On elastic-plastic deformation of pipelines at repeated variable loading

The article presents mathematical models for calculating cylindrical bodies under repeated-variable loading. On the basis of the theory of small elastic-plastic deformations and the Hamilton-Ostrogradsky variational principle, a system of differential equations of motion (equilibrium) under spatial loading is obtained and a boundary value problem is formulated. To solve the boundary value problem, a central difference scheme of the second order of accuracy and the matrix sweep method are used. A practical problem is solved on the basis of the given algorithm.