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 Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]: Year: Volume: Issue: Page: Find

 Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2012, Issue 4(29), Pages 97–105 (Mi vsgtu1132)

Mechanics of Solids

Method of pure shear problem solving for stochastically inhomogeneous plane in a steady-state creep

N. N. Popov, O. Chernova

Samara State Technical University, Samara, Russia

Abstract: 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.

Keywords: pure shear, small parameter method, steady-state creep, second approximation, stochastic problem
Author to whom correspondence should be addressed

DOI: https://doi.org/10.14498/vsgtu1132

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Bibliographic databases:

UDC: 539.376
MSC: Primary 35Q74; Secondary 74E35, 74K20
Original article submitted 01/XI/2012
revision submitted – 19/XI/2012

Citation: N. N. Popov, O. Chernova, “Method of pure shear problem solving for stochastically inhomogeneous plane in a steady-state creep”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 4(29) (2012), 97–105

Citation in format AMSBIB
\Bibitem{PopChe12} \by N.~N.~Popov, O.~Chernova \paper Method of pure shear problem solving for stochastically inhomogeneous plane in a~steady-state creep \jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.] \yr 2012 \vol 4(29) \pages 97--105 \mathnet{http://mi.mathnet.ru/vsgtu1132} \crossref{https://doi.org/10.14498/vsgtu1132}