Explicit solutions of the boundary value problems of the theory of consolidation with double porosity for the half-plane

The solution of the Dirichlet BVP in the fully coupled theory of elasticity for spherical layer with double porosity

“…So, the solution of Problem B has the form (17), where w j ðxÞ are given by formulae (24). For absolutely and uniformly convergence of series in (11), (16), (23) and (24), together with their first derivatives, it is sufficient to assume that x AE ; h AE and h AE 1 satisfy the following conditions h AE 2 C 5 ðS i Þ; h AE 1 2 C 5 ðS i Þ; x AE 2 C 5 ðS i Þ; i ¼ 1; 2:…”

“…Many authors have investigated the BVPs of the theory of elasticity for materials with double porosity, that are published in a large number of papers (some of these results can be see in [15][16][17][18][19][20][21][22][23][24][25] and references therein).…”

Explicit solution of one boundary value problem in the full coupled theory of elasticity for solids with double porosity

“…Substituting the values of X ki = (X ki1 , X ki2 ), into (23), and the obtained into (21), we define the vector v(x).…”

“…In the last years, many authors have investigated the BVPs of the 2-dimensional and 3-dimensional theories of elasticity for materials with double porosity, publishing a large number of papers(for details, see [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] and references therein). There the explicit solutions on some BVPs in the form of series and in quadratures are given in a form useful for engineering practice.…”

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

“…Porous media theories play an important role in many branches of engineering, including material science, petroleum industry, chemical engineering, and soil mechanics, as well as biomechanics. In recent years, many authors investigated the BVPs of the 2D and 3D theories of elasticity for materials with double porosity structure, publishing a large number of papers (some of these results can be seen in [9][10][11][12][13][14][15][16][17] and references therein). In those works, the explicit solutions on some BVPs in the form of series are given in a form useful for the engineering practice.…”