Civil Engineering Reference
In-Depth Information
3 (2.5, 2)
4 (1.25, 1.75)
y
x
1 (1, 1)
2 (3, 1)
Figure 6.22
Quadrilateral element for
Example 6.3.
known coordinates of nodes 2 and 3, we have
Node 2:
1
=
3
m
+
b
Node 3:
2
=
2
.
5
m
+
b
Solving simultaneously, the slope is
m
=−
2
and the
y
intercept is
b
=
7
Therefore, element edge 2-3 is described by
y
=−
2
x
+
7
Using the interpolation functions given in Equation 6.56 and substituting nodal
x
and
y
coordinates, the geometric mapping of Equation 6.80 becomes
1
4
(1
−
r
)(1
−
s
)(1)
+
1
4
(1
+
r
)(1
−
s
)(3)
+
1
4
(1
+
r
)(1
+
s
)(2
.
5)
x
=
1
4
(1
−
r
)(1
+
s
)(1
.
25)
+
1
4
(1
−
r
)(1
−
s
)(1)
+
1
4
(1
+
r
)(1
−
s
)(1)
+
1
4
(1
+
r
)(1
+
s
)(2)
y
=
1
4
(1
−
r
)(1
+
s
)(1
.
75)
+
Noting that edge 2-3 corresponds to
r
=
1
, the last two equations become
3
2
(1
−
s
)
+
2
5
2
.
5
5
2
.
0
5
2
.
x
=
(1
+
s
)
=
−
s
1
2
(1
−
s
)
+
(1
+
s
)
=
3
2
+
1
2
s
y
=
Eliminating
s
gives
14
2
2
x
+
y
=
