Abstract
Continuous and integrable solutions and one-to-one relationships between boundary forces and displacements are found through the direct integration of the differential equations of the plane elastic problem for a half-plane with boundary conditions for either forces or displacements or with mixed boundary conditions. The necessary equilibrium conditions for forces and the compatibility conditions for displacements that ensure the correctness of the solutions are formulated
Similar content being viewed by others
REFERENCES
V. Ya. Arsenin, Methods of Mathematical Physics and Special Functions [in Russian], Nauka, Moscow (1974).
S. Bochner, Lectures on Fourier Integrals, Princeton Univ. Press., Princeton (1959).
Yu. A. Brychkov and A. P. Prudnikov, Integral Transforms of Distributions [in Russian], Nauka, Moscow (1977).
A. G. Butkovskii, Characteristics of a Distributed-Parameter System [in Russian], Nauka, Moscow (1979).
V. M. Vigak, “Direct integration of plane problems of elasticity and thermoelasticity,” Dop. NAN Ukrainy, No. 12, 62-67 (1998).
W. Kecs and P. P. Teodorescu, Introducere in Teoria Distributiilor cu Aplicatii in Tehnica, Bucuresti (1975).
P. N. Knyazev, Integral Transforms [in Russian], Vysheish. Shkola, Minsk (1969).
A. I. Lur'e, Theory of Elasticity [in Russian], Nauka, Moscow (1970).
N. I. Muskhelishvili, Some Basic Problems in the Mathematical Theory of Elasticity [in Russian], Izd. AN SSSR, Moscow (1954).
W. Nowacki, Theory of Elasticity [Russian translation], Mir, Moscow (1975).
I. N. Sneddon, Fourier Transforms, McGraw-Hill, New York (1951).
G. M. Fikhtengol'ts, A Course of Differential and Integral Calculus [in Russian], Vol. 2, Nauka, Moscow (1969).
H. G. Hahn, Elastizitatstheorie. Grundlagen der Linearen Theorie und Anwendungen auf Eindimensionale, Ebene und Raumliche Probleme, B. G. Teubner, Stuttgart (1985).
G. Ya. Popov, “Construction of the exact solution to a torsion problem for an elastic shaft of variable cross section,” Int. Appl. Mech., 38, No. 8, 967–973 (2002).
V. M. Vigak and A. V. Rychagivskii, “Solution of a three-dimensional elastic problem for a layer,” Int. Appl. Mech., 38, No. 9, 1094–1102 (2002).
V. M. Vigak and Yu. V. Tokovyi, “Construction of elementary solutions to a plane elastic problem for a rectangular domain,” Int. Appl. Mech., 38, No. 7, 829–836 (2002).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vigak, V.M. Correct Solutions of Plane Elastic Problems for a Half-Plane. International Applied Mechanics 40, 283–289 (2004). https://doi.org/10.1023/B:INAM.0000031910.20827.19
Issue Date:
DOI: https://doi.org/10.1023/B:INAM.0000031910.20827.19