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Advances in Mathematical Physics
Volume 2016, Article ID 4792148, 9 pages
http://dx.doi.org/10.1155/2016/4792148
Research Article

Elastic Equilibrium of Porous Cosserat Media with Double Porosity

Ilia Vekua Institute of Applied Mathematics of Ivane Javakhishvili Tbilisi State University, 2 University Street, 0186 Tbilisi, Georgia

Received 11 May 2016; Accepted 30 June 2016

Academic Editor: John D. Clayton

Copyright © 2016 Roman Janjgava. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The static equilibrium of porous elastic materials with double porosity is considered in the case of an elastic Cosserat medium. The corresponding three-dimensional system of differential equations is derived. Detailed consideration is given to the case of plane deformation. A two-dimensional system of equations of plane deformation is written in the complex form and its general solution is represented by means of three analytic functions of a complex variable and two solutions of Helmholtz equations. The constructed general solution enables one to solve analytically a sufficiently wide class of plane boundary value problems of the elastic equilibrium of porous Cosserat media with double porosity. A concrete boundary value problem for a concentric ring is solved.