Modeling of Stress Distribution in a Semi-infinite Piecewise-homogeneous Body

Oleg Yaremko¹, Natalia Yaremko^1, and Elena Mogileva¹

¹Physical and mathematical faculty, Penza state university, Penza, Russia

Cite this paper:
Oleg Yaremko, Natalia Yaremko and Elena Mogileva. Modeling of Stress Distribution in a Semi-infinite Piecewise-homogeneous Body. International Journal of Partial Differential Equations and Applications. 2015; 3(2):29-34. doi: 10.12691/ijpdea-3-2-2

Abstract

In this paper the Fourier vector integral transforms method with discontinuous coefficients developed by authors is used for elasticity theory problems solving. The analytical solving dynamic problems for theory of elasticity in piecewise homogeneous half-space is found. The explicit construction of direct and inverse Fourier vector transforms with discontinuous coefficients is presented. Unknown tension in the boundary conditions and in the internal conjugation conditions don’t commit splitting in a considered dynamic problem, so the application of the scalar Fourier integral transforms with piece-wise constant coefficients does not lead to success. Conformable theoretical bases of a method are presented in this paper. The technique of applying Fourier vector transforms for solving problems of the dynamic problems the elasticity theory.

Keywords:
piecewise homogeneous medium theory of elasticity Fourier vector transform

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