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

The present paper considers the equilibrium theory of thermo-microstretch elastic solids with microtemperatures. 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. | Turk J Math (2018) 42: 2101 – 2111 © TÜBİTAK doi: Turkish Journal of Mathematics Research Article On one BVP for a thermo-microstretch elastic space with spherical cavity Lamara BITSADZE∗, I. Vekua Institute of Applied Mathematics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia Received: • Accepted/Published Online: • Final Version: Abstract: The present paper considers the equilibrium theory of thermo-microstretch elastic solids with microtemperatures. 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. Key words: Thermo-microstretch elastic solids, microtemperatures, explicit solution, sphere 1. 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 theory of micromorphic elastic solids with microtemperatures was presented by Ieşan in [12,15]. In [18], Ieşan and Quintanilla discussed various problems using thermoelasticity with microtemperatures. Many investigators studied different types of problems for thermo-microstretch medium in detail (some of those works can be seen in [1-8,13,14,17,20-24,26,27] and the references therein). The