Derivation of system of the equations of equilibrium for shallow shells and plates, having double porosity

Author: Bakur Gulua
Co-authors: Roman Janjgava
Annotation:

In the report the three-dimensional system of equations of equilibrium for solids with double porosity is considered. From this system of equations, using a reduction method of I. Vekua, we receive the equilibrium equations for the shallow shells having double porosity. Further we consider the case of plates with constant thickness in more detail. Namely, the systems of equations corresponding to approximations N=0 and N=1 are written down in a complex form and we express the general solutions of these systems through analytic functions of complex variable and solutions of the Helmholtz equation. The received general representations give the opportunity to solve analytically boundary value problems about elastic equilibrium of plates with double porosity.