Keyword: «mathematical modeling»

The article considers the spatial altitude of the pipeline affected by interaction with frost heaving. The study shows the results of measuring planned-high-altitude positions (PHAP) of the underground pipeline obtained in different seasons to identify the peculiarities of pipeline deformation from frost heaving. According to the data obtained, the deformations are of a complex shape. The spatial position of the pipeline changes after freezing and thawing of the soil, i.e., twice a year. The level of deformations is beyond the limits of safe operation. An observation of the current state of research on the impact of frost heaving on underground pipelines revealed that the applied mathematical models consider a deformation as a single arch. Our PHAP measurements show a complex picture – specifically, bulges are replaced by concavities.

Due to the global warming of the climate in the northern regions, the erosion and deformation of river banks has increased. The article deals with mathematical modeling of the heat and humidity regime of the soil, taking into account the influence of above-frozen, flood and sub-frozen groundwater. In winter, a water-saturated zone forms in the coastal part of the soil, which completely freezes and is accompanied by frost-breaking cracking, and the loose soil is easily eroded by flood water, which enhances the process of thermal abrasion.

The paper proposes a study of the thermal process in a radial self-lubricating polymer sliding bearing operating in a swinging motion mode. The thermal process in a sliding bearing is described by a three-dimensional heat conduction equation in cylindrical coordinates. The technique for determining the kinematic conditions is proposed on the basis of a numerical analysis of the temperature field in the contact zone of the shaft and the bearing, under which the mathematical model of the thermal process must take into account the speed of the shaft. The results obtained can be used in thermal diagnostics of friction in real sliding bearings.

Based on the analysis of the stress-strain state of welded joints, it is shown that when welding saddle branches to existing gas pipelines at low temperatures using the proposed technology and standard welding, the differences in the values of stresses and displacements occurring are insignificant. Numerical calculations have shown that when welding a saddle branch at low temperatures using the proposed technology, it can be expected that the joint strength will not be lower than when welding under standard conditions.