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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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