it
h
te
m
p
er
atu
r
e.
RE
F
E
R
E
NC
E
S
[1
]
H
.
F
.
Br
in
so
n
a
n
d
L
.
C
.
Brin
s
o
n
,
"
No
n
li
n
e
a
r
V
isc
o
e
las
ti
c
it
y
,
"
in
P
o
lym
e
r
En
g
i
n
e
e
rin
g
S
c
ien
c
e
a
n
d
Vi
sc
o
e
la
sticity
,
S
p
rin
g
e
r,
B
o
sto
n
,
M
A
,
2
0
1
5
,
p
p
.
339
-
3
7
7
,
d
o
i:
1
0
.
1
0
0
7
/
9
7
8
-
1
-
4
8
9
9
-
7
4
8
5
-
3
_
1
0
.
[2
]
R
.
H.
Ew
o
ld
t,
A
.
E.
Ho
so
i
,
a
n
d
G
.
H.
M
c
Kin
le
y
,
"
Ne
w
m
e
a
su
re
s
f
o
r
c
h
a
ra
c
teriz
in
g
n
o
n
li
n
e
a
r
V
i
sc
o
e
las
ti
c
it
y
in
larg
e
a
m
p
li
tu
d
e
o
sc
il
lat
o
ry
sh
e
a
r
,
"
J
o
u
rn
a
l
o
f
Rh
e
o
lo
g
y
,
v
o
l
5
2
,
n
o
.
6
,
p
.
1
4
2
7
,
2
0
0
8
,
d
o
i
:
1
0
.
1
1
2
2
/
1
.
2
9
7
0
0
9
5
.
[3
]
K.
M
iy
a
z
a
k
i1
,
H.
M
.
Wy
s
s,
D.
A
.
W
e
it
z
a
n
d
D.
R.
Re
ich
m
a
n
,
"
No
n
li
n
e
a
r
V
isc
o
e
las
ti
c
it
y
o
f
m
e
t
sta
b
le
c
o
m
p
lex
f
lu
id
s
,
"
EP
L
(
Eu
ro
p
h
y
sic
s L
e
tt
e
rs
)
,
v
o
l.
7
5
,
n
o
.
6
,
p
.
9
1
5
,
2
0
0
6
,
d
o
i:
1
0
.
1
2
0
9
/ep
l/
i2
0
0
6
-
1
0
2
0
3
-
9
.
[4
]
P
.
F
e
rn
á
n
d
e
z
,
P
.
A
.
P
u
ll
a
rk
a
t
a
n
d
A
.
Ott,
"
A
M
a
ste
r
R
e
latio
n
De
f
in
e
s
th
e
No
n
li
n
e
a
r
V
isc
o
e
las
ti
c
it
y
o
f
S
in
g
le
F
ib
ro
b
las
ts
,
"
Bi
o
p
h
y
sic
a
l
jo
u
rn
a
l
,
v
o
l.
9
0
,
n
o
.
1
0
,
p
p
.
3
7
9
6
-
3
8
0
5
,
2
0
0
6
,
d
o
i:
1
0
.
1
5
2
9
/b
io
p
h
y
sj.1
0
5
.
0
7
2
2
1
5
.
[5
]
H
.
F
.
Brin
so
n
a
n
d
L
.
C
.
Brin
s
o
n
,
"
P
o
ly
m
e
riza
ti
o
n
a
n
d
c
las
sif
i
c
a
ti
o
n
,
"
in
Po
lym
e
r
En
g
in
e
e
rin
g
S
c
ien
c
e
a
n
d
Vi
sc
o
e
la
sticity
,
S
p
rin
g
e
r,
B
o
sto
n
,
M
A
,
2
0
0
8
,
p
p
.
99
-
1
5
7
,
d
o
i:
1
0
.
1
0
0
7
/
9
7
8
-
0
-
3
8
7
-
7
3
8
6
1
-
1_
.
[6
]
F
.
T
o
rre
n
s
a
n
d
G
.
C
a
ste
ll
a
n
o
,
"
M
o
lec
u
lar
Clas
si
f
ica
ti
o
n
o
f
5
-
a
m
in
o
-
2
-
a
ro
y
lq
u
in
o
li
n
e
s
a
n
d
4
-
a
ro
y
l
-
6
,
7
,
8
-
tri
m
e
th
o
x
y
q
u
in
o
li
n
e
s
a
s
Hig
h
ly
P
o
ten
t
T
u
b
u
li
n
P
o
ly
m
e
riz
a
ti
o
n
I
n
h
i
b
it
o
rs
,
"
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
d
v
A
p
p
l Sci
I
SS
N:
2
2
5
2
-
8814
N
o
n
-
lin
ea
r
creep
o
f
p
o
lyp
r
o
p
y
len
e
u
tili
z
in
g
mu
ltip
le
in
teg
r
a
l
(
Ma
h
mo
u
d
F
a
d
h
el
I
d
a
n
)
295
Ch
e
mo
in
f
o
rm
a
ti
c
s
a
n
d
Ch
e
m
ica
l
En
g
in
e
e
rin
g
(
IJ
CCE)
,
v
o
l.
3
,
n
o
.
2
,
p
p
.
1
-
26
,
2
0
1
3
,
d
o
i:
1
0
.
4
0
1
8
/
ij
c
c
e
.
2
0
1
3
0
7
0
1
0
1
.
[7
]
H.
F
.
Bri
n
so
n
a
n
d
L
.
C.
Bri
n
so
n
,
Po
lym
e
r e
n
g
i
n
e
e
rin
g
sc
ien
c
e
a
n
d
Vi
sc
o
e
la
sticity
,
S
p
rin
g
e
r,
B
o
sto
n
,
M
A
,
2
0
0
8
.
[8
]
L
.
C.
S
.
,
Nu
n
s,
F
.
W
.
R.
Dia
s
a
m
d
H.S
.
d
a
Co
sta
M
a
tt
o
s
,
“
M
e
c
h
a
n
ica
l
b
e
h
a
v
io
r
o
f
p
o
ly
tetra
f
lu
o
ro
e
t
h
y
len
e
in
ten
sile
lo
a
d
i
n
g
u
n
d
e
r
d
if
f
e
r
e
n
t
stra
in
ra
tes
,
”
Po
lym
e
r
tes
ti
n
g
,
v
o
l.
30
,
n
o
.
7
,
p
p
.
7
9
1
-
7
9
6
,
2
0
1
1
,
d
o
i:
1
0
.
1
0
1
6
/
j.
p
o
ly
m
e
rtes
ti
n
g
.
2
0
1
1
.
0
7
.
0
0
4
.
[9
]
M
.
C.
Ko
e
tt
in
g
,
J
.
T
.
P
e
ters
,
S
.
D.
S
teic
h
e
n
a
n
d
N
.
A
.
P
e
p
p
a
s
,
"
S
ti
m
u
lu
s
-
re
sp
o
n
siv
e
h
y
d
ro
g
e
ls:
T
h
e
o
r
y
,
m
o
d
e
rn
a
d
v
a
n
c
e
s,
a
n
d
a
p
p
li
c
a
ti
o
n
s
,
"
M
a
ter
ia
ls
S
c
ien
c
e
a
n
d
E
n
g
i
n
e
e
rin
g
:
R:
Rep
o
rts
,
v
o
l.
9
3
,
p
p
.
1
-
49
,
2
0
1
5
,
d
o
i
:
1
0
.
1
0
1
6
/
j.
m
se
r.
2
0
1
5
.
0
4
.
0
0
1
.
[1
0
]
G
e
o
rg
e
Dv
o
ra
k
,
M
icr
o
me
c
h
a
n
ics
o
f
c
o
m
p
o
site ma
ter
ia
l
,
S
p
ri
n
g
e
r,
Do
rd
re
c
h
t
,
2
0
1
2
.
[1
1
]
D.
T
o
u
a
ti
a
n
d
G
.
Ce
d
e
rb
a
u
m
,
"
On
th
e
p
re
d
icti
o
n
o
f
stre
ss
re
lax
a
ti
o
n
f
ro
m
k
n
o
w
n
c
re
e
p
o
f
n
o
n
li
n
e
a
r
m
a
teria
l
s
,
"
J
o
u
rn
a
l
o
f
E
n
g
i
n
e
e
rin
g
M
a
ter
i
a
ls
a
n
d
T
e
c
h
n
o
l
o
g
y
,
v
o
l.
1
1
9
,
n
o
.
2
,
p
p
.
1
2
1
-
124
,
1
9
9
7
,
d
o
i:
1
0
.
1
1
1
5
/
1
.
2
8
0
5
9
8
2
.
[1
2
]
J.
S
.
Y.
L
a
i
a
n
d
W
.
N.
F
in
d
ley
,
"
P
re
d
ictio
n
o
f
Un
iax
ial
S
tres
s
Re
lax
a
ti
o
n
f
ro
m
Cr
e
e
p
o
f
No
n
li
n
e
a
r
V
isc
o
e
las
ti
c
it
y
M
a
teria
l
,
"
T
ra
n
sa
c
ti
o
n
s
o
f
t
h
e
S
o
c
iety
o
f
Rh
e
o
lo
g
y
,
v
o
l
.
12
,
n
o
.
2
,
p
.
2
4
3
,
1
9
6
8
,
d
o
i:
1
0
.
1
1
2
2
/
1
.
5
4
9
1
2
0
.
[1
3
]
J.
S
.
Y.
L
a
i
a
n
d
W
.
N.
F
in
d
le
y
,
"
Cre
e
p
o
f
P
o
ly
u
re
th
a
n
e
a
t
V
a
ry
in
g
T
e
m
p
e
ra
tu
re
u
n
d
e
r
No
n
li
n
e
a
r
a
x
ial
stre
ss
,
"
T
ra
n
sa
c
ti
o
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s
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f
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9
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6
.
[1
4
]
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.
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a
rk
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W
.
N
.
F
in
d
ley
,
"
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li
n
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a
r
Cre
e
p
o
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ly
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r
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v
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ted
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e
m
p
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re
,
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ra
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o
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0
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1
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2
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5
4
9
3
6
1
.
[1
5
]
M
.
G
a
rrid
o
,
J
.
R.
C
o
rre
ia
a
n
d
T
.
Ke
ll
e
r
,
"
Eff
e
c
t
o
f
se
r
v
ice
te
m
p
e
ra
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re
o
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th
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r
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p
re
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o
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o
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id
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in
c
o
m
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n
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w
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f
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,
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n
stru
c
ti
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n
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n
d
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in
g
M
a
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v
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l.
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p
.
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d
m
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t.
2
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6
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0
5
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0
7
4
.
[1
6
]
A
.
G
.
De
n
a
y
,
S
.
Ca
sta
g
n
e
t,
A
.
Ro
y
a
n
d
G
.
A
li
s
e
,
"
Cre
e
p
c
o
m
p
re
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n
b
e
h
a
v
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o
f
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p
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ly
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e
f
o
a
m
f
ro
m
c
r
y
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e
n
ic t
e
m
p
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ra
tu
re
s: si
z
e
e
ffe
c
t
a
n
d
lo
n
g
-
term
p
re
d
ictio
n
,
"
EP
J
W
e
b
o
f
Co
n
fer
e
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c
e
s
,
v
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l.
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p
.
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5
0
0
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o
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jco
n
f
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0
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6
2
5
0
0
6
.
[1
7
]
R.
M
a
rk
a
n
d
W
.
N.
F
in
d
ley
,
"
Te
m
p
e
ra
tu
re
H
isto
ry
De
p
e
n
d
e
n
c
e
in
C
o
m
b
in
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d
T
e
n
sio
n
T
o
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n
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p
o
f
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ly
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a
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u
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d
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r
V
a
ry
in
g
Te
m
p
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ra
tu
re
,
"
T
ra
n
sa
c
ti
o
n
s
o
f
th
e
S
o
c
iety
o
f
Rh
e
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lo
g
y
,
v
o
l.
19
,
n
o
.
2,
p
p
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2
1
3
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1
9
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5
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d
o
i:
1
0
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1
1
2
2
/
1
.
5
4
9
3
6
9
.
[1
8
]
D
.
A
.
S
ig
in
e
r
a
n
d
M
.
F
.
L
e
telier
,
"
He
a
t
tran
sfe
r
a
s
y
m
p
to
te
in
lam
in
a
r
f
lo
w
o
f
n
o
n
-
li
n
e
a
r
Visc
o
e
las
ti
c
it
y
f
lu
id
s
i
n
stra
ig
h
t
n
o
n
-
c
ircu
lar
t
u
b
e
s
,
"
I
n
ter
n
a
ti
o
n
a
l
jo
u
rn
a
l
o
f
e
n
g
in
e
e
rin
g
s
c
ien
c
e
,
v
o
l.
48
,
n
o
.
1
1
,
p
p
.
1
5
4
4
-
1
5
6
2
,
2
0
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0
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d
o
i
:
1
0
.
1
0
1
6
/
j.
ij
e
n
g
sc
i.
2
0
1
0
.
0
7
.
0
1
0
.
[1
9
]
M
.
F
.
L
e
telier,
D.
A
.
S
ig
in
e
r,
G
.
A
rria
g
a
d
a
a
n
d
A
.
G
o
n
z
á
lez
,
"
H
e
a
t
T
ra
n
s
f
e
r
Op
ti
m
iza
ti
o
n
in
L
a
m
in
a
r
F
lo
w
o
f
No
n
-
L
in
e
a
r
V
isc
o
e
las
ti
c
it
y
F
lu
id
s in
As
y
m
m
e
tri
c
S
traig
h
t
Du
c
ts
w
it
h
In
c
lu
sio
n
s
,
"
AS
M
E
2
0
1
7
In
ter
n
a
ti
o
n
a
l
M
e
c
h
a
n
ic
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l
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g
i
n
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rin
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o
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ss
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n
d
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o
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t
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m
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,
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7
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o
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:
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1
1
1
5
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2
0
1
7
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7
0
9
9
4
.
[2
0
]
F
.
Ha
g
a
n
i,
M
.
Bo
u
tao
u
s,
R
.
Kn
i
k
k
e
r,
S
.
X
in
a
n
d
D
.
S
ig
in
e
r
,
"
Nu
m
e
rica
l
M
o
d
e
li
n
g
o
f
No
n
-
Aff
in
e
V
isc
o
e
las
ti
c
it
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F
lu
i
d
F
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In
c
lu
d
i
n
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V
isc
o
u
s
Diss
ip
a
ti
o
n
T
h
ro
u
g
h
a
S
q
u
a
re
Cro
s
s
-
S
e
c
ti
o
n
Du
c
t:
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a
t
T
ra
n
s
f
e
r
En
h
a
n
c
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m
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d
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t
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e
In
e
rti
a
a
n
d
t
h
e
El
a
stic
Ef
f
e
c
ts
,
"
AS
M
E
2
0
2
0
In
ter
n
a
ti
o
n
a
l
M
e
c
h
a
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ica
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g
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o
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0
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1
1
5
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2
0
2
0
-
2
3
5
5
8
.
[2
1
]
M
.
F
.
L
e
telier
,
C
.
B.
Hin
o
j
o
sa
a
n
d
D
.
A
.
S
ig
in
e
r
,
"
A
n
a
l
y
ti
c
a
l
so
lu
ti
o
n
o
f
th
e
G
re
a
t
p
ro
b
lem
f
o
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n
o
n
-
li
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e
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r
V
isc
o
e
las
ti
c
it
y
f
lu
id
s
in
t
u
b
e
s
o
f
a
rb
i
trary
c
ro
ss
-
se
c
ti
o
n
,
"
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
T
h
e
rm
a
l
S
c
ien
c
e
s
,
v
o
l.
1
1
1
,
p
p
.
369
-
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,
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0
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7
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d
o
i:
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6
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e
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m
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lsc
i.
2
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6
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0
5
.
0
3
4
.
[2
2
]
S
.
D.
A
b
ra
m
o
w
it
c
h
,
X
.
Zh
a
n
g
,
M
.
Cu
rra
n
a
n
d
R
.
Kilg
e
r
,
"
A
c
o
m
p
a
riso
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o
f
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q
u
a
si
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sta
ti
c
m
e
c
h
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ica
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d
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o
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r
V
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o
e
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ti
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it
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p
ro
p
e
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e
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o
f
th
e
h
u
m
a
n
se
m
i
t
e
d
io
u
s
a
n
d
ten
d
o
n
s
,
"
Cli
n
ica
l
b
io
me
c
h
a
n
ics
,
v
o
l
.
25
,
n
o
.
4
,
p
p
.
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-
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,
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o
i:
1
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1
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6
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.
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o
m
e
c
h
.
2
0
0
9
.
1
2
.
0
0
7
.
[2
3
]
W
.
Qi
-
Ye
，
W
.
Jin
-
Ga
n
，
X
.
M
.
W
e
n
，
X
.
W
a
n
g
，
L
.
I
P
e
n
g
a
n
d
S
.
Y
.
W
a
n
g
,
"
T
h
e
Ex
tra
d
a
te
Disto
rti
o
n
a
n
d
th
e
No
n
-
li
n
e
a
r
V
isc
o
e
las
ti
c
it
y
o
f
L
in
e
a
r
P
E
a
n
d
it
s Co
p
o
ly
m
e
r
M
e
lt
s [J]
,
"
Po
lym
e
r B
u
ll
e
ti
n
,
v
o
l
.
1
,
p
.
66
,
2
0
0
5
.
[2
4
]
Jia
n
y
e
L
iu
,
"
P
o
ly
m
e
r
c
h
a
in
to
p
o
l
o
g
ica
l
m
a
p
a
s
d
e
term
in
e
d
b
y
li
n
e
a
r
V
isc
o
e
las
ti
c
it
y
,
"
,
J
o
u
rn
a
l
o
f
R
h
e
o
lo
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y
,
v
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l
.
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5
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o
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o
i:
1
0
.
1
1
2
2
/
1
.
3
5
6
9
1
3
6
.
[2
5
]
S
.
M
.
Be
ň
o
v
á
,
Ľ.
M
ik
o
v
á
a
n
d
P
.
Ka
šš
a
y
,
"
M
a
teria
l
p
ro
p
e
rti
e
s
o
f
ru
b
b
e
r
-
c
o
r
d
f
lex
ib
le
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le
m
e
n
t
o
f
p
n
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m
a
ti
c
f
le
x
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le
c
o
u
p
l
in
g
,
"
M
e
ta
ll
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rg
ica
l
,
v
o
l.
5
4
,
n
o
.
1
,
1
9
4
-
1
9
6
,
2
0
1
5
.
[2
6
]
S.
R.
Ry
u
a
n
d
D.
J.
L
e
e
,
"
E
ff
e
c
ts
o
f
in
terp
h
o
n
e
a
n
d
sh
o
r
t
f
ib
e
r
o
n
p
u
n
c
tu
re
a
n
d
b
u
rst
p
ro
p
e
rti
e
s
o
f
sh
o
rt
-
f
ib
e
r
re
in
f
o
rc
e
d
c
h
lo
ro
p
re
n
e
ru
b
b
e
r
,
"
J
o
u
rn
a
l
o
f
El
a
sto
me
rs
&
Pl
a
s
ti
c
s
,
v
o
l.
42
,
n
o
.
2
,
v
o
l.
1
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9
7
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2
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o
i
:
1
0
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1
1
7
7
/
0
0
9
5
2
4
4
3
1
0
3
6
2
3
9
7
.
[2
7
]
R.
M
.
Og
o
rk
iew
icz
,
En
g
in
e
e
rin
g
p
ro
p
e
rties
o
f
th
e
rm
o
p
la
st
ic
,
Jo
h
n
W
il
y
&
so
n
s’
ltd
.
,
1
9
7
0
.
[2
8
]
V
.
P.
Cy
ra
s
,
L
.
B.
M
a
n
f
re
d
i,
M
.
-
T
.
T
o
n
-
T
h
a
t
a
n
d
A
.
V
á
z
q
u
e
z
,
"
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h
y
sic
a
l
a
n
d
m
e
c
h
a
n
ica
l
p
ro
p
e
rti
e
s
o
f
th
e
rm
o
p
las
ti
c
sta
rc
h
/m
o
n
tm
o
ril
lo
n
it
e
Na
n
o
c
o
m
p
o
sites
f
il
m
s,
"
Ca
rb
o
h
y
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ra
te
Po
lym
e
rs
,
v
o
l.
7
3
,
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o
.
1
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p
p
.
55
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3
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o
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0
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6
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c
a
rb
p
o
l.
2
0
0
7
.
1
1
.
0
1
4
.
[2
9
]
W
.
Bro
sto
w
a
n
d
H.
E.
H.
L
o
b
lan
d
,
"
P
re
d
ictin
g
w
e
a
r
f
ro
m
m
e
c
h
a
n
ica
l
p
ro
p
e
rt
ies
o
f
th
e
r
m
o
p
las
ti
c
p
o
ly
m
e
r
s
,
"
Po
lym
e
r E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
,
v
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l.
4
8
,
n
o
.
1
0
,
2
0
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8
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o
i:
1
0
.
1
0
0
2
/
p
e
n
.
2
1
0
4
5
.
[3
0
]
L.
A
v
e
ro
u
s
,
L
.
M
o
ro
,
P
.
Do
le
a
n
d
C.
F
r
in
g
a
n
t
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Evaluation Warning : The document was created with Spire.PDF for Python.