Numerical Investigation of Pipe Deformation Under Pressure With Branch

Abstract

The stress–strain state of a pipeline segment with a branch pipe of smaller diameter, which is under internal pressure, is investigated. The mathematical model of this mechanical object is a boundary value problem for a system of six partial differential equations. This boundary value problem describes the deformation of an elastic surface containing a singular line and immersed in three-dimensional space. From this three-dimensional mathematical model in a domain with curved boundary, a resolving boundary value problem in a planar domain is obtained. An algorithm for numerical analysis of the deformed state of a pipeline with a branch pipe by the finite element method is created and implemented. An approach to suppress the error of the numerical solution, which significantly improved the accuracy of the results, is proposed. As a result of numerical experiments, it is found that the proposed algorithms and methods make it possible to approximate a given solution of the reduced pipe deformation problem with a branch pipe by its numerical solution with high accuracy.