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Journal of Elasticity

Erschienen in:

01.03.2017

Potential Method in the Theory of Elasticity for Triple Porosity Materials

verfasst von: Merab Svanadze

Erschienen in: Journal of Elasticity | Ausgabe 1/2018

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Abstract

In the present paper the basic boundary value problems (BVPs) of the full coupled linear theory of elasticity for triple porosity materials are investigated by means of the potential method (boundary integral equation method) and some basic results of the classical theory of elasticity are generalized. In particular, the Green’s identities and the formula of Somigliana type integral representation of regular vector and regular (classical) solutions are presented. The representation of Galerkin type solution is obtained and the completeness of this solution is established. The uniqueness theorems for classical solutions of the internal and external BVPs are proved. The surface (single-layer and 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 and the theory of singular integral equations.

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Titel: Potential Method in the Theory of Elasticity for Triple Porosity Materials
verfasst von: Merab Svanadze
Publikationsdatum: 01.03.2017
Verlag: Springer Netherlands
Erschienen in: Journal of Elasticity / Ausgabe 1/2018
Print ISSN: 0374-3535
Elektronische ISSN: 1573-2681
DOI: https://doi.org/10.1007/s10659-017-9629-2

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