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1

Potential method in the theory of thermoelasticity for materials with triple voids

Svanadze M.

Archives of Mechanics

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2019

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Vol. 71, nr 2

113--136

EN

In the present paper the linear theory of thermoelasticity for isotropic and homogeneous solids with macro-, meso- and microporosity is considered. In this theory the independent variables are the displacement vector field, the changes of the volume fractions of pore networks and the variation of temperature. The fundamental solution of the system of steady vibrations equations is constructed explicitly by means of elementary functions. The basic internal and external boundary value problems (BVPs) are formulated and the uniqueness theorems of these problems are proved. The basic properties of the surface (single-layer and double-layer) and volume potentials are established and finally, the existence theorems for regular (classical) solutions of the internal and external BVPs of steady vibrations are proved by using the potential method (boundary integral equation method) and the theory of singular integral equations.

2

Boundary value problems of steady vibrations in the theory of thermoelasticity for materials with a double porosity structure

Svanadze M.

Archives of Mechanics

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2017

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Vol. 69, nr 4-5

347--370

EN

The purpose of the present paper is to develop the classical potential method in the linear theory of thermoelasticity for materials with a double porosity structure based on the mechanics of materials with voids. The fundamental solution of the system of equations of steady vibrations is constructed explicitly by means of elementary functions and its basic properties are established. The Sommerfeld-Kupradze type radiation conditions are established. The basic internal and external boundary value problems (BVPs) are formulated and the uniqueness theorems of these problems are proved. The basic properties of the surface (single-layer and double-layer) and volume potentials are established and finally, the existence theorems for regular (classical) solutions of the internal and external BVPs of steady vibrations are proved by using the potential method and the theory of singular integral equations.

3

Some considerations of fundamental solution in micropolar thermoelastic materials with double porosity

Kumar R., Vohra R., Gorla M. G.

Archives of Mechanics

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2016

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Vol. 68, nr 4

263--284

EN

This paper is concerned with micropolar thermoelastic materials which have a double porosity structure. The system of the equations of the assumed model is based on the equations of motion, equilibrated stress equations of motion and heat conduction equation for material with double porosity. The explicit expressions for the fundamental solution of the system of equations in the case of steady vibrations are presented. The desired solutions are obtained by the use of elementary functions. Some basic properties are also established.

4

Fundamental solutions in the full coupled theory of elasticity for solid with double porosity

Svanadze M., De Cicco S.

Archives of Mechanics

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2013

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Vol. 65, nr 5

367--390

EN

This paper discusses the full coupled linear theory of elasticity for solids with double porosity. The system of the governing equations is based on the equations of motion, conservation of fluid mass, the constitutive equations and Darcy’s law for material with double porosity. Four spatial cases of the dynamical equations are considered: equations of steady vibrations, equations in Laplace transform space, equations of quasi-static and equations of equilibrium. The fundamental solutions of the systems of these partial differential equations (PDEs) are constructed by means of elementary functions and finally, the basic properties of these solutions are established.