Problem of large displacements of buried pipelines. Part 1. Working out a numerical procedure

Abstract

An effective numerical iteration procedure has been worked out for the analysis of the stress-strain state of a flat pipeline in a medium with allowance for possible presence of supports and branches. The governing equilibrium equations and geometrical equations used have been written in geometrically nonlinear formulation and supplemented with boundary conditions, obtained analytically for a semi-infinite pipeline under transverse-longitudinal elastic bending. The article considers an elastoplastic law of interaction between pipeline and the ground with the possibility of additional limitation of absolute pipeline displacements. The computational algorithm is based on the concepts of corrective and basic solution. Basic solution is refined in each iteration step using corrective solution. Corrective solution is direct solution of a system of linearized equations, in which, e.g., basic displacements of pipeline are used to determine forces of interaction between the pipe and the ground. The algorithm uses an efficient method of run in each iteration step, which minimizes the number of unknowns. The results of the calculations are compared with numerical and theoretical solutions presented in publications: cantilever curling by the action of end bending moment; laying of an underwater pipeline; stability loss in air, etc.