 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| V.V. Vasil'ev, "Stress Tensor Symmetry and Singular Solutions in the Theory of Elasticity," Mech. Solids. 45 (2), 205-213 (2010) |
| Year |
2010 |
Volume |
45 |
Number |
2 |
Pages |
205-213 |
| DOI |
10.3103/S0025654410020068 |
| Title |
Stress Tensor Symmetry and Singular Solutions in the Theory of Elasticity |
| Author(s) |
V.V. Vasil'ev (Moscow State Aviation Technological University, Orshanskaya 3, Moscow, 121552 Russia, vvvas@dol.ru) |
| Abstract |
In the plane problem of the theory of elasticity about a cantilever strip bending, we study the stress state near its fixed end. It is found that the solution singularity at the corner points does not have any physical nature and is generated by specific characteristics of the statement of the problem in which it is assumed that the stress tensor symmetry is violated at these points.
We consider Reissner's problem about the stress state of the corner region one of whose sides is loaded by constant tangential stresses. We found that the statement of this problem in polar coordinates, which does not violate the stress tensor symmetry for a given loading, results in a regular solution. But the statement of the problem in Cartesian coordinates, which contradicts the stress tensor symmetry, results in a solution with singularities.
On the basis of the obtained results, we conclude that the singularity of solutions of elasticity problems is related to the statement of these problems, which explicitly or implicitly assumes violations of the stress tensor symmetry. |
| Keywords |
plane problem, stress, bending, singular solution, symmetry |
| References |
| 1. | S. P. Timoshenko and J. N. Goodyear,
Theory of Elasticity
(McGraw-Hill, New York, 1951; Nauka, Moscow, 1975). |
| 2. | V. V. Vasil'ev and S. A. Lur'e,
"A Variant of the Refined Theory of Bending for a Laminar Plastic Beam,"
Mekh. Polimer.,
No. 4, 674-681 (1972)
[Polymer Mech. (Engl. Transl.)
8 (4), 582-588 (1972)]. |
| 3. | S. A. Lurie and V. V. Vasiliev,
The Biharmonic Problem in the Theory of Elasticity
(Gordon and Breach, Australia etc., 1995). |
| 4. | E. Reissner,
"Note on the Theorem of the Symmetry of the Stress Tensor,"
in Proc. of the 4th Midwestern Conf. on Solid Mechanics
(University of Texas Press, Austin, 1959),
pp. 192-194. |
|
| Received |
20 February 2009 |
| Link to Fulltext |
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