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FIGURE 6.42
A triangular element.
stretching. The displacements in the
x
direction are approximated by
u
x
=
N
u
(ξ
,
η)
u
x
(6.140)
with the linear expression
N
u
=
[1
ξη
]
where
u
x
3
]
T
contains the generalized displacements. The transformation to nodal displacement
v
x
fol-
lows the procedure described in Section 6.4.1. Define
v
x
=
=
u
x
1
u
x
2
u
x
[
[
u
x
1
u
x
2
u
x
3
]
T
. Then substitute
the
ξ
,
η
coordinates of Fig. 6.42 into Eq. (6.140)
u
x
1
u
x
2
u
x
3
101
100
110
u
x
1
=
=
N
u
u
x
2
or
v
x
u
x
u
x
3
It follows that
=
N
−
u
v
x
u
x
=
Gv
x
with
010
0
G
=
−
11
1
−
10
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