Civil Engineering Reference
In-Depth Information
Here
d
1
, d
2
are absolute values of the intrinsic coordinate of the interpolation nodes.
q
[
()
e
q
e
e
3
q
q
[
1
2
3
1
2
d
d
2
Figure 3.23
One dimensional quadratic discontinuous element
It can be easily verified that for
d
1
=d
2
=1 the shape functions for the continuous element
are obtained. For a quadratic element we have
1
[
1
[
N
()
[
(
d
[
)(1
) ;
N
()
[
(
d
[
)(1
)
1
1
2
2
(
dd
)
d
(
dd
)
d
1
2
2
1
2
1
(3.37)
1
N
()
[
(
d
[
)(
d
[
)
3
1
2
dd
12
K
d
2
d
1
q
[K
(, )
e
q
4
3
4
d
4
e
q
3
4
[
e
3
q
d
3
1
e
q
1
2
1
2
2
Figure 3.24
Two-dimensional linear discontinuous element
For the two-dimensional linear element shown in Figure 3.24 the shape functions are
given for the corner nodes by
1
1
N
(, )
[K
(
d
[
)(
d
K
) ;
N
(, )
[K
(
d
[
)(
d
K
)
1
1
3
2
2
3
c
c
(3.38)
1
1
N
(, )
[K
(
d
[
)(
d
K
) ;
N
(, )
[K
(
d
[
)(
d
K
)
3
2
4
4
1
4
c
c
cdddd
(
)(
)
1
2
3
4
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