Issue 50
H. Saidi et alii, Frattura ed Integrità Strutturale, 50 (2019) 286-299; DOI: 10.3221/IGF-ESIS.50.24
Substituting Eq. (4) into Eq. (6) and the subsequent results into Eqs. (10), the stress resultants are obtained in terms of strains as following compact form:
s N A B B M B D D k M B D H k , b s b s s s s s
s S A ,
(16)
in which
t
t
t
b
b x
b
b
s
s
s
s
, xy N N N N , x y
, xy M M M M , y
, xy M M M M , x y
,
,
,
(17a)
0 0 0 , , t x y xy
t
t
, , b b b x y xy k k k k b
, , s s x y xy k k k k s s
,
,
,
(17b)
11 A A A A A
11 B B B B B
11 D D D D D
0 0
0 0
0 0
12
12
12
,
,
,
(17c)
12
22
12
22
12
22
A
B
D
0 0
0 0
0 0
66
66
66
11 B B B B B s s s
s
11 D D D D D s s s
s
11 H H H H H s s s
s
0 0
0 0
0 0
12
12
12
s
s
s
,
,
,
(17d)
12
22
12
22
12
22
s
s
s
B
D
H
0 0
0 0
0 0
66
66
66
s
A
0
, t s s xz yz
0 0 , t xz yz
44
s
S S S
,
,
,
(17e)
A
s
A
0
55
and stiffness components are given as:
1 2 1
s
s
s
11 A B D B D H A B D B D H C z z f z z f z f z 11 11 11 11 11 /2 2 2 1, , , ( ), ( ), ( ) h s s s
dz
,
(18a)
12
12
12
12
12
12
11
h
/2
s
s
s
A B D B D H
66
66
66
66
66
66
22 22 22 22 22 22 s s A B D B D H A B D B D H , 11 11 11 11 11 11 , , , , , , , , , s , s s s
(18b)
h
/2
2
44 h A A C g z dz 55 44 /2 ( ) s s
,
(18c)
A NALYTICAL SOLUTION FOR SIMPLY - SUPPORTED FG PLATES
ased on Navier technique, the following expansions of generalized displacements are considered to automatically respect the simply supported boundary conditions: B
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