Abstract
A new representation of the stress tensor in the linear theory of elasticity is proposed. The representation satisfies the equilibrium equations and the compatibility conditions for strains. In this representation, the stress tensor is expressed in terms of a harmonic vector. The second boundary-value problem for an elastic half-space and elastic layer is considered as an example.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
REFERENCES
N. M. Borodachev, “Construction of exact solutions to three-dimensional elastic problems in stresses,” Int. Appl. Mech., 37, No.6, 762–768 (2001).
N. M. Borodachev, “Solution of a spatial stress problem for an elastic layer,” Int. Appl. Mech., 38, No.5, 556–561 (2002).
V. T. Grinchenko and A. F. Ulitko, Equilibrium of Canonical Elastic Bodies [in Russian], Naukova Dumka, Kiev (1985).
Yu. A. Krutkov, Tensor of Stress Functions and General Solutions in Static Elasticity [in Russian], Izd. AN SSSR, Moscow-Leningrad (1949).
A. I. Lur’e, Theory of Elasticity [in Russian], Nauka, Moscow (1970).
A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, Cambridge Univ. Press (1959).
W. Nowacki, Theory of Elasticity [in Polish], PWN, Warsaw (1970).
P. F. Papkovich, Theory of Elasticity, Oborongiz, Moscow-Leningrad (1939).
E. N. Borisov, “Approximate analytical solution of a physically nonlinear spatial problem on the elastic equilibrium of a multilayer rectangular plate,” Int. Appl. Mech., 39, No.8, 961–968 (2003).
N. M. Borodachev, “Solution of the three-dimensional thermoelastic problem in stresses,” Int. Appl. Mech., 39, No.4, 438–444 (2003).
B. Davies, Integral Transforms and Their Applications, Springer-Verlag, New York-Heidelberg-Berlin (1978).
Yu. N. Podil’chuk and Yu. K. Rubtsov, “Development of the boundary-element method for three-dimensional problems of static and nonstationary elasticity,” Int. Appl. Mech., 40, No.2, 160–168 (2004).
J. J. Rushchitsky, “Joint effect of microstructure and load on the static stress state of elastic bodies,” Int. Appl. Mech., 40, No.4, 370–387 (2004).
Author information
Authors and Affiliations
Additional information
Translated from Prikladnaya Mekhanika, Vol. 40, No. 11, pp. 85–91, November 2004.
Rights and permissions
About this article
Cite this article
Borodachev, N.M. On a representation of the solution of the linear elasticity equations. Int Appl Mech 40, 1263–1268 (2004). https://doi.org/10.1007/s10778-005-0033-4
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10778-005-0033-4