PSI - Issue 65

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E. Yu. Prosviryakov et al. / Procedia Structural Integrity 65 (2024) 177–184 E. Yu. Prosviryakov, O. A. Ledyankina, L. S. Goruleva / Structural Integrity Procedia 00 (2024) 000–000

181 5

( ) k

( ) k

( ) k

U

U

U

( ) k

( ) k

x

x

1

2

1

2

t

t

t

  

  

2 ( ) k U

2 ( ) k U 1

2 ( ) k U 2

( ) k P P x P x  ( ) ( ) k k ( ) ( ) k k 11 1 12 2 1

( ) k

( ) k

( ) k

x

x

 

1

2

( )2 k

( )2 k

( )2 k

x

x

x

3

3

3

,

( ) k W W W x     ( ) k ( ) k 1

( ) k

( ) k

x

2 t

1

2

t

t

  

  

2 ( ) k W

2 ( ) k W

2 ( ) k W

( ) k P P x P x  ( ) ( ) k k ( ) ( ) k k 12 1 22 2 2

( ) k

( ) k

( ) k

x

x

 



1

2

1

2

( )2 k

( )2 k

( )2 k

x

x

x

3

3

3

,

  ( ) 2 1 k x

( ) k P P 

( ) k

( ) k

( ) k

( ) k

P

P

w

( ) k

( ) k

x

x

 

0

1

2

11

1

2

 

( ) k

( ) k

( ) k

( ) k

t

x

x

x

x

2

3

3

3

3

  ( ) 2 2 k x

   

( ) k

( ) k

2 ( ) k w

P

P

( ) ( ) k k

( ) k

12 ( ) 1 2 k x x

22

( ) k

( )2 k

x

x

x

2

3

3

3

,

  ( ) 1 k x

  ( ) 2 k x

2

2

( ) k T T 

( ) k

( ) k

( ) k

( ) k

( ) k

T

T

T

T

( ) k

( ) k

( ) ( ) k k

x

x

x x

0

1

2

11

12

22

1

2

1 2

t

t

t

t

t

t

2

2

  ( ) 1 k x

  ( ) 2 k x

2

2

2 ( ) k

( ) k

( ) k

( ) k

T

T

T

T

( ) k

x

x x

2 k

11

12

22

2

1 2

( ) k

( ) k

( ) k

( )2

x

x

x

x

2

2

3

3

3

3

  ( ) 1 k x

  ( ) 2 k x

   

2

2

2 ( ) k

2 ( ) k

2 ( ) k

T

T

T

( ) ( ) k k

x x

11

12

22

1 2

( )2 k

( )2 k

( )2 k

x

x

x

2

2

3

3

3

( ) k  

   

2

       2 2 ( ) ( ) 1 2 k k U W U W    ( ) k 2

( ) k    w

2

( ) k

  

2

2

 

 

1

( ) k

( ) 3 k

c

x

p

2

( ) k  

  

( ) k

( ) k

( ) k

U

U

U

( ) k

( ) k

x

x

1

2

 

1

2

( ) k

( ) k

( ) k

( ) k

c

x

x

x

p

3

3

3

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