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

Abstract

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.