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Potential Method in the Theory of Elasticity for Triple Porosity Materials

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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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Authors and Affiliations

  1. Ilia State University, K. Cholokashvili Ave., 3/5, 0162, Tbilisi, Georgia

    Merab Svanadze

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  1. Merab Svanadze
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Correspondence to Merab Svanadze.

Additional information

This work was supported by Shota Rustaveli National Science Foundation (SRNSF) [Project \(\#\) FR/18/5-102/14].

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Svanadze, M. Potential Method in the Theory of Elasticity for Triple Porosity Materials. J Elast 130, 1–24 (2018). https://doi.org/10.1007/s10659-017-9629-2

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  • DOI: https://doi.org/10.1007/s10659-017-9629-2

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