Elastoplastic state of a thin-walled pipe under pressure in the process of bending with tension (Compression)

Abstract

We analyze the elastoplastic state of a rectilinear element of a thin-walled pipeline under pressure in the process of bending with tension (compression) and determine the characteristics of its stiffness. To solve this problem, we use a numerical method based on the deformation theory of plasticity and the momentless theory of shells. The problem is reduced to a one-dimensional problem and the proposed approach enables us to substantially simplify the procedure of numerical calculations. The idea of this approach can be described as follows: the longitudinal stresses and the components of strains are decomposed into two parts, one of which depends only on internal pressure and the second of which reflects the work of the pipe as a rod. By using this computational procedure and also the Mathcad PLUS-6.0 mathematical package, we analyzed the influence of internal pressure and longitudinal forces on the bending strength of the rectilinear elements of main pipelines. A numerical example is presented. The results of numerical calculations are displayed in the form of plots.