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C
case
a
/
b
0.0
0.1
0.2
(a)
14.68
14.00
13.26
(b)
4.19
4.00
3.70
13.30
S
uppose a circular plate with no center hole is subject to a nonsymmetrical load
p
z
=
p
0
b
cos
φ.
The outer rim at
r
=
b
is hinged.
Use Eq. (13.76) with
p
s
m
(
Hint:
r
)
=
0 and
m
=
1
.
Answer:
r
b
1
r
b
2
r
b
2
cos
p
0
b
4
w
=
−
(
7
+
ν)
−
(
3
+
ν)
φ
192
(
3
+
ν)
K
r
b
1
r
b
2
cos
p
0
b
2
48
m
r
=
(
5
+
ν)
−
φ
Stiffness (or Transfer) Matrix Methods
13.31 Find the radial displacements and internal forces in a circular disk subject to a radial
pressure of
p
0
(force/length) on the inner periphery at
r
=
.
a
The disk is of thickness
t
1
for
a
≤
r
≤
a
1
and thickness
t
2
for
a
1
<
r
≤
b
.
The outer rim at
r
=
b
is free of
loading.
13.32 A simply supported rectangular plate is twice as long
(
L
x
=
2
L
)
as it is wide
(
L
y
=
L
).
The plate rests on a midspan
(
x
=
L
)
rigid knife edge support that begins at
y
=
0
L
y
.
13.33 Find the deflection, slope, shear force, and moment distributions in the symmetrically
loaded circular plate of Fig. P13.33.
and ends at
y
=
FIGURE P13.33
13.34 Find the first three natural frequencies of the plate of Fig. P13.33 if
ν
=
0
.
3
,E
=
207
GN/m
2
,
a
=
0
.
5m,
a
1
=
1
.
0m,
b
=
1
.
5m,
t
1
=
0
.
01
,
and
t
2
=
0
.
005
.
Finite Elements
13.35 Consider a rectangular element with eight nodes, four of which are at the corners and
four at the midpoints of the sides. Use Kirchhoff plate theory to develop a stiffness
matrix for this element. Assume there are eight DOF, with four deflection DOF at the
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