CASPIAN JOURNAL

MANAGEMENT AND HIGH TECHNOLOGIES

Asymptotic solutions of equations in the problems of longitudinal stability of the main gas pipeline section

Read Miklush Alexandr S., Voevodin Ilya G. Asymptotic solutions of equations in the problems of longitudinal stability of the main gas pipeline section  // Caspian journal : management and high technologies. — 2013. — №2. — pp. 42-47.

Miklush Alexandr S. - Leading Design Engineer of the First Category, Production and Commercial Company “Vertical” Ltd, 6 Sezzhinsky pereulok, Moscow, 105120, Russian Federation, mklsh_lksndr_srgvch@mail.ru

Voevodin Ilya G. - Ph.D. (Engineering), Associate Professor, Astrakhan State University, 20a Tatishchev St., Astrakhan, 414056, Russian Federation, vvdn_l_gnndvch@mail.ru

The paper presents a mathematical model for calculating the process parameters for fixing gas main pipelines on non-cohesive soils with anchors. The model uses the elements of the theory of the stress-strain state of pipelines. The study includes mathematical modeling of the longitudinal forces acting to the pipeline, and developing of method for determining possibility of stability loss of the object. The paper describes using of the small parameter method that extended to the systems with the distributed load, for the elastic system of the complex structure with friction. The study allowed obtaining the general kinds of differential equations and boundary conditions. The paper shows applications of this method in the analysis of states of the fixed by anchors section of the main pipeline. Presence of a maximum in the curve will indicate the status of the loss of stability at considered point of the analyzed pipeline section. The study uses Lagrange-Dirichlet theorem, according to which the equilibrium positions, corresponding to the minimum potential energy, are stable, and the equilibrium positions, corresponding to the maximum potential energy, are unstable.

Key words: main gas pipeline,anchors,non-cohesive soils,retention capacity,longitudinal and transverse load,small parameter