Civil Engineering Reference
In-Depth Information
Ans:
N
10
=
c
1
+
c
2
L
1
+
c
3
L
2
+
c
4
L
1
+
c
5
L
1
L
2
+
c
6
L
2
+
c
7
L
1
+
c
8
L
1
L
2
+
c
9
L
1
L
2
+
c
10
L
2
27 27 0 27 0 0 27 0 0 0
27 027 0027 00027
7000000000
27 18 9 12 6 3 8 4 2 1
27 918 3612 124 8
27 018 0012 000 8
7090030001
7903001000
27 18 0 12 0 0 8 0 0 0
7993331111
c
1
c
2
c
3
c
4
c
5
c
6
c
7
c
8
c
9
c
10
0
0
0
0
0
0
0
0
0
27
=
1
4
9
5
8
10
7
6
2
3
Figure 5.45
11. Figure 5.46 shows a cubic, 8-node, 3D finite element with side length 2 units. The
origin of the coordinate system is at the centroid of the element, so all nodal coordi-
nates are
1
)
etc.). Choose suitable terms for the shape
functions of this element, and hence set up the system of simultaneous equations that
would enable you to derive shape function
N
7
. Do not attempt to solve the equations.
Ans:
N
7
=
c
1
+
c
2
x
+
c
3
y
+
c
4
z
+
c
5
xy
+
c
6
yz
+
c
7
zx
+
c
8
xyz
±
1 (e.g. node 1 is at
(
−
1
,
−
1
,
−
1
−
1
−
1
−
1111
−
1
c
1
c
2
c
3
c
4
c
5
c
6
c
7
c
8
0
0
0
0
0
0
1
0
1
−
1
−
111
−
1
−
11
11
−
11
−
1
−
11
−
1
11
−
1
−
1
−
11
−
11
=
1
−
11
−
1
−
1
−
111
1
1
11111111
111
−
111
−
11
−
1
−
−
−
−
−
11
1
1
1
