Abstract
The mixed dynamic problem of the theory of elasticity is solved for an isotropic half plane. The dynamic equations are reduced to integration of fourth-degree equations in partial derivatives with constant coefficients, after whose solution, the components of the stress tensor and displacement vector are written in a form similar to that introduced by Lekhnitskii for an anisotropic body. The stress state of a rock mass subjected to rapid face advance in a seam is investigated using the solution obtained. The stress distribution is analyzed numerically. The existence of a critical rate at which the stress increases without restriction is demonstrated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. S. Kosmodamianskii and A. A. Levshin, "Solution of the mixed problem of the theory of elasticity for an anisotropic half plane," Dokl. Akad. Nauk UkrSSR, Ser. A, No. 9, 34–37 (1986).
A. A. Levshin, "On one mixed problem of the theory of elasticity for an anisotropic half plane," Izv. Akad. Nauk SSSR, Ser. Mekh. Tverd. Tela, No. 5, 180–182 (1981).
L. A. Galin, Contact Problems of the Theory of Elasticity and Coelastiċity [in Russian], Moscow (1980).
S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Body [in Russian], Moscow (1977).
N. I. Muskhelishvili, Singular Integral Equations [in Russian], Moscow (1968).
G. I. Barenblatt and S. A. Khristianovich, "On roof collapse during mine excavations," Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, No. 11, 73–86 (1955).
Additional information
Donetsk. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 21, pp. 56–61, 1990.
Rights and permissions
About this article
Cite this article
Levshin, A.A., Shepelenko, O.V. Mixed dynamic problem for a half plane and its application to rock mechanics. J Math Sci 68, 671–675 (1994). https://doi.org/10.1007/BF01249401
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01249401