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

612 4









0

0

0

0

where l b              . We will assume that such shell is hinged on supports and symmetrically loaded. The expression for the function development (2) will be 1 1 2 ( , ): S b             , 1 1 0 0 ; 2 1 2 ( , ): 1 1 1 0 0 ; S

  

 

k



   

,

(3)

1 2 ( , )  

( , , )   

sin

1 cos    m

q

k m A



H

m km

l

1,3,...

0

k

m





1

2

2

     

1   k

            

2   m

     

  

  

  

  

1

 

sin

sin

,

0,

m



2

2

2 /2 h h    ;



 

,

where

2 1,

( , , ) k m  



m

1   k

2   m

m  

1.

2

2

1 2 ( , ) H q   , taking into account the outlined contact areas (3)

We obtain the Fourier coefficient of the function

  

  

  

  

4

k

k









0     1 1 1

0      1 2

(

, )sin

cos( )

1 1 1 m d d q l     (

, )sin

cos( )

.   

A

q

m d d

1 

1 



(4)

1

km

l

l

l



1

1

1

0

0

S

S

1

2

As it was determined that the bandage is the flexible tape, we will consider the contact pressure to be close to the constant width of the bandage and vary according to the trigonometric cosine in the circular direction, then to develop dependence (1) into series (3) we will have the following expression of the development coefficients

  

 

0  1

k

8

sin

0 0 0 N a b

l

 





1

 

(12)

(13)

1 ( 1)

,

k   

1,3,...,

1,2,... ,

A

I

I

k

m











km

k

m

(

0 0 1 sh a b l ) ( )

R

  



0

0

2

 

  

   

 

  

  

  

  

  

  

k b 

k b 

k b 

k b 

where

2 ( ) ; a b  0 0

(12)

2 ( ) ( )cos a b sh a b 0 0 0 0

0 0 ( )sin

I

ch a b







0

0

0

0

   

k

l

l

l

l

1

1

1

1



 0 sin     0

1

(13)

(13)

 

( 1) cos cos( ) , m m   

.

( 1) m  ;

( 1) m  .

I

m I





0 

0 



1

2

2

1

m



Finally, for the contact pressure model according to expression (1), we will have the following development into trigonometric series

  

  

8

N

k



1 

   

(5)

0 ( , , ) sin 

1 2 ( , )  

0 1 0       ( , , ) B k m b m km

cos , m 

q

0





H

R l

l



1,3,...

0

k

m





0 1

1

  

  

0  1

k

0 0 2 sin a b 

l

.

where

1

0 ( , , ) b    0 1 0 B km

(12)

(13)

I

I











k

m

0 0 sh a b (

)

  

0

The second component of the load on the shell should be considered as the excessive internal pressure and weight of the liquid in the tank.