იერარქიული მოდელები თერმოდრეკადი კელვინ-ფოიგტის პიეზოელექტრული პრიზმული გარსებისათვის

In 1955 Ilia Vekua [1] published his models of elastic prismatic shells, prismatic shells whose cross-sections area vanishes at least at one end of the prismatic shells, he called “cusped” prismatic shells and In 1965 he offered analogous models for standart shells [2]. In both papers he considered a very important investigation of well-posedeness of BVPs (boundary value problems) of peculiar types which could arise in the case of cusped shells. In practice, cusped prismatic shells areoften encountered in spatial structures with partly fixed edges e.g., stadiumceilings, aircraft wings, submarine wings etc., in machine-tool design, as incutting-machines, planningsmachines, in astronautics, turbines, and in manyother application fields of engineering.
Investigation of elastic cusped prismatic shells, considered as 3D ones, may occupy 3D domains with, in general, non-Lipschitz boundaries.
The problem mathematically leads to equation of setting and solving of boundary value problems for even order equations and systems of elliptic type with the order degeneration in the statical case and of initial boundary value problems for even order equations and systems of hyperbolic type with the order degeneration in the dynamical case.(for corresponding investigations see the survey [3],[4] and also I.Vekua’s comments in[5] (p.86) and [12]). Piezoelectric materials are widely used in modern engineering structures and technology. hence it is important to construct and investigate algorithms of approximation of three-dimensional models of them by twodimensional.