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Content available remote 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
Content available remote 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
Content available remote 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.
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