Civil Engineering Reference
In-Depth Information
The plate will be divided into 10 segments in the horizontal and vertical
directions. Since the plate is square with a uniform load and fixed on all
edges, it has horizontal and vertical symmetry. It is also symmetric about
both diagonals of the plate. The symmetry will result in only 21 unique points
on the plate for the 121 possible locations. This is shown in Figure 3.11.
The difference operator for Equation 3.12 is repeated here and can be
shown in graphical form in Figure 3.12.
1
282
1820 81
282
1
−
q
D
d
4
z
z
dx dy
d
4
d
4
z
1
=+ +=
2
−
−
4
22
4
4
dx
dy
h
−
The operator is laid upon each of the 21 unique points on the plate result-
ing in 21 equations involving the deflections. Figure 3.13 shows the oper-
ator laid upon point 1.
The result will be a non-homogenous set of 21 equations involving
the unknown deflections. Since the plate is fixed at the boundaries, the
13
14
9
4
9
13
16
17
18
17
19
20
19
17
14
10
5
10
14
16
10
5
10
14
15
14
13
12
8
17
19
20
21
17
18
6
18
20
15
11
11
14
13
12
8
10
5
4
3
2
10
17
19
17
14
20
17
9
9
16
18
16
8
8
13
15
13
7
2
7
9
10
11
9
3
1
2
3
5
6
4
4
8
7
2
38
7
8
12
9
10
11
9
12
8
13
14
15
13
Figure 3.11.
Example 3.19 Plate bending.
