Method of pure shear problem solving for stochastically inhomogeneous plane in a steady-state creep - Nikolay N Popov; Olga O Chernova (Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2012)
The analytical method for nonlinear problem of steady-state creep solving for pure shear of stochastically inhomogeneous plane on the basis of the second approximation method of small parameter was developed. It is supposed that elastic deformations are insignificant and they can be neglected. Stochasticity was introduced into the determinative creep equation, which was taken in accordance with the nonlinear theory of viscous ﬂow, through a homogeneous random function of coordinates. By using the decomposition technique of stress tensor components in a small parameter to the members of the second order of smallness, partial diﬀerential system of the ﬁrst and the second approximation of stress was obtained. This system was solved by the introduction of the stress function. The mathematical expectation and variances of the random stress ﬁeld were calculated. The analysis of the results in the ﬁrst and second approximations was obtained.