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Problem 14.22(a)
Given:
The sketch represents three nodes on a z=constant face of an axisymmetirc quadratic element.
Nodes shown are uniformly spaced.
Determine the consistent nodal load vector if zdirection traction
z
is
applied to the face as follows:
a)
z
has a constant value p over the face.
b)
z
has a parabolic variation based on nodeal values p
4
, p
7
, and p
3
.
Solution:
rS
N
T
Φ
d
=
along edge 3, 7, 4
η
1
=
N
1
N
2
=
N
5
=
N
6
=
N
8
=
0
=
N
0
0
0
0
0
0
0
0
N
3
0
0
N
3
N
4
0
0
N
4
0
0
0
0
0
0
0
0
N
7
0
0
N
7
0
0
0
0
=
Φ
0
p
=
N
3
1
4
1
ξ
()
1
η
1
4
1
ξ
1
η
2
1
4
1
ξ
2
1
η
=
applying
η
1
=
N
3
ξ
2
ξ
2
=
similarily
N
4
ξ
2
ξ
2
=
N
7
1
ξ
2
=
rN
3
r
3
N
4
r
4
N
7
r
7
=
since node 7 is at the middle:
r
7
r
3
r
4
2
=
r
ξ
2
ξ
2
r
3
ξ
2
ξ
2
r
4
1
ξ
2
r
3
r
4
2
=
simplify
r
r
3
2
r
4
2
ξ
r
3
2
ξ
r
4
2
=
r
1
2
r
3
r
4
ξ
r
3
r
4
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This note was uploaded on 01/11/2011 for the course MAE 5020 taught by Professor Folkman during the Fall '10 term at Utah State University.
 Fall '10
 Folkman

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