Issue 48
Y. Khalfi et alii, Frattura ed Integrità Strutturale, 48 (2019) 208-221; DOI: 10.3221/IGF-ESIS.48.22
x y xy yz xz
x y xy yz xz
0 0 0 0 0 0
Q Q Q Q
12 22 12 22 0 0
(4)
0 0
Q
66
0 0 0
0
Q
44
0 0 0 0
Q
55
where ( σ x
, σ y
, τ xy
, τ yz
, τ yx
) and ( ε x
, ε y , γ xy , γ yz , γ yx ) are the stress and strain components, respectively. Q ij
are the elements of the
reduced stiffness matrix that are defined as follows:
E
E
E
1
12 2
2
(5)
,
,
,
66 12 44 Q G Q G Q G 23 55 , ,
Q
Q
Q
11
12
22
13
1
1
1
12 21
12 21
12 21
Based on the present refined shear plate theory, the stress resultants are related to the stresses by the equations [19]
x N N N M M M M M M y b x b y
1
xy
/2
h
b
(6a)
, ,
( ) z dz f z
xy
x y xy
/2
h
s x
s y
s
xy
/2
h
( , s
s xz yz
(6b)
)
( , ) ( ) xz yz
S S
g z dz
/2
h
Using Eq. (4) in Eq. (6), the stress resultants of the can be related to the total strains by
s
0
N A
B
b s
b M s
s
s
0
, D D k S A
(7)
s
s
s
M B D H k
where
t
t
t
, b b b xy N N N N M M M M M M M M s s s s x y xy x y xy x y , , , , , , b
(8a)
t
t
t
0 0 0 , , , x y xy
, , b b b x y xy x y xy k k k k k k k k , , , s s s b s
(8b)
0
0 0
A A
D D
11 12
11 12
0 ,
A A A
D D D
(9a)
12 22 0 0
12
22
0 0
A
D
66
66
s
s
s
s
s
s
0
0
0 0
B B
D D
11 H H
11 12
11 12
12
s
s
s
s
s
s
s
s
s
0 ,
0 ,
B B B
D D D
H H H
(9b)
12 22 0 0
12
22
12
22
s
s
s
0 0
0 0
B
D
H
66
66
66
s
0
A
t
t
44
s
s
s
, S S S
,
,
,
A
(9c)
yz xz
yz xz
s
0
A
55
211
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