Novosibirsk, Russia, May, 30 – June, 4, 2011

"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

## Миколайчук М.А. Князева А.Г.## Coupled two dimensional problem of diffusion under external loading## Reporter: Миколайчук М.А.Two dimensional problem of one-axis loaded plate admixture saturation was considered. Mechanical part of problem was formulated under the Bernoulli-Euler hypothesis. Lateral displacements are negligible. We are supposed that axial deformation is an linear function of coordinates in the cross-sectional plane. Stresses was obtained as functions of deformations which was expressed in terms of displacements. Relation between deformations and stresses described with Duhamel–Neumann Law. In the defining relationship we have volume changing function which depends on admixture concentration. Thereby, without external loading plate stressed state depend on concentration stresses. Unknown functions from axis displacement definition was obtained from system of linear algebra equations which was written as result of conditions of equilibrium for resultant forces and torques
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