Calculation of displacements and forces during longitudinal oscillations of an underground pipeline

In this study, a straight-line underground section of a pipeline of finite length is considered, one (right) end of which is rigidly sealed, which excludes the possibility of its movement. The differential equations of equilibrium in displacements, based on the application of the principles of linear elasticity theory and the finite displacement method, have been formulated and derived. In this case, it is assumed that the geometric and physical-mechanical characteristics of the pipeline, as well as the temperature gradient and internal pressure, are constant throughout the entire length of the considered section. The mathematical model takes into account the temperature deformations caused by the thermal expansion of the material and the internal forces arising from the pressure of the working medium. Numerical calculations of the pipeline’s stress-strain state were performed using appropriate boundary conditions and assumptions. The results of the calculation analysis are presented in the form of graphical dependencies of displacements, stresses, and forces along the length of the pipeline section, which allows visualizing the influence of the main factors on its mechanical behavior. The obtained dependencies can be used for engineering assessment of the pipeline’s operability under long-term operation conditions.

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