 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| A. I. Aleksandrovich, P. A. Kuvshinov, and D. F. Titorenko, "A solution of 3D elasticity equations using a holomorphic expansion of complex displacements in terms of power and Bessel functions," Mech. Solids. 36 (2), 26-35 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
2 |
Pages |
26-35 |
| Title |
A solution of 3D elasticity equations using a holomorphic expansion of complex displacements in terms of power and Bessel functions |
| Author(s) |
A. I. Aleksandrovich (Moscow)
P. A. Kuvshinov (Moscow)
D. F. Titorenko (Moscow) |
| Abstract |
Methods of one-dimensional complex analysis for solving plane elasticity
problems were first suggested in [1]. Later, these methods have been
developed in numerous publications (see, for example, [2, 3]).
Methods of the multidimensional complex analysis for solving
3D elasticity problems were suggested in [4, 5] and then developed
in [6-8]. The applicability of the theory of functions of two complex
variables to 3D problems is based on the consideration of
three-dimensional solids as sections of four-dimensional bodies by a
hyperplane x4=0. Such an approach allows one to introduce a
two-dimensional complex structure in a space of four real variables
and seek the solution of equations in the form of holomorphic
expansions, which leads to a system of linked differential equations. The
general solution of this system can be expressed in terms
of a finite number of holomorphic functions of two complex variables.
These functions can be found after substituting these into the boundary
conditions. |
| References |
| 1. | G. V. Kolosov, Application of a Complex Diagram and the Theory
of Functions of a Complex Variable to the Theory of Elasticity [in
Russian], ONTI, Leningrad, Moscow, 1935. |
| 2. | N. I. Muskhelishvili, Some Basic Problems of the Mathematical
Theory of Elasticity [in Russian], Nauka, Moscow, 1966. |
| 3. | A. Ya. Aleksandrov and Yu. I. Solov'ev, Three-dimensional
Problems of the Theory of Elasticity [in Russian], Nauka, Moscow, 1978. |
| 4. | A. I. Aleksandrovich, "Application of the theory of functions
of two complex variables to the theory of elasticity," Doklady AN SSSR,
Vol. 232, No. 3, pp. 542-544, 1977. |
| 5. | A. I. Aleksandrovich, "Application of the theory of functions
of two complex variables to the solution of three-dimensional problems
of the theory of elasticity," Izv. AN SSSR. MTT [Mechanics of Solids],
No. 2, pp. 164-168, 1977. |
| 6. | A. I. Aleksandrovich and A. M. Semov, "Application of the
theory of functions of two complex variables to the solution of some
boundary value problems of the three-dimensional theory of elasticity,"
in Selected Problems of Dynamics [in Russian], pp. 54-62, Nauka, Moscow,
1979. |
| 7. | A. I. Aleksandrovich and A. Yu. Rodionov, "Study of anisotropic
and thermoelastic problems by methods of complex analysis," in Problems
of Mechanics of Solids [in Russian], pp. 74-84, Moscow, 1987. |
| 8. | A. I. Aleksandrovich, P. A. Kuvshinov, and D. F. Titorenko,
Solution of Problems of the Three-dimensional Theory of Elasticity by
Methods of Complex Analysis [in Russian], Izd-vo VTs RAN, Moscow, 1998. |
|
| Received |
18 December 1998 |
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