Geodesic
Construction of~analitical solution of~2D~stochastically nonlinear boundary value problem of steady creep state with respect to the~boundary effects
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 228-235

Voir la notice de l'article provenant de la source Math-Net.Ru

The solution of nonlinear stochastically boundary value problem of creep of a thin plate under plane stress is developed. It is supposed that elastic deformations are insignificant and they can be neglected. Determining equation of creep is taken in accordance with nonlinear theory of viscous flow and is formulated in a stochastic form. By applying the method of small parameter nonlinear stochastic problem reduces to a system of three linear partial differential equations, which is solved about fluctuations of the stress tensor. This system with transition to the stress function has been reduced to a single differential equation solution of which is represented as a sum of two series. The first row gives the solution away from the boundary of the body without boundary effects, the second row represents the solution boundary layer, its members quickly fade as the distance increases from plate boundary. Based on this solution, the statistical analysis random stress fields near the boundary of the plate was taken.
Keywords: steady creep, stochastically inhomogeneous plate, random field of stresses, perturbation theory, boundary effect. 
@article{VSGTU_2011_1_a28,
     author = {L. V. Kovalenko and N. N. Popov},
     title = {Construction of~analitical solution {of~2D~stochastically} nonlinear boundary value problem of steady creep state with respect to the~boundary effects},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {228--235},
     publisher = {mathdoc},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a28/}
}
TY  - JOUR
AU  - L. V. Kovalenko
AU  - N. N. Popov
TI  - Construction of~analitical solution of~2D~stochastically nonlinear boundary value problem of steady creep state with respect to the~boundary effects
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2011
SP  - 228
EP  - 235
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a28/
LA  - ru
ID  - VSGTU_2011_1_a28
ER  - 
%0 Journal Article
%A L. V. Kovalenko
%A N. N. Popov
%T Construction of~analitical solution of~2D~stochastically nonlinear boundary value problem of steady creep state with respect to the~boundary effects
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2011
%P 228-235
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a28/
%G ru
%F VSGTU_2011_1_a28
L. V. Kovalenko; N. N. Popov. Construction of~analitical solution of~2D~stochastically nonlinear boundary value problem of steady creep state with respect to the~boundary effects. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 228-235. http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a28/