Analytical Solution to the Boundary Value Problem of Steady Creep of a Nonaxisymmetric Thick-Walled Tube under the Action of Internal Pressure

The boundary value problem of the steady-state creep of a nonaxisymmetric thick-walled tube under the action of internal pressure is considered under the assumption that the material is incompressible for creep deformations. An approximate analytical solution of the problem by the small parameter method up to the third order of approximation, inclusively, for a plane deformed state is presented. The small parameter in the problem is the displacement of the centers of the inner and outer radii of the tube. The error in solving the problem is estimated by comparing the approximate analytical solution with a numerical solution obtained by the finite element method for some special cases. The analytical and numerical solutions for stresses are analyzed by dependence on the small parameter and the stress exponent of the steady-state creep. The error of the approximate analytical solution for the stress tensor components in the minimum cross section is analyzed in accordance with the industrial standards for the permissible deviation of the wall thickness in the industrial production of tubes.