On one BVP for a thermo-microstretch elastic space with spherical cavity

Lamara BITSADZE

doi:10.3906/mat-1705-46

Abstract

On one BVP for a thermo-microstretch elastic space with spherical cavity

Highlights

The theory of thermoelasticity for elastic materials with microtemperatures, whose particles contain a displacement vector and temperature field, was established by Grot [11].Eringen developed the theory of micromorphic bodies and the theory of thermo-microstretch elastic solids
The theory of micromorphic elastic solids with microtemperatures was presented by Ieşan in [12,15]
The present paper considers the equilibrium theory of thermo-microstretch elastic solids with microtemperatures

Summary

Introduction

The theory of thermoelasticity for elastic materials with microtemperatures, whose particles contain a displacement vector and temperature field, was established by Grot [11]. Eringen developed the theory of micromorphic bodies and the theory of thermo-microstretch elastic solids. An extensive review and basic results in the microcontinuum field theories for solids (micromorphic, microstretch, and micropolar) including electromagnetic and thermal interactions are given in his works [9,10]. In [16], Ieşan and Quintanilla formulated the boundary value problems of the theory of thermoelasticity with microtemperatures and presented a unique result and a solution of Boussinesq–Somigliana–Galerkin type. The method to solve the Neumann-type boundary value problem (BVP) for the whole space with spherical cavity is presented. The solution of this BVP in the form of absolutely and uniformly convergent series is obtained

Basic equations

Solution of the Neumann boundary value problem

Conclusions