Abstract
A simple representation is obtained of the general solution of the Lame system of equations for an isotropic material in the form of a linear combination of the first derivatives of the three functions satisfying three independent wave or harmonic (in the static case) equations. In the two-dimensional case of plane deformation, the found solution directly implies the Kolosov-Muskhelishvili representation of the displacements by two analytic functions of a complex variable. A formula for generation of new solutions is given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
N. I. Ostrosablin, “General Solution and Reduction of the System of Equations of Linear Isotopic Elasticity to the Diagonal Form,” in Differential Equations. Function Spaces. Approximation Theory: Proceedings of the International Conference Dedicated to the 100th Anniversary of the Birthday of S. L. Sobolev (Novosibirsk, Russia, October 5–12, 2008) (Inst.Mat., Novosibirsk, 2008), p. 538.
V. B. Poruchikov, Methods of Dynamical Elasticity Theory (Nauka, Moscow, 1986) [in Russian].
N. I. Ostrosablin, “Symmetry Operators and General Solutions to the Equations of the Linear Theory of Elasticity,” Prikl. Mekh. Tekh. Fiz. 36(5), 98–104 (1995) [J.Appl.Mech. Tech.Phys. 36 (5), 724–729 (1995)].
N. I. Ostrosablin, “On the General Solution of Equations of Linear Elasticity,” Dinamika Sploshn. Sredy 92, 62–71 (1989).
N. I. Ostrosablin, “Eigenoperators and Eigenvectors for the System of Differential Equations of Linear Elasticity Theory for AnisotropicMaterials,” Dokl. Akad. Nauk 337(5), 608–610 (1994) [Phys.-Dokl. 39 (8), 584–586 (1994)].
N. I. Muskhelishvili, Some Main Problems of the Mathematical Theory of Elasticity (Nauka, Moscow, 1966) [in Russian].
A. A. Svetashkov, “About Solving the Plane Problems of Elasticity Theory by Means of a Diagonalizable System of Equilibrium Equations,” Vychisl. Tekhnologii 12(3), 87–108 (2007).
N. I. Ostrosablin, “New Representation of a Solution to the Lame Equation of the Linear Elasticity Theory of an Isotropic Body,” in Numerical Methods for Solving the Problems of Elasticity and Plasticity Theory: Proceedings of the 18th Inter-Republican Conference (Kemerovo, Russia, 1–3 July, 2003) (Nonparel’, Novosibirsk, 2003), pp. 130–135.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © N.I. Ostrosablin, 2009, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2009, Vol. XII, No. 2, pp. 79–83.
Rights and permissions
About this article
Cite this article
Ostrosablin, N.I. The general solution and reduction to diagonal form of a system of equations of linear isotropic elasticity. J. Appl. Ind. Math. 4, 354–358 (2010). https://doi.org/10.1134/S1990478910030075
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1990478910030075