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FIGURE 13.12
Plate element subjected to compression forces (force/length).
or
w
w
0
0
−
1
0
0
2
y
ν∂
0
0
1
/
K
0
θ
θ
∂
∂
=
+
2
4
y
2
y
x
K
(
1
−
ν
)∂
0
0
−
ν∂
−
p
z
V
V
(13.58b)
2
y
0
−
2
K
(
1
−
ν)∂
1
0
m
x
m
x
0
∂
z
=
A
z
+
P
∂
x
The nonlinear effect of compressive in-plane forces on bending (buckling) can be intro-
duced in an approximate manner. Treat these forces in the sense of the theory of second
order of Chapter 11. If the in-plane compression forces (force per unit length along an edge),
n
x
=
n
and
n
y
, are applied in the middle plane of the plate as in the case of Fig. 13.12, the
equilibrium conditions in the
z
direction would be
n
dx
sin
θ
x
dx
dy
+
∂
n
θ
x
+
∂
∂
−
n
sin
θ
x
dy
+
sin
∂
x
x
n
y
+
∂
dy
sin
θ
y
dy
dx
n
y
∂
θ
y
+
∂
∂
−
n
y
sin
θ
y
dx
+
y
sin
=
0
y
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