steady-state creep, perturbation method, heavy-walled tube

The formulation of the boundary value problem of stochastical mechanics deformable solids is given. The pertrubation method is well designed to solve linear inhomogeneous elastic solids. Here it is proposed to use to solve stochastic nonlinear creep problems. The analytical solution stochastic nonlinear boundary value problem is formulated for thick-walled pipe under the action of internal pressure under steady-state creepage. The problem is considered in cylindrical coordinates for case of plane strain. Stochastic properties of the pipe described by a random function of one variable (radius r). By expanding the radial stress in a series of the small parameter was build a system of linear statistical differential equations, from which we can find the components of radial stress with any degree of accuracy. We give a generalization of the problem for a thick-walled tube, where the properties of material are described by a random function of two arguments. There was made a research of boundary effects by solving stochastical boundary problem as a sum of two series based on a first approximation of the small parameter.

1. Radchenko, Vladimir Pavlovich Dr. of Phys. & Math. Sci., Professor, Head of the Department of Applied Mathematics and Computer Science, Samara State Technical University, Samara e-mail: radch@samgtu.ru

2. Popov, Nikolai Nikolaevich Candidate of Phys.&Math., Assoc. Professor, Samara State Technical University, Samara e-mail: ponick25@gmail.com