Analytical solution of the stochastic steady-state creep boundary value problem for a thick-walled tube

A non-linear steady-state creep stochastic boundary value problem is solved for a thick-walled tube acted upon by an internal pressure for the case of a plane strain state. It is assumed that the properties of the tube material are described by a random function of its radius. The constitutive creep relations are taken in accordance with non-linear viscous flow theory in a stochastic form. A recurrent form of the system of stochastic differential equations is obtained by expanding the radial stress in a series in powers of a small parameter, from which the components of the radial stress can be found to any degree of accuracy. The random stress field and strain rate field are analised statistically as a function of the non-linearity exponent and the degree of inhomogeneity of the material. A comparative analysis of the solutions of the stochastic steady-state creep boundary value problem for a thick-walled tube, obtained is the fourth approximation of the small parameter method and the Monte carlo method, is performed.