PSI - Issue 33

Anna Fesenko et al. / Procedia Structural Integrity 33 (2021) 509–527 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

524 16



   1 1

  2    . 2 * 1 I r 

       ;   2 * 1 1 1 2 1 I r I r 

2( 1)  

 

 

 

 

r



2     2

2 p I r

r

21

1





22

*

  

   

s

s s

1

11 12



S

 

Y

( ) r

:

Elements of the matrix



p

2 p s

2

21 22

 



  1 r         1 r  0 2

  2 r     0

  2 r

2

2

2

 

 

   ;

s s s

p



* 

* 



1 1

1 1

1 1

 

 

 

 

 

 



11

2

  1 r 

  1 r

  2 r 

  2 r

* 1 0                 2 * 2 0  

   ;

12

2



   1 1 r     2 2 * 1 p

  r          ;   2 r * 1 1 1 2 1   

  2 r    .

2( 1)  

 

 



2

2

s



* 

21

22

1





t t

t t



  

1



1

11 12

S

R

 

 

   

Y

Y

( ) r

( ) r

:

Elements of the matrix







p

p

21 22

  

         

  

2

2



* 

  1 r

  2 r 

 

  2

t

I r

2 1    I r 

*         



1 1

 

 

11

1 0

0

1 1

  r                  * 1 1 1 2 r r I r I r                2 r   1   2 2  1 * 1 * 0 * 0 I r I r  1 0 2

;

 

 

1 1 * 1 1         

  

t

1 0        



12

2 



  

  

2

* 

  r       2 r 1 1 1        

  1

  2 

;

1 0   I r

0 I r







2 

  

  

2

* 

  1 1    

  1 r       2 r * 0 * 0         1                          1 * 0 2 * 1 1 * 1 2 2 * 2 1 2 1 0 1 0 2 r r I r I r r r I r I r                                  2   1 r      2 r 1 1 2 * 0 * 0 * 1 * 1 I r I r         * 0 2 1 1 2 1 I r 2 1    I r       1

  2

t





21

  1    

;

 



     

t

1 1

    

 



22

  

.

*       

1 1

 

 

 

1

2

c c

c c

2



  



1

p

2



  

 

1

11 12





S

S

 Y Y  ( ) r R p

R

 

 

 С Y Y   ( ) r ( ) r



    

( ) r

( ) r

Elements of the matrix

:





p

p

p

21 22

C r

( )

21 s t

22 s t

11 s t

12 s t

  

  

c

r

c

r





 



12

22

12

22

;

;

11

22

12

12





21 s t

22 s t

11 s t

12 s t

  

  

c

r

c

r

 







11

21

11

21

;

;

21

21

22

11





( ),         ( ), ( ), ( ) s s  

Appendix C. The form of functions

11

12

11

12



( )    



( )    

( ) 

( ) 

( ) s 

d s

d

( ) s 

d s

d





11 11      ( ) r 

12 12      ( ) r 

11

11 12

21

11

12 12

22

;

;



