  Journal of Applied Mathematics and Mechanics Russian Academy of Sciences   Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 00218928 (print version) 
Archive of Issues
Total articles in the database:   1813 
In Russian (ÏÌÌ):   1014

In English (J. Appl. Math. Mech.):   799 

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L.V. Kovalenko, N.N. Popov and V.P. Radchenko, "Solution of the plane stochastic creep boundary value problem," J. Appl. Math. Mech. 73 (6), 727733 (2009) 
Year 
2009 
Volume 
73 
Issue 
6 
Pages 
727733 
Title 
Solution of the plane stochastic creep boundary value problem 
Author(s) 
L.V. Kovalenko (Samara, Russia)
N.N. Popov (Samara, Russia)
V.P. Radchenko (Samara, Russia, radch@samtgu.ru) 
Abstract 
The solution of the nonlinear stochastic boundaryvalue problem of the creep of a thin plate in a plane stress state when the elastic strains are small and can be neglected is presented. The plate material is stochastically inhomogeneous so that the stress and strain tensors are random functions of the coordinates. The constitutive creep relation, taken as in nonlinear viscous flow theory, is formulated in a stochastic form. Using the perturbation method, the nonlinear stochastic problem is reduced to a system of three linear partial differential equations in the fluctuations of the stress tensor and, then, changing by implementing the stress function, to a differential equation, the solution of which is represented in the form of the sum of two series. The first series is the solution far from the boundary of the plate, ignoring edge effects, and the second is the solution in the boundary layer, and its terms rapidly decay as the distance from the boundary of the plate increases. The stretching of a stochastically inhomogeneous halfplane in the direction of two mutually orthogonal axes is considered as an example. The stress concentration in the boundary of the halfplane is investigated. It is shown that the spread of the stresses in the surface layer, the width of which depends on the degree of nonlinearity of the material, can be much greater than in the deep layers. 
Received 
3 December 2008 
Link to Fulltext 
http://www.sciencedirect.com/science/journal/00218928 
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