Issue 48
Y. Khalfi et alii, Frattura ed Integrità Strutturale, 48 (2019) 208-221; DOI: 10.3221/IGF-ESIS.48.22
4
2 2
4 0 2 H A A N N K s s s 2 2
0 2 y
2 2
s
s
s
(23)
( 2( H H H
66 2 )
(
)
)
a
K
44
11
12
22
55
44
x
g
W
By applying the static condensation approach to eliminate the coefficients associated with the in-plane displacements, Eq. (20) can be rewritten as
11 T K K K K 22 12 1 2 12 0 0
(24)
where
0 0
a a a a
a a a a
a a
11 12
14
33 34
11 K
12 K ,
22 K
(25a)
,
12 22
24
34 44
2 , mn bmn mn smn U W V W
1
(25b)
Equation (24) represents a pair of two matrix equations:
11 1 K K 12 2
(26a)
0
12 T K K 1 22 2 0
(26b)
Solving Eq. (26a) for Δ 1 and then substituting the result into Eq. (26b), the following equation is obtained:
22 2 0 K
(27)
where
a a a b
1
T
22 22 12 11 12 K K K K K
33 34
(28a)
34 44
and
33 a a a a 34 33 34 ,
b
b b
1
2
43 34 44 44 14 a a b a a ,
a
24
b
0
0
2 0 11 22 12 1 14 22 12 24 2 11 24 12 14 , , , b a a a b a a a a b a a a a
(28b)
For nontrivial solution, the determinant of the coefficient matrix in Eq. (27) must be zero. This gives the following expression for the mechanical buckling load
2
a b a
1
0
0 y
33 44 34
(29)
N N
x
2 2
33 44 a a a 2
34
215
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