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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