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JOURNALS // Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences // Archive

Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2011 Issue 1(22), Pages 228–235 (Mi vsgtu930)

Procedings of the 2nd International Conference "Mathematical Physics and its Applications"
Mechanics

Construction of analitical solution of 2D stochastically nonlinear boundary value problem of steady creep state with respect to the boundary effects

L. V. Kovalenko, N. N. Popov

Dept. of Applied Mathematics and Computer Science, Samara State Technical University, Samara

Abstract: 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.

UDC: 539.376

MSC: Primary 35Q74; Secondary 74E35, 74K20

Original article submitted 16/XII/2010
revision submitted – 14/II/2011

DOI: 10.14498/vsgtu930



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