ИСТИНА

The canonical formulation of the second initial boundary value problem of the classical (micropolar) theory of elasticity for any anisotropic material is given. In particular, the canonical formulations of initial boundary value problems are considered in the case of isotropic, transversely isotropic and orthotropic materials. Expressions for tensors-operators of classical (micropolar) equations in displacements (in displacements and rotations) are found. For these tensors-operators the tensors-operators of cofactors are found, on the basis of which the equations are split. It should be noted here that the equations are always split, and the boundary conditions only for bodies with a piecewise plane boundary. From three dimensional canonical equations the corresponding canonical equations for the theory of prismatic bodies are obtained. For prismatic bodies the canonical equations were obtained also in moments with respect to any system of orthogonal polynomials. For each moment of the unknown vector function the equation of elliptic type of high order is obtained, the characteristic roots of which are easily found. Using the Vekua method, we can obtain their analytical solution. Similar questions are considered for the micropolar theory of prismatic thin bodies with two small dimensions. Acknowledgements: this research were supported by the Shota Rustaveli National Science Foundaiton (project no. DI-2016-41) and the Russian Foundation for Basic Research (project no. 15-01-00848-a).