Numerical modeling of the stress-strain state of a gas pipeline with a corrosion ulcer

Numerical modeling of the stress-strain state of a gas pipeline with a corrosion ulcer is considered. The mathematical model of the stress-strain state is described by the stationary Lame equations for stresses and strains. Three pipelines with diameters of 529, 530 and 720 mm are considered as models. The corrosion ulcer model is described by discrete thinning of the pipe wall. The Dirichlet boundary condition is applied to the ends of the gas pipeline to prevent movements along the X-axis. The Neumann boundary condition is applied to the external surface of the gas pipeline, for contact with the environment. The spatial approximation is performed by the standard Galerkin method. Based on the obtained results, the maximum permissible depth of corrosion is determined.