On static hierarchical models of thermoelastic piezoelectric shells

Author: Gia Avalishvili
Co-authors: Mariam Avalishvili
Keywords: thermoelastic piezoelectric shells, hierarchical models, error estimate
Annotation:

In this paper thermoelastic piezoelectric shell with thickness, which may vanish on a part of the lateral boundary, consisting of several inhomogeneous anisotropic layers. Applying variational approach boundary value problem corresponding to static three-dimensional model of thermoelastic piezoelectric body with regard to magnetic field is studied, when along certain parts of the boundary mechanical displacement vector, temperature, electric and magnetic potentials vanish, while on the remaining parts of the boundary components of electric displacement, magnetic induction and heat flux vectors along the outward normal vector of the boundary are given, and on the interface surfaces between layers the rigid contact conditions are fulfilled. In order to construct two-dimensional models of the thermoelastic piezoelectric shell spectral approximation method is used, which is a generalization of dimensional reduction method suggested by I. Vekua in the classical theory of elasticity for prismatic shells. Applying variational approach a hierarchy of static two-dimensional models is constructed and the existence and uniqueness of solutions of the corresponding boundary value problems in suitable weighted Sobolev spaces is investigated. Moreover, it is proved that the sequence of vector-functions of three variables restored from the solutions of the two-dimensional problems converges to the solution of the original three-dimensional problem in the corresponding spaces and under additional conditions estimate of the rate of convergence is obtained. This work was supported by Shota Rustaveli National Science Foundation (SRNSF) [Grant number 217596, Construction and investigation of hierarchical models for thermoelastic piezoelectric structures].

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თერმოდრეკადი პიეზოელექტრული გარსების სტატიკური იერარქიული მოდელების შესახებ [ka]
On static hierarchical models of thermoelastic piezoelectric shells [en]