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FIGURE 8.13
Loading on triangles 5 and 7.
from equilibrium requirements as
h
12
p
0
h
6
p
0
p
7
=
p
8
=
(9)
For triangle 7, the traction distribution on the side connecting nodes 8 and 9 is a trapezoid.
The loading on nodes 8 and 9 is found to be
4
h
12
p
0
5
h
12
p
0
p
8
=
p
9
=
(10)
The principle of virtual work for the entire plate is formed by summing the virtual work
of each triangle. An assembly process, following that described in Chapter 5, leads to the
global stiffness matrix and to the global load vector. The boundary conditions
u
y
1
=
u
x
3
=
u
x
6
=
u
x
9
=
0
(11)
should be imposed, and the appropriate rows and columns deleted in the global matrix
K
.
Then we obtain a system of linear equations for the solution of the nodal displacements
KV
=
P
(12)
where
u
y
9
]
T
V
=
[
u
x
1
u
x
2
u
x
4
u
x
5
u
x
7
u
x
8
u
y
2
u
y
3
u
y
4
u
y
5
u
y
6
u
y
7
u
y
8
P
9
]
T
P
=
[0
0
···
P
7
P
8
=
00
p
9
T
p
7
p
8
+
p
8
···
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