Abstract
We propose a method for the solution of a three-dimensional problem of determination of displacements in a half space within the framework of the theory of elasticity. The wave field of displacements induced by the formation of discontinuities in the body and loads specified on the surface of the half space is represented in the form of a double-layer potential of the theory of elasticity. The fundamental solution of the problem is obtained for the case where the time dependences of the loads and opening displacements of discontinuities are described by a harmonic law.
Similar content being viewed by others
REFERENCES
L. V. Flitman, “Waves caused by the instantaneous formation of discontinuities in elastic media,” Prikl. Mat. Mekh., 4, No. 27, 618-628 (1963).
V. V. Panasyuk, O. N. Sergienko, and S. I. Mikitishin, “Acoustic emission in the process of fracture of materials,” Fiz.-Khim. Mekh. Mater., 19, No. 6, 50-53 (1983).
A. E. Andreikiv and N. V. Lysak, Method for Acoustic Emission in the Investigation of Fracture Processes [in Russian], Naukova Dumka, Kiev (1989).
V. Z. Stankevich and M. V. Khai, “Determination of displacements on the surface of a body caused by the discontinuities of a medium,” Prikl. Mekh., 30, No. 12, 25-33 (1994).
V. V. Mikhas'kiv, V. Z. Stankevich, and M. V. Khai, “Boundary integral equations in three-dimensional problems of steady vibrations of a half space with plane cracks,” Izv. Akad. Nauk Rossii, Mekh. Tverd. Tela, No. 6, 44-53 (1993).
V. Z. Stankevych, “Evaluation of some two-dimensional integrals encountered in dynamic problems of the theory of cracks in semiinfinite bodies,” Mat. Met. Fiz.-Mekh. Polya, Issue 39, 56-61 (1995).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Khai, M.V., Stankevych, V.Z. Fundamental Solution of a Quasistatic Problem for a Half Space with Two-Dimensional Discontinuities. Materials Science 38, 338–343 (2002). https://doi.org/10.1023/A:1021713431061
Issue Date:
DOI: https://doi.org/10.1023/A:1021713431061