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and the associated shear stresses
λ
λ
+
μ
−
+
ξ
3
)
2
Q
2
B
x
1
−
ξ
1
Q
3
3
(
x
3
τ
13
=
,
(1.475)
λ
λ
+
μ
−
+
ξ
3
)
2
Q
2
τ
23
=
B
x
2
−
ξ
2
Q
3
3
(
x
3
,
(1.476)
2
Q
+
x
3
+
ξ
3
(
Q
B
(
x
1
−
ξ
1
)(
x
2
−
ξ
2
)
Q
3
3
x
3
+
ξ
3
Q
2
τ
12
=
+
ξ
3
)
2
−
.
(1.477)
+
x
3
The stress field generated by the Galerkin vector
G
2
produces the traction per unit
area, on a small sphere of radius
a
surrounding the image point, with components
F
1
=
B
x
1
−
ξ
1
a
2
1
3
x
3
+
ξ
3
a
2
+
ξ
3
−
,
(1.478)
a
+
x
3
B
x
2
−
ξ
2
a
2
3
x
3
+
ξ
3
a
2
1
F
2
=
x
3
+
ξ
3
−
,
(1.479)
a
+
a
2
λ
+
ξ
3
)
2
a
2
B
3
(
x
3
F
3
=
λ
+
μ
−
.
(1.480)
=
=
The total traction on the small sphere is found to have components
T
1
T
2
0
and
λ
λ
+
μ
−
sinθ
d
θ
d
φ
B
2π
0
π
3cos
2
=
T
3
θ
0
2π
B
π
−
λ
λ
+
μ
cos
3
=
cosθ
+
θ
0
2π
B
2λ
2
=
λ
+
μ
−
4π
B
μ
=−
λ
+
μ
.
(1.481)
For the third Galerkin vector
G
3
,wehave
1
1
C
e
1
x
1
−
ξ
1
Q
3
3
x
3
(
x
3
+
ξ
3
)
Q
2
C
e
2
x
2
−
ξ
2
Q
3
3
x
3
(
x
3
+
ξ
3
)
Q
2
∇
(
∇·
G
3
)
=−
−
−
−
C
e
3
2
x
3
Q
3
1
+
ξ
3
)
2
Q
2
+
ξ
3
Q
3
x
3
3
(
x
3
−
+
−
,
(1.482)
+
ξ
3
Q
3
.
2
C
e
3
x
3
2
G
3
∇
=−
(1.483)
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