The problem of computer simulation of mechanical behavior of drill strings in hyper deep vertical, inclined and horizontal bore-holes is stated with the aim of forecasting the possible initiation of emergency situations during carrying out drilling operations. The question of stability and post-critical non-linear deforming and dynamics of the drill strings are considered. It is shown that all of them are singularly perturbed from the mathematical point of view and because of this, they are poorly amenable to theoretical (computational) analysis. The algorithms allowing surmounting these difficulties are proposed.The software for study of these phenomena is elaborated.In the stages of design of an elongated curvilinear bore-hole with complicated 3D geometry and technological regimes of their drivage, the elaborated software permits one to construct its trajectory securing the smallest values of resistance forces and to choose the least energy-consuming and safe regimes of drilling. It ensures also the possibility to determine the requirements for the necessary accuracy of the bore-hole drivage and for the acceptable geometrical distortions and imperfections.In the stage of the bore-hole drivage, the created software permits to calculate forces and moments of resistance forces with allowance made for the real geometry of the bore-hole and admitted distortion of its axial line. It is possible to prognosticate possible emergency situations and design the measures for their exclusion. At the stage of the emergency situation liquidation, this software allows to simulate the mechanical behavior of the system and its responses to the methods used for elimination of the failure consequences.
The phenomena of the formation of local defects and cracks in asphalt concrete pavements of roads and bridges are most often observed in climatic zones with large temperature differences during their seasonal and daily changes. To a large extent, this is due to the heterogeneity of the thermomechanical properties of the materials of the coating layers and the base. To prevent these phenomena, reinforcing rods and meshes are introduced into the coating structure. In this work, using the theory of thermoelasticity, it is shown by the method of mathematical modelling that in cases of incompatibility of the thermomechanical characteristics of asphalt concrete materials and reinforcement, additional localized thermal stresses arise in its small vicinity, which, even at moderate temperatures, can reach critical values and lead to local defects and cracks. Since these defects are latent, they cannot always be detected in practice. The presented results of analytic calculation validated these conclusions. They can be used in both road building and composite design.
Enhancement of technology and techniques for drilling deep directed oil and gas bore hole is one of the most important problems of the current petroleum industry. Not infrequently, the drilling of these bore holes is attended by occurrence of extraordinary situations associated with technical accidents. Among these is the Eulerian loss of stability of a drill string in the channel of a curvilinear bore hole. Methods of computer simulation should play a dominant role in prediction of these states. In this paper, a new statement of the problem of critical buckling of the drill strings in 3D curvilinear bore holes is proposed. It is based on combined use of the theory of curvilinear elastic rods, Eulerian theory of stability, theory of channel surfaces, and methods of classical mechanics of systems with nonlinear constraints. It is noted that the stated problem is singularly perturbed and its solutions have the shapes of localized harmonic wavelets. The calculation results showed that the friction effects lead to essential redistribution of internal axial forces, as well as changing the eigenmode shapes and sites of their localization. These features make the buckling phenomena less predictable and raise the role of computer simulation of these effects.
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