Civil Engineering Reference
In-Depth Information
3
7
8
6
10
9
2
5
4
1
Figure P6.13
Show that node 10 in Figure P6.13 is located at the element centroid.
6.14
Use the integration formula for area coordinates to evaluate the following
integrals in terms of total area
A
:
6.15
L
2
(2
L
2
−
1)
2
d
A
a.
A
b.
4
L
1
L
2
L
3
(2
L
1
−
1) d
A
A
L
1
L
2
L
3
d
A
c.
A
L
1
L
2
L
3
d
A
d.
A
The interpolation functions for the four-node rectangular element as given by
Equation 6.56 are such that
6.16
4
N
i
(
r
,
s
)
=
1
i
=
1
What is the significance of this observation?
Show that Equation 6.56 is such that constant values of the partial derivatives
∂
/∂
r
,
∂
/∂
s
are possible in an element. Note that this ensures satisfaction of
the completeness requirement for
C
0
6.17
problems.
Two three-node triangular elements share a common boundary, as shown in
Figure P6.18. Show that the field variable
is continuous across this
interelement boundary.
6.18
