 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10512 |
| In Russian (ΟΜΜ): | | 9713
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| In English (J. Appl. Math. Mech.): | | 799 |
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| G.Z. Sharafutdinov, "Functions of a complex variable in problems in the theory of elasticity with mass forces," J. Appl. Math. Mech. 73 (1), 48-62 (2009) |
| Year |
2009 |
Volume |
73 |
Issue |
1 |
Pages |
48-62 |
| Title |
Functions of a complex variable in problems in the theory of elasticity with mass forces |
| Author(s) |
G.Z. Sharafutdinov (Moscow, Russia, sharaf@imec.msu.ru) |
| Abstract |
The general equations of the theory of elasticity are reduced to an inhomogeneous fourth-order equation assuming that there is a linear dependence of the third component of the displacement vector on the third coordinate and that a mass force potential exists. The solution of this equation is presented, in particular, using two complex Kolosov-Muskhelishvili potentials. A third complex potential is introduced in addition to these. Using the three complex potentials, expressions are obtained for the components of the displacement vector and the stress and strain tensors that take account of mass forces. The application of the three potentials is analysed in problems in the theory of elasticity, and analytical solutions of several plane strain problems are presented. |
| References |
| 1. | G.V. Kolosov, Application of Complex Diagrams and the Theory of Functions of a Complex Variable to the Theory of Elasticity, ONTI, Moscow, Leningrad (1935). |
| 2. | N.I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Leyden (1977). |
| 3. | G.Z. Sharafutdinov, Application of functions of a complex variable to some three- dimensional problems of the theory of elasticity, Prikl Mat Mekh 64 (4) (2000), pp. 659–669. |
| 4. | G.Z. Sharafutdinov, Solution of the Kirsch problem in a three-dimensional formulation, Vestn MGU Ser 1 Matematika Mekhanika 6 (2001), pp. 20–25. |
| 5. | G.Z. Sharafutdinov, Stress and concentrated forces in thin annular plates, Prikl Mat Mekh 68 (1) (2004), pp. 45–59. |
| 6. | I.N. Sneddon and D.S. Berry, The Classical Theory of Elasticity, Springer, Berlin (1958). |
| 7. | S.P. Timoshenko and J.N. Goodier, Theory of Elasticity, McGraw-Hill, New York (1970). |
|
| Received |
30 May 2008 |
| Link to Fulltext |
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