PSI - Issue 59

Andrii Babii et al. / Procedia Structural Integrity 59 (2024) 609–616 Andrii Babii et al. / Structural Integrity Procedia 00 (2019) 000 – 000

614 6

  

  

  

  

k b 

k b 

k b 

2 ( ) ( )cos ab sh ab

1 1 ( )sin

ch ab



1

1

1

1 1

1 1

l

l

l

2 ) ( m chaR m aR shaR m        ( )sin( ) ( )cos( ) 

(23)

1

1

1

.

I

(22)

;

2 0

2 0

2 0



I



m

k



   2   

2

2

2 0 a R m

  

  

k b 

2

1 1 ( ) ab



1

l

1

Let us rewrite row (10) in the following form

8

A



  

  

k



   

  m 

q

0 ( , , ) k m     m km

1 2 ( , )  

sin

cos

q

,

(11)

1 



l

l



1,3,...

0

k

m





1

1

  

  

0 l  1 1

k

0 

(22) (23)

4 sin b 

cos(

) m I I 

where

.



1

0

km

k

m

q A in dependence (11) remains undetermined, which can be expressed in terms of the vertical

The coefficient

B p of the contact pressure on one support

component

0

0 b     b   0

  

1 1



(12)

1 2 ( , )  

1 2 ( , )cos      1 d d . q

p q 

ds R 

0

B

0

0

  

D

1

1 1

q A , by substituting the corresponding expression (9) into (12)

Where we find the unknown coefficient

p a

A



1 ( )cos B 1 1

.

(13)

q

(23) R I sh ab  0 1 4

0 

In the final result, the total loading on the shell will be as follows

1 2 ( , ) q q            , 1 1 2 ( , ) ( , ) p 1 1 2 2 1 2 ( , ) p

(14)

where: 1 1 2 ( , ) q   corresponds to the model of contact pressure on the bandages (3); 2 1 2 ( , ) q   corresponds to the contact pressure on the supports (9). Then the corresponding developments of the total loading in the row will be as follows

  

 

k



   

1 2 ( , )  

( , , )(  

)sin

1 cos    , m

p

k m p q q



1 km km km   1 2

(15)

l

1,3,...

0

k

m





1

8(

) 

4

p R 

R



p

p

0

0

0





0, 1,3,... m k   );

1, 1,3,... m k   ); 1

0 km p  (

1, 1,3,... m k   );

(

(

where

1

1

km

km

k

k





  

  

0  1

k

0 0 2 sin a b



8

A

m



l

  

  

0 l  1 1

k

8

N



q

1

(22) (23)

4 sin b 

cos(

0 ) m I I   m k

q

(12) (13)

 

;

.

q

I I

0  

2

1

km

m

1

km

k m

(    

) (

)

l

R l

0 0 sh a b



1

0 1

0

q A , or according to formula (13), we write it in the following form

The unknown value is the coefficient