Civil Engineering Reference
In-Depth Information
0
0
2
h
a
2
w
(a)
4
19
20
21
22
23
5
39
37
18
43
24
44
40
42
36
25
38
33
17
26
2
28
1
35
29
48
32
41
34
46
47
45
30
31
6
8
7
3
16
15
14
13
12
11 10
9
(b)
Figure 9.8
(a) A uniformly loaded plate in plane stress with a central hole of
radius
a
. (b) A coarse finite element mesh using quadrilateral
elements. Node numbers are as shown (31 elements).
To examine the solution convergence, a refined model is shown in Figure 9.8c, using
101 elements. For this model, the maximum stress also occurs at node 1 and has a calcu-
lated magnitude of 3032 psi. Hence, between the two models, the maximum stress values
changed on the order of 2.3 percent. It is interesting to note that the maximum displacement
given by the two models is essentially the same. This observation reinforces the need to
examine the derived variables for convergence, not simply the directly computed variables.
As a final step in examining the convergence, the model shown in Figure 9.8d con-
taining 192 elements is also solved. (The node numbers are eliminated for clarity.) The
maximum computed stress, again at node 1, is 3024 psi, a miniscule change relative to
the previous model, so we conclude that convergence has been attained. (The change in
maximum displacement is essentially nil.) Hence, we conclude that the stress concentra-
tion factor
K
t
=
max
/
0
=
3024
/
1000
=
3
.
024
is applicable to the geometry and load-
ing of this example. It is interesting to note that the theoretical (hence, the subscript
t
)
