PSI - Issue 36

A. Babii et al. / Procedia Structural Integrity 36 (2022) 203–210 A. Babii, T. Dovbush, N. Khomuk et al. / Structural Integrity Procedia 00 (2021) 000 – 000

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model are (conventionally) designated as respectively b11, b21, b31, b41. The length of longeron zone from marginal traverse to the front cross member is b11, b21, b31, b41 are the lengths of longeron zones between neighboring cross members, respectively V-VI, VI-VII, VII-VIII. ІІ is lateral longitudinal longeron of Z-like cross-section, divided into sections 13, 15, 17, 19. The size of these sections at building a load model are designated as b 12 , b 22 , b 32 , b 42 respectively. ІІІ is central longitudinal longeron made of Z-like cross- sections, divided into sections 21, 22, 23, 24. The size of these sections at building a load model are designated as respectively b 11 , b 21 , b 31 , b 41 . IV is front traverse of the pipelike cross-section divided into sections 1, 2, 11, 12. The size of these sections at building a load model are designated as respectively a 11 , a 21 , a 12 , a 22 . The distances from the central longeron to the attaching point of the hauling chains are designated as a 11 , a 12 . The distances from the marginal longeron to the attaching point of the hauling chains are designated as a 21 , a 22 . V , VI , VII are middle traverses of the pipelike cross-section which are divided into sections 4, 14; 6, 16; 8, 18. The size of these sections at building a load model are designated as a 11 + a 21 , a 12 + a 22 . VIIІ is back traverse of the pipelike cross-section divided into two sections 10, 20. The size of these sections at building a load model are designated as a 11 + a 21 , a 12 + a 22 . The built design model of the distributor base supporting system enables to obtain its analytical description in order to determine the internal force factors taking into account the real loading dynamics. It is possible to do using the modified method of minimum of potential energy of deformation (MMMPED). The supporting frame is divided into three parts in order to optimize the analytical calculations. The central part is conventionally designated as ІІІ , two symmetrical lateral parts are conventionally designated as І and ІІ (Fig. 3). Within the conditional symbols of geometric or physical parameters the first index indicates the geometric or physical magnitude order, the second one shows the section of the frame structure which the given magnitude belongs to. Solid organic fertilizers are being loaded on the trailer body by a conveyor or a loader; their distribution is mostly nonuniform. Figure 4 describes an arbitrary schematization of external loads distribution on the distributor supporting frames parts. General external loading 0 Q , acting on the distributor frame design consists of solid fertilizer weight Д Q and the weight of metalworks with mechanisms M Q . In the general case for an arbitrary form of load we will write that (Popovych et al. (2012)),

0  B

0  A

0  A

0  0  B B

( ) Q q s ds q s ds q s ds q s ds + + + = ( ) ( ) ( )

+

0

11

21

31

12

(1)

0  A

0  B

0  B

( ) , q s ds q s ds q s ds q s ds + + + ( ) ( ) ( )

+

22

31

32

13

where ( ) q s 31 , ( ) q s 32 , ( ) q s 13 are the functions of load intensity distributed on the frame supporting parts according to the directions shown on Figure 3; А , В are geometric parameters of frame-body contact. ( ) q s 11 , ( ) q s 21 , ( ) q s 31 , ( ) q s 12 , ( ) q s 22 , ( ) q s 32 ,

Fig. 4. Schematization of design model of distributor frame loading.

A base frame is a complex framed supporting system, statically indeterminate. To evaluate the indeterminate expression of complex framed structures the modified method of minimum of potential energy of deformation (MMMPED) is the most efficient one as it considerably simplifies the solution of such problems and it is easily presented with algorithms. The main advantage of the method is that after writing the expression of potential energy of deformation as a function from unknown parameters ( , , ) U Q M K , which has an adaptive feature , we can use some constituents of energies depending upon a structural system and its loading (Rybak et al. (2013b)). The solution of obtained equations including the unknown parameters is performed by means of application program package (APP) Wolfram Mathematica 7. Some aspects of problems solution using MMMPED as a function of potential energy of deformation from the bending moments which include the load ( ) q s , are the part of the differencial dependencies of internal force factors when considering the bending deformation ((Pidhurskyi et al. (2018), Pidhurskyi et al. (2006)).