Mathematical modeling in the problems of the geodesic control of the stressed-formated state of the gas pipelines at above-ground parts
DOI:
https://doi.org/10.31471/1993-9868-2020-1(33)-56-65Abstract
Geodetic methods of monitoring the stress-strain state of gas pipelines in the areas of overhead pipeline crossing involve obtaining discrete data on the deformation of its axis in the form of a set of three coordinates (x, y, z). For their elaboration a mathematical model of the experimental-theoretical method of geodetic control of gas pipelines’ SSS is proposed. The simulation process was performed on the basis of geodetic discrete data, based on which, using the Lagrange interpolation polynomial, the equation of the line of bending of the axis of the gas pipeline was obtained, which allowed to pass further to the bending moments along the entire span. The accuracy of the proposed method has been estimated, which showed that the obtained bending moment diagrams reflect the SSS of gas pipelines with an accuracy of 1.5% in the central part of its span, and with the approach to the peripheral sections the error increases to 6%. It is shown that the obtained expression of the maximum bending moment allows us to form the required number of additional equations for the disclosure of a statically indeterminate system of "gas pipeline-support", taking into account the possibility of fastening on stretch marks. The mathematical model is presented aimed at decomposition of overburden gas pipeline structures, which allows to model the SSS at each of the spans separately within the integral structure.. It is established that additional stretch marks reduce the maximum bending stress by 22%, and in case of loss of one of the stretches of the bearing capacity of the gas pipeline SSS increases by 11.1-14.8% depending on the previous stretch tension. The proposed mathematical model for the processing of discrete data forms the basis of the experimental-theoretical method of geodetic control of the gas pipelines’ SSS, taking into account their structural and technological factors.
Downloads
References
Hrudz V. Ya., Tymkiv D. F., Mykhalkiv V. B., Kostiv V. V. Obsluhovuvannia i remont hazoprovodiv: monohrafiia. Ivano-Frankivsk: Lileia-NV, 2009. 711 p. [in Ukrainian]
Taraievskyi O.S. Zabezpechennia pratsezdatnosti tryvalo ekspluatovanykh hazo-provodiv za skladnykh hirnycho-heolohichnykh umov: avtoref. dys... dokt. tekhn. nauk: 05.15.13; Ivano-Frank. nats. tekhn. un-t nafty i hazu. Ivano-Frankivsk, 2017. 39 p. [in Ukrainian]
Shlapak L.S., Hadash O.M., Haidash L.M. Zghyn vyhnutykh trub u vyhliadi duhy kola rivnomirno-rozpodilenoho navantazhenniam iz ploshchyny pochatkovoi kryvyzny. Nafta i haz Ukrainy. Zbirnyk naukovykh prats. Materialy 6-oi Mizhnarodnoi naukovo-praktychnoi konferentsii «Nafta i haz Ukrainy», Ivano-Frankivsk, 1 zhovtnia – 3 lystopada Tom 3, Ivano-Frankivsk, 2000. P. 53–59. [in Ukrainian]
Kharchenko Ye.V., Kychma A.O., Savula R.S. Analiz pruzhno-plastychnoho deformuvannia dilianky mahistralnoho hazoprovodu z urakhu-vanniam zmitsnennia materialu. Visnyk Natsional-noho universytetu "Lvivska politekhnika". Teoriia i praktyka budivnytstva. 2013. № 755. P. 442–448. [in Ukrainian] URL: http://nbuv.gov.ua/UJRN/ VNULPTPB_2013_755_80
Pakshyn M.Iu., Liaska I.I., Burak K.O., Kovtun V.M., Dorosh L.I. Heodezychnyi monitorynh deformatsii metodom radarnoi interferometrii. Mizhnarodna naukovo-praktychna konferentsiia «Rozvytok tekhnichnykh nauk: problemy ta rishennia» (m. Brno, Cheska Respublika, 27–28 kvitnia 2018 ) [in Ukrainian]
Zhovtulia L.Ia., Oliinyk A.P., Yavorskyi A.V., Karpash M.O. Rozroblennia metodyky otsinky napruzheno-deformovanoho stanu liniinykh dilianok mahistralnykh truboprovodiv. Metody ta prylady kontroliu yakosti. 2017. No 38. P. 57–63. [in Ukrainian]
Banakhevych R.Iu. Krupka V. O., Marchuk O. M. Dosvid diahnostychnoho obstezhennia vantovoho perekhodu MH Ivatsevychi – Dolyna II n. cherez riku Dnister. Teoriia i praktyka budivnytstva. 2011. No 7. P. 24–27. [in Ukrainian]
Trevoho I., Ilkiv Ye., Kukhtar D. Osoblyvosti vyznachennia prostorovoho polozhennia nadzemnykh perekhodiv mahistralnykh hazoprovodiv z vykorystanniam elektronnoho takheometra u bezreflektornomu rezhymi. Suchasys dosiahnennia heodezychnoi. nauky ta vyrobnytstva. 2011. Vol. 2. P. 124–127. [in Ukrainian]
Ripetskyi Ye.I., Ripetskyi R.I., Korobkov O.Iu. Heodezychnyi kontrol napruzheno-deformovanoho stanu prolotnykh konstruktsii z otrymanniam rivniannia zihnutoi osi. Zb. nauk. prats za materialamy IKh mizhnarodnoi naukovo-praktychnoi konferentsii «Novi tekhnolohii v heodezii, zemlevporiadkuvanni, lisovporiad-kuvanni ta pryrodokorystuvanni» 4–6 zhovtnia 2018. Uzhhorod. 2018. P.68–71. [in Ukrainian]
Bilobran, B.S., Dziubyk A.R., Yanovskyi S.R. Vplyv montazhnoho pruzhnoho zghynu na napruzheno-deformovanyi stan nadzemnykh perekhodiv mahistralnykh naftoprovodiv u horakh. Naftohazova haluz Ukrainy. 2013. No 4. P. 30-33. [in Ukrainian]
Starovierov V.S., Adamenko O.V. Metodyka vyznachennia tochnosti heodezychnykh robit pry budivnytstvi mostovykh perekhodiv shliakhom modeliuvannia napruzheno-deformovanoho stanu konstruktsii. Visnyk heodezii ta kartohrafii. 2009. No 5 (62). P. 7–12. [in Ukrainian]
Derkach M.P., Zubyk Y.L., Kychma A.O. Kompleksnyi pidkhid do otsinky tekhnichnoho stanu perekhodiv mahistralnykh hazoprovodiv balkovoho typu. Metody ta prylady kontroliu yakosti. 2005. No 15. P. 105-108. [in Ukrainian]
Tveito A. Introduction to differential equations. URL hhttp://hplgit.github.io/primer.html/doc/pub/ode1, http://hplgit.github.io/
primer.html/doc/pub/ode1.
Khalid A. H. The Lagrange Interpolation Polynomial for Neural Network Learning/ IJCSNS International Journal of Computer Science and Network Security, VOL.11 No.3, March 2011. P255–261. URL: http://paper.ijcsns.org/07_book/201103/20110336.pdf.
.png)
1.png){kind=logo}
