Lamara Bitsadze

Explicit Solution of the First BVP of the Elastic Mixture for Half-Space

We consider the first BVP of elastic mixture theory for a transversally-isotropic half-space. The solution of the first BVP for the transversally-isotropic half-space is given in [V. D. Kupradze, T. G. Gegelia, M. O. Basheleishvili, and T. V. Burchuladze, Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity. Translated from the second Russian edition. Edited by V. D. Kupradze. North-Holland Series in Applied Mathematics and Mechanics, 25.North-Holland Publishing Co., Amsterdam-New York, 1979]. The present paper is an attempt to use this result for the BVP of elastic mixture theory for a transversally-isotropic elastic body. Using the potential method and the theory of integral equations, the uniqueness theorem is proved for a half-space and the first BVP previously is solved effectively (in quadratures), which has not been solved.

Mathematics Subject Classification: 74E30, 74G05

Key words and phrases: Elastic mixture, uniqueness theorem, potential method, explicit solution