Issue 47

V. Rizov, Frattura ed Integrità Strutturale, (2047) 468-481; DOI: 10.3221/IGF-ESIS.47.37

ai y y  and 1

0 z  in (18), one obtains

By substituting of 1

1





m

1  i

i     

i 





i 

1  i



 

y

cos

0

(19)

i

ai i

where

E

d

 

(20)

1 i

i

m

H

i

i

E

f

 

(21)

1 i

i

m

H

i

i





i 

(22)







y

y

2

1 1 i 

i

1



y

i

1

i 



(23)







y

y

2

1 1 i 

i

1

ai y y  and 1

0 z  in the first derivative of (18) with respect to 1

y , one arrives at

Further, by substituting of 1



i m

1

1

i

1





1   ) i i m

m

2 



i i  





i     

i 





i 

1  i

2 



 

y

y

sin(

cos

0

(24)

i

i

ai i

ai i

i

m

i

ai y y  and 1

0 z  in the first derivative of (18) with respect to 1

z , one obtains

Similarly, by substituting of 1



m

1

i

1





m

1  1  cos( E E y  di f



    

i 

3 

i 

i 





i 

1  i

3 

 

y

(25)

)

cos

i



ai i

i

ai i

i

m

i

i

ai y y  and 1

0 z  in the second derivatives of (18) with respect to 1 y , 1

y and 1

z , and 1 z ,

Further, by substituting of 1

one arrives at





m

m

1

1

1

  

i

i

1

1

1   ) i i m

m

m

2

4 



i i  







i i  





i 

1  i

2 

 

i i  





i 

1  i



y

y

y

2

cos(

sin(

)

sin(

)

i

i

i

i

ai i

ai i

i

ai i

m

m

i

i

(26)

1 2 



m

m

1

  

i

i

m 

m

1

1









m

m

i

i     



2    i  





i 



i 

1 

2 

2 

i 



i 

1  i

4 

 

 

y

y

cos

cos

0

i

i

ai i

i

i

i

ai i

i

2

m

i

i



m

1

i

1

m



1 

sin( E y  f i



5     ) i  i

i i  





i 

1  i

3 



y

sin(

)

i

ai i

ai i

i

m

i

i

(27)

1 2 



m

m

1

    

  

i

i



m

1

1

,





m

m

i

i 



i 





i 

1  i

3 2 i  





5 

 

y

cos

i

i

ai i

i

i

i

1

m

m

i

i

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