Approximate solution to the nonlinear problem of an underground pipeline deformation

Some geometrically nonlinear mathematical model is constructed of a pipeline as a shell in a strongly viscous medium. We find a universal procedure for reducing the two-dimensional equations of motion to the one-dimensional equations for long bent pipes. We also constructed a difference scheme and propose a software complex for numerical analysis of the equations under study. Some numerical experiments are conducted for a particular case of a bent pipeline, the deformations of the pipe wall are found, and the displacement of its centerline is calculated.