The plane problem on the action of an arbitrarily oriented concentrated force, applied at some point of an elastic plane, composed of two different anisotropic half-planes, is considered. By a special choice of a particular solution the problem reduces to a well-known differential equation of the anisotropic theory of elasticity with discontinuous coefficients. The latter reduces, by the method of the integral Fourier transform, to the Riemann boundary value problem. Expressions for the stresses and displacement derivatives at an arbitrary point of the plane are obtained. The application of the obtained results is illustrated on the example of a problem on an elastic linear inclusion (strap).
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
S. G. Lekhnitskii, “The plane static problem in the theory of elasticity of an anisotropic body,” Prikl. Mat. Mekh.,1, No. 1, 67–72 (1937).
L. A. Fil'shtinskii, “Boundary value problems of the theory of elasticity for an anisotropic half-plane, weakened by a hole or a cut,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 6, 47–53 (1980).
A. I. Lur'e, Theory of Elasticity [in Russian], Nauka, Moscow (1970).
W. Kecs and P. P. Teodorescu, Applications of the Theory of Distributions in Mechanics, Editura Academiei Române, Bucharest; Abacus Press, Tunbridge Wells (1974).
S. G. Lekhnitskii, Anisotropic Plates [in Russian], Gostekhizdat, Moscow (1957).
G. Ya. Popov, “On a method of solving mechanics problems for domains with slits or thin inclusions,” Prikl. Mat. Mekh.,42, No. 1, 122–135 (1978).
F. D. Gakhov and Yu. I. Cherskii, Equations of Convolution Type [in Russian], Nauka, Moscow (1978).
L. A. Fil'shtinskii, “On the singularities of the stress field in an elastic anisotropic half-plane with an outgoing rib on the boundary,” Prikl. Mekh.,17, No. 10, 79–85 (1981).
F. D. Gakhov, Boundary Value Problems (3rd edition, revised and augmented) [in Russian], Nauka, Moscow (1977).
Translated from Dinamicheskie Sistemy, No. 4, pp. 40–45, 1985.
About this article
Cite this article
Krivoi, A.F., Radiollo, M.V. Fundamental solution of a plane problem of elasticity theory for a composite anisotropic medium. J Math Sci 60, 1365–1368 (1992). https://doi.org/10.1007/BF01679639
- Differential Equation
- Fourier Transform
- Fundamental Solution
- Plane Problem