Issue 51

S. Merdaci et alii, Frattura ed Integrità Strutturale, 51 (2020) 199-214; DOI: 10.3221/IGF-ESIS.51.16

 N N N M k M k M k M k M k M k S S d q w ws d                                            0 0 y 0 0 b b b b b b s s x x y xy xy x x y y xy xy x x s s s s s s s s y y xy xy yz yz xz xz b

(10)

where the stress resultants N, M, and S are defined by

      

      

, N N N M M M M M M , , , , , x y b x b y s s

1           ( ) f z

xy

h

/2

h

/2













( ) n

( ) n

 

h    

b

, s xz yz s







, , x y xy   

S S

g z dz

z dz

,

( ) .

,

(11)

xy

xz yz



h

/2

/2

s

x

y

xy

where A is the top surface, and the stress resultants N, M, and s are defined by:

, N A B B M A D D k S A M B D H k                                     B B B A A B N A A B B B B M B B D D D D B B D D D D M B B D D H H M B B D D H H                                , s b s b s s s s s s 12 11 11 12 11 12 22 12 22 12 11 12 11 12 11 12 22 12 22 12 11 12 11 12 11 s x s y b x s b s s y s s s s s s x s s s s s s N M 0               11 N A B B M B D D k B D H M k S A A S                                                            66 66 66 66 66 66 66 66 44 55 0 0 s xy xy b s b xy xy s s s s s xy xy s s yz yz s s xz xz 12 22 12 22 12 y   

(12)

0                       0 y x b x k k k k   b y s x s y

          

s

12

s

22

s

12



22

s

12

s

22

(13)

where Aij , Bij , etc. are the plate stiffness defined by

        

       

s

s

s

     

     

11 A B D B D H A B D B D H A B D B D H 11 11 11 11 12 12 12 12 12 s s s s

1

11

h

3



n

1





1 n h   

s

( ) n

( ) n

2

2





1, , , ( ), ( ), ( ) Q z z f z z f z f z

dz

(14a)

12

11

 

s

( ) n



1

n

66

66

66

66

66

66

2

E z

2 ( ) 



  

 ( ) 11 , n

s

s

s

s

s

s



22 22 22 22 22 22 A B D B D H A B D B D H Q 11 11 11 11 11 11 , , , , , , , , , ,

(14b)



1

h

3

E z

( )



n

1

1 n h   





2

s

s

 

44 A A

( ) g z dz

,

(14c)

 2 1



55





n

203