Merab Svanadze

FUNDAMENTAL SOLUTIONS OF THE EQUATIONS OF THE THEORY OF THERMOELASTICITY WITH MICROTEMPERATURES

By means of elementary functions, the fundamental solutions of the equations of the equlibrium and steady oscillations of the theory of thermoelasticity with microtemperatures are constructed, and basic properties are established.

ON THE REPRESENTATION OF SOLUTIONS OF THE THEORY OF THERMOELASTICITY WITH MICROTEMPERATURES

In the present paper the linear theory of thermoelasticity with microtemperatures is considered. First, the representation of Galerkin type solution of equations of motion is obtained. Then, the representation theorem of Galerkin type of the system of equations of steady oscillations (vibrations) is presented. Finally, the general solution of the system of homogeneous equations of steady oscillations in terms of nine metaharmonic functions is established.

Basic Theorems in the Equilibrium Theory of Thermoelasticity with Microtemperatures

In this paper we consider the linear equilibrium theory of thermoelasticity with microtemperatures and some basic results of the classical theories of elasticity and thermoelasticity are generalized. The Greens formulae in the considered theory are obtained. The uniqueness theorems of the internal and external basic boundary value problems (BVPs) are proved. The representation of Galerkin type solution is obtained and the completeness of this solution is established. The formulae of integral representations of regular vector and regular (classical) solutions are obtained. The basic properties of thermoelastopotentials and singular integral operators are presented. Finally, the existence theorems for the internal and external basic BVPs are proved by means of the potential method and the theory of singular integral equations.

Fundamental Solution in the Theory of Micropolar Thermoelasticity for Materials with Voids

This paper concerns with the linear theory of micropolar thermoelasticity for materials with voids. We construct the fundamental solution of the system of differential equations in the case of steady oscillations in terms of elementary functions. Some basic properties of this solution are established.

Fundamental Solutions in the Theory of Thermoelasticity for Solids with Double Porosity

In this article, the linear theory of thermoelasticity for solids with double porosity is considered. The fundamental solutions for the systems of steady vibrations (including quasi-static case) and equilibrium equations are constructed by means of elementary functions; the basic properties of such solutions are also established.

Potential Method in the Linear Theory of Thermoelasticity with Microtemperatures

In the present paper the linear theory of thermoelasticity with microtemperatures is considered. The basic boundary value problems of steady vibrations are investigated using the potential method. Sommerfeld–Kupradze type radiation conditions and the basic properties of thermoelastopotentials are established. The uniqueness and existence theorems of classical solutions of the external (with respect to an unbounded domain) boundary value problems are proved.

Mathematical problems in the coupled linear theory of bone poroelasticity

This paper concerns with the quasi-static coupled linear theory of bone poroelasticity for materials with double porosity and some basic results of the classical theories of elasticity and thermoelasticity are generalized. The system of equations of this theory is based on the equilibrium equations, conservation of fluid mass, the effective stress concept and Darcys law for material with double porosity. The Greens formulas in the considered theory are obtained, the formulas of Somigliana type integral representations of regular vector and regular (classical) solutions are presented. The uniqueness theorems for classical solutions of the internal and external boundary value problems (BVPs) are proved. The single-layer, double-layer and volume potentials are constructed and their basic properties are established. Finally, the existence theorems for classical solutions of the BVPs are proved by means of the potential method (boundary integral method) and the theory of singular integral equations.

Representations of Solutions in the Theory of Thermoelasticity with Microtemperatures for Microstretch Solids

Here, the linear theory of thermoelasticity with microtemperatures for isotropic microstretch solids is considered. First, the representation of Galerkin type solution of equations of motion is obtained. Then, the representation theorem of Galerkin type for the system of equations of steady vibrations is presented. Finally, the representation formula for general solution of the system of homogeneous equations of steady vibrations in terms of 10 metaharmonic functions is established.

Fundamental Solution in the Theory of Micropolar Thermoelasticity without Energy Dissipation

ABSTRACT This paper concerns the linear theory of micropolar thermoelasticity without energy dissipation. We construct the fundamental solution of the system of differential equations in the case of steady oscillations in terms of elementary functions.

FUNDAMENTAL SOLUTIONS IN THE THEORY OF MICROMORPHIC ELASTIC SOLIDS WITH MICROTEMPERATURES

By means of elementary functions, the fundamental solutions of equations of equilibrium and steady oscillations of the theory of micromorphic elastic solids with microtemperatures are constructed, and basic properties are established.