PSI - Issue 52
J.C. Wen et al. / Procedia Structural Integrity 52 (2024) 625–646
632
8
Author name / Structural Integrity Procedia 00 (2019) 000 – 000
N
N
N
N
x
x
y
y
8
8
8
8
(20)
,
,
,
.
x
x
y
y
=
=
=
=
i
i
i
i
i
i
i
i
1
1
1
1
i
i
i
i
=
=
=
=
For 2-D orthotropic media, the elastic equation with the mapping technique becomes
2
2
2
u
u
u
2
2
2
u
u
u
u
u
y
y
y
A
B
C
x D E F + + x
1 G H u + 2
+
+
+
+
x
x
x
1
1
1
1
1
1
1
2
2
2
(21)
u
( ) , x
y
y
0,
I
J
X t
+
+
−
=
1
1
2
2
2
u
u
u
2
2
2
u
u
u
u
u
y
y
y
A
B
C
x D E F + + x
2 G H u + 2
+
+
+
+
x
x
x
2
2
2
2
2
2
2
2
2
2
(22)
u
( ) , x
y
y
0,
I
J
Y t
+
+
−
=
2
2
where
( ) x
( ) x
( ) x
( ) x
2
2
2
2
,
,
A k E =
2 k E
B k E =
2 k E
+
+
1
1
11
21
1
1
12
22
( )( C E k = x 2
)
,
2 21 22 + k
1
1 11 12
( ) x
( ) x
E
E
( ) D E k = x
,
k
k
k
k
k
+
+
+
+
+
11
11
21
21
1
1 11
1 12
2 21
2 22
1
11
2
21
x
y
( ) x
( ) x
E
E
( ) E E k = x 1
,
k
k
k
k
k
+
+
+
+
+
12
12
22
22
1
12
2
22
1 11
1 12
2 21
2 22
x
y
( ) x
( ) x
( ) x
( ) x
,
,
,
F k E =
G k E =
H k E =
3 k E
+
1
3
11 21
1
3
12 22
1
3
11 22
12 21
( ) x
( ) x
E
E
( ) x
,
I k E =
k
k
11
11
+
+
+
1
3
21
22
1
21
2
11
x
y
( ) x
( ) x
E
E
( ) x
,
J k E =
k
k
+
+
+
12
12
1
3
21
22
1
22
2
12
x
y
( ) x
( ) x
( )( x
)
,
,
,
A k E =
B k E =
C k E =
11 22 + 12 21
2
3
11 21
2
3
12 22
2
3
( ) x
( ) x
E
E
( ) x
,
D k E =
k
k
+
+
+
11
11
2
3
21
22
1
11
2
21
y
x
( ) x
( ) x
E
E
( ) x
,
E k E =
k
k
+
+
+
12
12
2
3
21
22
1
12
2
22
y
x
( ) ( F E k = x 2
)
( ) ( G E k = x 2
)
2 + 2 2 11 1 21 k
2 + 2 2 12 1 22 k
,
,
( )( E k x
)
2
,
H
21112 12122 k +
=
2
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