Issue 59
H.A. Mobaraki et alii, Frattura ed Integrità Strutturale, 59 (2022) 198-211; DOI: 10.3221/IGF-ESIS.59.15
x u w z x
w
0
xz
x
y v w z y
w
0
yz
y
where x , , y and xy denote the normal and shear strains of an arbitrary point, respectively. Furthermore, 0 x , 0 y , and 0 xy are the mid-plane strains, and x k , y k and xy k are the bending curvatures.
Figure 1: Laminated composite plate under the action of a moving vehicle
According to the transformed constitutive relations for a 2D orthotropic lamina, the stress-strain relations for the k th lamina can be written as [24]:
k
k
k
x y xy
x y xy
11 Q Q Q Q Q Q Q Q Q 12 12 22
k
k
k
16
yz xz
yz xz
44 Q Q Q Q 45
45
,
(3)
26
55
16
26
66
where ij Q is the reduced stiffness. The strain energy of the laminated composite plate is:
h
1 2
2 0 0 a b
k k
k k
xy
k yz
k
k xz
k
k k
x x
U
dz dy dx
(4)
(
)
P
y
y
xy
yz
xz
h
2
Substituting Eqn.3 into Eqn.4 and then integrating over the thickness leads to:
0 0 U 1 [ P a b
2
2
2
2
2
2
A u A v 11 0, 22 0, x
D D 11 , x x
66 0, A u v y
0, u v
2
y
x
0, y x
y y
0,
22 ,
2
2
2
2
2
2 x y y x , x y , y x , ,
A w
B u v 16 , 0, 2 x x y
D
w
2
y
y
y
y
x
66
44
0,
0,
0,
2
2
A w
A u v u 16 0, 0, y x
w
12 0, A u v
2
2 2
2
x
x
0, x x
0, x y
x
55
0,
0,
B u 11 ,
B u 12 , y y
x y ,
u v 0, y
B
u
B
2 2
2
2
(5)
0, x x x
x
, y x
x
y y
x
0,
16
0,
26 ,
0,
A u v v 26 0, 0, y x
B v 12 ,
B v 22 , y y
x y ,
B
v
2
2
2
y
0, x x y
y
, y x
y
0,
0,
26
0,
200
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