146 ELASTOSTATICS
6
L
2
CM
b
έ
o
-2
-L
I
M
—
T"
V
-
1
1
v
V
V
-i 1
e
-0-5
/10
X
20
l·
r
V
I
1
-i—
7/
/
_l_
—i 1 1
1
S / i
1/ / i
7 / /
l'
L·—H
J
1,
,
45
90 135
0(deg.)
180
Figure 5.19 Hoop stress {a
h
) around circular
hole
for tension in x
2
direction
and transverse tension respectively, λ was taken to be equal to 1-5. In
both diagrams the dashed lines represent the case where we have
double roots with
where
2
v
V
G E
i
£i = l/a
uu
El=
1/^2222
G=l/4o
1212
V12/E1 = -a
1122
= 1
(a)
(b)
(c)
(d)
(e)
where the a's are the usual components of the tensor relating stress to
ELASTOSTATICS 147
strain in an anisotropic solid. We have written
ε = /Ε
1
/Ε
2
(f)
From the
figures
we
can see that the interaction between the circles
is small.
Example 5.6
s
Lachat
8
examined the case of a rubber sheet with embedded steel
wires under plane longitudinal strain (Figure 5.20). He used cubic
E D
U
mm
Figure 5.20 Sheet of
rubber
with embedded steel wires
Figure 5.2 J Discretisation for boundary element analysis: (a) coarse discretisation (9
segments);
(b) fine discretisation (18 segments)
2*
Ε
ε
6"
90
(α)
67-5 45 22-5 0
Angle (deg) B
2
Ε
£ 1
90
-0-5,
45 22-5
Angle (deg )
Figure 5.22 Variation of σ
ιχ
along the curve AB: (a) v = 0.45; (b) v = 0.5
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