Mathematical modeling of the stress–strain state of T‐shaped connection of cylindrical pipes

Abstract

Equations of elastic cylindrical shells in term displacements for the T‐shaped connection of pipes are derived. Three‐dimensional mathematical model is constructed within the framework of the membrane shells theory. Geometric and force conjugation conditions are set on the pipe intersection line, and boundary conditions are imposed on the ends of the pipes. Complete three‐dimensional mathematical model is presented in a Cartesian coordinate system, to achieve a unified approach to solving the problem. Dimension of the original problem is reduced by one. This result is obtained from the symmetry conditions of the mechanical system with respect to the plane of the T‐shaped connection. The resulting two‐dimensional boundary value problem is divided into two sub‐problems, each of which is posed in a rectangular domain. Conjugation conditions are eliminated from the final formulation of the boundary value problem. A numerical experiment is carried out, which proved the permissibility of replacing the conjugation conditions with sleeve contact. Numerical examples showed a weak dependence of the approximation of the conjugation conditions by the sleeve contact on the choice of the dimension of the finite elements: three‐dimensional or two‐dimensional. The existence of a stress field singularity in the vicinity of the shell joining line is established.