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

611

3

shell structure, which is small-sized sprayer tank. The distinguishing feature of such load is that the fastening elements act only on a certain area of the shell, while on the rest areas they are equal to zero. In order to be able to evaluate the stressed state of the tank, it is necessary to define the load function at any point of the tank. Therefore,

various models of contact interaction between the bandages and supports with the tank shell, which expressions are developed into trigonometric series are considered in this paper. On their basis, graphical dependencies of the modeled loading which makes it possible to judge the nature of fastening elements impact on the shell and its stress state in general are obtained. Let us represent the general scheme of the tank fastening, Fig. 2. Cylindrical tank with 0 R radius and 1 l length is supported by four supports with which it contacts in areas 0 i D and is symmetrically pressed against 0 1  from the edge of the tank. The supports have wrapping

Fig. 2. General scheme of the tank fastening.

them by two bandages with contact areas 0

i S at distance

angle  and are placed at angle

0  from the vertical. The tank itself is filled with liquid (completely or partially)

and is subjected to internal pressure for the working fluid displacement. Let us describe each of the components of the tank loading separately. First, let us model the loading from the shell tightening with flexible bandage with interaction, we accept the law of contact pressure distribution in the following form

0 2 b width, Fig. 2. For such

N a

' ( , )   1 2

' )sin(     )

( ch a

,

(1)

q

0 0



0 1

0

н

(

0 0 ) ( ) sh a b

R

  

0

0

where 0 a is the coefficient determining the unevenness of bandage contact interaction in width within the local coordinate system ' 1  ; 0  is the angle that marks the bandage action limits. According to the scheme, Fig. 2, we get: ' 0 1 0 b b     , 0 0       . Tension force 0 N is chosen from the condition that the tank can be fixed on the supports while it can make small vibrations within the boom stabilization system. The coefficient 0 a characterizes the distribution of contact pressure across the bandage width and is determined by additional investigations. The contact pressure according to expression (1) has local effect on the shell, and therefore, in order to evaluate the effect of two such bandages on the shell as a whole, it is necessary (1) to develop, for example, into trigonometric series. This is one of the simplest methods. The obtained results serve as the initial loading expressions for the evaluation of the stress state according to the theory of slope shells of Timoshenko type (Shopa (2019), Sukhorolsky (2018)). According to the scheme (Fig. 2), the cylindrical tank has length 1 l and radius 0 R . It is loaded with two symmetrically placed bandages. The centerlines of the bandages are at distance 0 1  from the edges of the tank. You can consider half of the shell since it is symmetrical. Let us define the area of the mid-surface as   1 2 1 1 2 2 ( , ):0 , 0 l l          , where 2 0 l R   , 2 0 R    . Then, under the action of two bandages, we have the following general loading function:

0                             0 1 1 2 , ), ( , ) 1 2 1 0 1 2 ( , ) 1 1 q l 1 2 , ), ( , ) 1 2 0 1 2 0, ( , ) 1 1 2 , ( , ) ( ( , q S S

0

,

q

S

(2)

2 0

н

,

S



2