Abstract
The construction of solutions in explicit form is especially important from the point of view of its application, since it makes it possible to effectively carry out a quantitative analysis of the problem under study. This paper investigates the processes of deformation of solids in the quasi-static case. Two-dimensional boundary value problems of Dirichlet and Neumann for an elastic body with double porosity are considered. In Using the Laplace transform, these problems are reduced to auxiliary boundary value problems. Special representations of solutions to auxiliary boundary value problems are constructed using elementary functions that allow reducing the original system of equations to equations of a simple structure and facilitate the solution of the original problems. Auxiliary boundary value problems are solved for a specific elastic body - a porous disk. Solutions to these problems are obtained in the form of series. Conditions are provided that ensure the absolute and uniform convergence of these series and the use of the inverse Laplace theorem. It is proved that the inverse transforms provide a solution to the initial problems.
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