# MATHEMATICAL MODELING OF THE DEFORMATION PROCESS OF PIPELINES OPERATING IN UNDERGROUND AND ABOVE-GROUND MODES

## Authors

• A. P. Olijnik Institute of information technology, ІFNTUOG
• L. I. Feshanych Institute of information technology, ІFNTUOG
• M. Yu. Chernyshov Institute of information technology, ІFNTUOG

## Keywords:

напружений стан, трубопровід, аеродинамічні характеристики, деформація перерізів, еліптичність

## Abstract

In the process of long-term exploitation the section’s deformations are inherent both for evaluated and  underground sections different purposes pipelines. The article deals with the problems of pipelines deformation process mathematical modeling through which the transport of gas-liquid mixtures with aggressive components is carried out. Models of the pipeline deformation process by known displacements of a certain set of points of a surface are constructed. The construction of the deformation process model does not use information about the nature and duration of the forces and loads acting on the pipeline. The law of pipeline motion was constructed taking into account the deformation of sections in three directions. A mathematical model of the process of flow around deformed sections of the pipeline is implemented in order to evaluate the dependence of the aerodynamic characteristics of the sections on their spatial configuration. The apparatus of Fredholm integral equations of the second kind is used. According to the computational algorithms created on the basis of the mentioned models, the stresses of the pipelines and the aerodynamic characteristics of the deformed sections were calculated. The analysis of the results of calculations - the intensity of stresses and dependencies of aerodynamic charac teristics on the degree of ellipticity of the section and the angle of attack of the deformed section is presented.It ws discovered that during over-ground section’s stress-strained staate  control it is very important take into attention the value of aerodynamics loadings  and momentums.  It was considered the  situation when after  deformation the  section has received the eliptical configurations, which are inherent  for the real pipelines. Directions for further research are identified- modeling of flow in a pipeline that transports gas-liquid mixtures with aggressive components due to the presence of zones with a potential loss of tightness due to a change in the stress-strain state and detection of the spread of harmful substances in the zone surrounding the pipeline when it is depressurized, studying deformed cros s-sections of a non-elliptical configuration.

## References

Dubovoy V.M., Kvyetnyy R.N, Mykhalʹov O.I., Usov A.V. Modelyuvannya ta optymizatsiya system: pidruchnyk. Vinnytsya: PP «Edelʹveys», 2017. 804 st. [in Ukrainian]

Mandryk O., Oliynyk A., Mykhailyuk R., Feshanych L. Flood development process forecasting based on water resources statistical data. Grassroots Journal of Natural Resources, 2021 4(2). P. 65 – 76.

Oliynyk A.P. Matematychni modeli protsesu kvazistatsionarnoho deformuvannya truboprovidnykh ta promyslovykh system pry zmini yikh prostorovoyi konfihuratsiyi: Naukove vydannya. Ivano-Frankivsʹk: IFNTUNH, 2010. 320s. [in Ukrainian]

Oliynyk A. P., Zhovtulya L. YA., Yavorsʹkyy A. V., Karpash M. O. Rozroblennya metodyky otsinky napruzheno-deformovanoho stanu liniynykh dilyanok mahistralʹnykh truboprovodiv. Metody ta prylady kontrolyu yakosti. 2017. №1(38), P.57 -63. [in Ukrainian]

Dyferentsialʹni rivnyannya / YU.D. Holovatyy, V.M. Kyrlych, S.P. Lavrenyuk. – Lʹviv: LNU im. Ivana Franka, 2011. 470 s. [in Ukrainian]

C.A.J. Fletcher Computational Galerkin methods. Springer Verlag. 1984, 352 p.

Origin of a magnetic easy axis in pipeline steel / [L. Clapham, C. Heald, T. Krause at al]. J. Appl. Phys. 1999. Vol. 86. № 36. Р. 1574–1580.

A.K. Cline, Scalar and Planar Valued Curve Fitting Using Splines Under Tension. Communications of the ACM. 1978. v.17, № 4, p. 218-228.

2022-12-26

## How to Cite

Olijnik, A. P., Feshanych, L. I., & Chernyshov, M. Y. (2022). MATHEMATICAL MODELING OF THE DEFORMATION PROCESS OF PIPELINES OPERATING IN UNDERGROUND AND ABOVE-GROUND MODES. METHODS AND DEVICES OF QUALITY CONTROL, (2(49), 89–94. https://doi.org/10.31471/1993-9981-2022-2(49)-89-94

## Section

MATHEMATICAL MODELLING FOR THE UNDESTROYED CONTROL PROBLEMS