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The quaternion method of regularizing integral equations of the theory of elasticity. (English. Russian original) Zbl 0788.73022

J. Appl. Math. Mech. 56, No. 5, 765-770 (1992); translation from Prikl. Mat. Mekh. 56, No. 5, 864-868 (1992).
Summary: Using quaternions, a new method of regularizing integral equations of the theory of elasticity is proposed which is identical for plane and spatial problems. The regularizors and the regularized equations are presented. The method does not use the theory of a symbol or the transition to the complex form. The quaternion technique has not been applied so far to integral equations of the theory of elasticity, but has been used to obtain the general solutions of Lamé’s equations.

MSC:

74B99 Elastic materials
45E05 Integral equations with kernels of Cauchy type
30G99 Generalized function theory
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[1] Kantor, I. L.; Solodovnikov, A. S., Hypercomplex Numbers (1973), Nauka: Nauka Moscow · Zbl 0669.17002
[2] Mikhlin, S. G., Multidimensional Singular Integrals and Integral Equations (1962), Fizmatgiz: Fizmatgiz Moscow
[3] Kupradze, V. D.; Gegelia, T. G.; Basheleishvili, M. O.; Burchuladze, T. V., Three-dimensional Problems of the Mathematical Theory of Elasticity (1976), Nauka: Nauka Moscow
[4] Maz’ya, V. G.; Sapozhnikova, V. D., Remark on the regularization of the singular system of isotropic elasticity, Vestn. LGU, Ser. Matem., Mekh., Astr., 7 (1964) · Zbl 0171.08901
[5] Kutrunov, V. N., Regularization of singular integral equations of the plane problem of the theory of elasticity basing on the spectrum, (Research on the Mechanics of Structures and Materials (1990), LISI: LISI Leningrad) · Zbl 0788.73022
[6] Lur’ye, A. I., Theory of Elasticity (1970), Nauka: Nauka Moscow
[7] Bitsadze, A. V., The inversion of a system of singular integral equations, Dokl. Akad. Nauk SSSR, 93, 4 (1953) · Zbl 0052.33606
[8] Bitsadze, A. V., The spatial analogue of the Cauchy-type integral and some of its applications, Dokl. Akad. Nauk SSSR, 93, 3 (1953)
[9] Perlin, P. I., Application of the regular representation of singular integrals for solving the second basic problem of the theory of elasticity, Prikl. Mat. Mekh., 40, 2 (1976) · Zbl 0348.73011
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