Construction and Investigation of Static Hierarchical Models for Prismatic Shells with Microtemperatures

Author: Gia Avalishvili
Co-authors: Mariam Avalishvili, David Gordeziani
Keywords: theory of thermoelasticity with microtemperatures, prismatic shells, hierarchical models
Annotation:

The present paper is devoted to the construction and investigation of two-dimensional hierarchical models of thermoelastic prismatic shells with microtemperatures applying variational approach. We consider the variational formulation of three-dimensional boundary value problem for static linear model of thermoelastic prismatic shell within the theory of thermoelasticity with microtemperatures, with thickness which may vanish on a part of the lateral boundary, and construct its two-dimensional hierarchical models in Sobolev spaces, when temperature and components of microtemperature and displacement vectors equal to zero along a part of the lateral boundary of the prismatic shell, and the surface forces, the heat flux and the first heat flux moment are given along the upper and the lower faces, and along the remaining part of the lateral boundary of the prismatic shell. We investigate the existence and uniqueness of solutions of the reduced two-dimensional problems in suitable weighted Sobolev spaces. Moreover, we prove the convergence of the sequence of vector-functions of three space variables restored from the solutions of the constructed two-dimensional problems to the exact solution of the original three-dimensional boun¬dary value problem and if it possesses additional regularity, we estimate the rate of convergence.

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Abstract [en]
ანოტაცია [ka]