Modeling of elastic-plastic deformation of main pipelines under repeated static and dynamic loading

The article presents mathematical models for calculating of main pipelines under repeated static and dynamic loading, taking into account accumulation of damage of materials. Based on deformation theory and the Hamilton-Ostrogradsky variational principle, a system of differential equations of motion (equilibrium) under spatially variable loading with corresponding boundary and initial conditions is obtained. To describe the elastic-plastic properties, the generalized Masing principle and the cyclic deformation diagram are used, taking into account secondary plastic deformations, the manifestation of the properties of hardening-softening and cyclic anisotropy. To solve the boundary value problem, the central difference scheme of the second order of accuracy and the Godunov matrix run method are used. On the basis of the developed algorithm for comparative analysis, numerical values of the displacement vector and forces under repeated static loads are given.