Explicit Solutions of the Boundary Value Problems for an Ellipse with Double Porosity

الملخص EN

The basic two-dimensional boundary value problems of the fully coupled linear equilibrium theory of elasticity for solids with double porosity structure are reduced to the solvability of two types of a problem.

The first one is the BVPs for the equations of classical elasticity of isotropic bodies, and the other is the BVPs for the equations of pore and fissure fluid pressures.

The solutions of these equations are presented by means of elementary (harmonic, metaharmonic, and biharmonic) functions.

On the basis of the gained results, we constructed an explicit solution of some basic BVPs for an ellipse in the form of absolutely uniformly convergent series.