A Finite Element Approach for the Elastic-Plastic Behavior of a Steel Pipe Used to Transport Natural Gas

A finite element technique, with two-dimensional isoparametric elements, is developed, for the analysis of a steel pipe, with a circular cross-section. The pipe is installed above the ground and is used to transport natural gas at very high pressures. The material of the pipe is assumed to obey a bilinear elastic-plastic model. Double symmetry is considered when setting up the mathematical model problem and creating the finite element mesh. Step increments or decrements on the internal pressure are applied (cyclic loading). Yielding is detected by the Von Mises yield criterion. Also, a flow rule is employed to handle the plastic strain component. A four-point Gauss-Legendre quadrature is used to numerically perform all necessary integrations. Finally, the so-called “shakedown phenomenon” is studied when cyclic loading is applied after the commencement of plastic deformations on the pipe. Numerical results obtained by the method compare favorably with the analytic solution. 1. Introduction The efficient and effective movement of natural gas from producing regions to consumption regions requires an extensive and elaborate transportation system. In many instances, natural gas produced from a particular well will have to travel a great distance to reach its point of use. The transportation system for natural gas consists of a complex network of pipelines, designed to quickly and efficiently transport natural gas from its origin to areas of high gas demand. In the USA and in Europe there are three major types of pipelines along the transportation route: the gathering system, the interstate pipeline system, and the distribution system. The gathering system consists of low pressure, small diameter pipelines that transport raw natural gas from the wellhead to the processing plant. Interstate highway system transports processed natural gas from processing plants to those areas with high natural gas requirements and can carry natural gas across state or country boundaries at pressures varying between 15 and 200？MPa. This reduces the volume of the natural gas being transported (by up to 600 times), as well as propelling of the gas through the pipeline. The distribution system consists of low pressure pipes which distribute the transported natural gas within any region with high natural gas requirements. Mainline transmission pipes, the principle pipelines in a given system, are usually between 200 and 1200？mm in diameter and with a wall thickness between 10 and 100？mm. The original part of a pipe, in which propelling of the gas is performed and pressures up to