PSI - Issue 33

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

523 15

  b b b b p 2 1

  

11 12

 A Y Y   (1) R

R

 

(1)

Elements of the matrix

:

p

p

21 22

  

  

2  *

 

 

  

 

 

2   * 0 1 I

2   * 0 2 I

2 p I

b

I

2 1 2    I 

 

3    

3 5 2( 1)    

3 5 2( 1)    

1 2

11

0 2

1 1

1

1 

      2 * 2 1 * I

   2 2 

 

 

2  

2 p I

;

1 1 2 1      

1 1

 

 

* 

 

  

 

  

 

 

2  *

2

* 1 1   I  

 

b

* 1 0 1    I

I

p

I

3 5 2( 1)    

3 5 2( 1)    

3

1 1 2 1    

12

0 2

1 2

1

          2 2 * 1 1 2 p I        2 * 1 2 1 2 2 2 I I    * 

;

 

1 2

  

 

  2    * 1 2 2 I 

  2 1 2    2 I

2     2

2 p I

.

;

b

b

1 1

 

 

22

*

1 1

21

1 

2

1

2

1

( , ), ( , ), ( , ) g r g r g r g r     . ( , ),

Appendix B. The form of functions

11

11

21

21

2

  , 

    11 c r 

    21 c r

1 11 g r

;

 

 

11  

12  

 

c r

2

    21 r c r s   

  , 

    11 r c r 

    22  

    21 r r  

 

2 11 g r

r r s 

11

12

11

12

  

 

c r

  r c r s     21  

    11 r c r      11 c r 

    11  

    12 r r  

 

;

r r s 

21

22

12

11

2

  , 

    21 c r

1 21 g r

;

 

 

21  

22  

 

c r

2

    21 r c r s   

  , 

    11 r c r 

    22  

    21 r r  

 

2 21 g r

r r s 

11

12

21

22

  

 

c r

  r c r s     21  

    11 r c r 

    11  

    12 r r  

 

;

r r s 

21

22

22

21

1

 

 

  22 11 12 21 r r r r     c r

t t

t t  

11 22 12 21 s s s s 

11 22 12 21

2

1

  12 

  11 

  22 

 

 

;

11 r s t 21

12 s t

21 r s t

22 s t

21 r s t

22 s t

11 r s t

12 s t

12

22

11

21

12

22

11

11

2

     

    r r          * 1 1 2 2 1 2 1 2

    2 0 1 r r 

.

 

1 2

*

1 1

 

 

1 2  

r r

r r

   

  

1

11 12

R

 

Y

( ) r

Elements of the matrix

:

p

2

p

2

21 22

   0 2   

  1 

  1 

  2

2

2

2 p I r

 

 

   ;

r r

I r

2 I r

2 I r

 

* 

1 1

1 1

1 1

 

 

 

 

 

11

* 0

  1 

  1

  2 

  2

* 1 0    

 

 

   ;

I r

2 I r

I r

2 I r

   

12

* 2 0

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