 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
|
| In English (Mech. Solids): | | 3212 |
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| << Previous article | Volume 44, Issue 5 / 2009 | Next article >> |
| N.D. Vaisfeld and G.Ya. Popov, "Mixed Boundary Value Problem of Elasticity for a Quarter Space," Mech. Solids. 44 (5), 712-728 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
5 |
Pages |
712-728 |
| DOI |
10.3103/S0025654409050082 |
| Title |
Mixed Boundary Value Problem of Elasticity for a Quarter Space |
| Author(s) |
N.D. Vaisfeld (Mechnikov Odessa National University, Dvoryanskaya 2, Odessa, 65026 Ukraine, vaysfeld@onu.edu.ua)
G.Ya. Popov (Mechnikov Odessa National University, Dvoryanskaya 2, Odessa, 65026 Ukraine, popovgya@mail.ru) |
| Abstract |
We consider the static elasticity problem for a quarter space with zero displacements on one of its surfaces and with given stresses on the other. The method for solving this problem is based on the use of new unknown functions in the form of a linear combination of the desired displacements, which reduces the system of three Lamè equations to two equations to be solved simultaneously and one equation to be solved separately. The exact solution of this problem was obtained earlier by the same method [1]. But it was shown in [2] that such a solution is exact only under certain restrictions on the given functions. In the present paper, the solution of this problem is constructed without restrictions on the given functions, which necessitates solving a one-dimensional integro-differential equation; this can be done approximately by the orthogonal polynomial method. We present numerical results obtained on the basis of our solution. |
| Keywords |
quarter space, new representation of equations of motion, integral transform |
| References |
| 1. | G. Ya. Popov,
"An Exact Solution of the Mixed Elasticity Problem in a Quarter-Space,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 31-39 (2003)
[Mech. Solids (Engl. Transl.)
38 (6), 23-30 (2003)]. |
| 2. | G. Ya. Popov, "New Transforms for the Resolving Equations in Elastic Theory and New Integral Transforms, with Applications to Boundary Value Problems of Mechanics," Prikl. Mekh. 39 (12), 46-73 (2003) [Int. Appl. Mech. (Engl. Transl.) 39 (12), 1400-1424 (2003)]. |
| 3. | W. Kecs and P. P. Teodorescu,
Applications of the Theory of Distributions in Mechanics
(Editura Academiei Romane, Bucharest, 1974; Mir, Moscow, 1978). |
| 4. | H. Bateman and A. Erdelyi,
Tables of Integral Transforms, Vol. 1
(McGraw-Hill, New York, 1954; Nauka, Moscow, 1969). |
| 5. | G. Ya. Popov, S. A. Abdymanapov, and V. V. Efimov, Green Functions and Matrices of One-Dimensional Boundary Value Problems
(Izd-vo Rauan, Almaty, 1999) [in Russian]. |
| 6. | Ya. S. Uflyand,
Integral Transforms in Elasticity Problems
(Izd-vo AN SSSR, Moscow-Leningrad, 1963)
[in Russian]. |
| 7. | I. S. Gradshtein and I. M. Ryzhik,
Tables of Integrals, Sums, Series, and Products
(Fizmatgiz, Moscow, 1963)
[in Russian]. |
|
| Received |
29 May 2007 |
| Link to Fulltext |
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