 | | 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
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| In English (Mech. Solids): | | 3212 |
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| << Previous article | Volume 48, Issue 4 / 2013 | Next article >> |
| V.V. Vasil'ev and S.A. Lurie, "On the Solution Singularity in the Plane Elasticity Problem for a Cantilever Strip On the Solution Singularity in the Plane Elasticity Problem for a Cantilever Strip," Mech. Solids. 48 (4), 388-396 (2013) |
| Year |
2013 |
Volume |
48 |
Number |
4 |
Pages |
388-396 |
| DOI |
10.3103/S0025654413040055 |
| Title |
On the Solution Singularity in the Plane Elasticity Problem for a Cantilever Strip On the Solution Singularity in the Plane Elasticity Problem for a Cantilever Strip |
| Author(s) |
V.V. Vasil'ev (Moscow State Aviation Technological University, Orshanskaya 3, Moscow, 121552 Russia, vvvas@dol.ru)
S.A. Lurie (Dorodnicyn Computing Center, Russian Academy of Sciences, Vavilova 40, Moscow, 119333 Russia, lurie@ccas.ru) |
| Abstract |
The plane elasticity problem of bending of a cantilever strip whose material is assumed to be incompressible in the transverse direction is solved. It is shown that, in the classical statement of of the boundary condition for the fixed edge of the strip, the solution has a singularity at the corner points of the edge. Several cases of the strip fixation and loading characterized by the presence or absence of the solution singularity are considered.
The strength of glass beams of three types, for which the theory of elasticity predicts whether the normal stress has a singularity, is studied experimentally. It is shown that the limit stresses for the beams of the types under study are practically the same, which testifies that the solution singularity does not have any physical nature. |
| Keywords |
plane problem, theory of elasticity, stresses, singular solution, strength |
| References |
| 1. | V. V. Vasil'ev and S. A. Lurie, "A Variant of the Refined Theory of Bending for a Laminar Plastic Beam," Mekh. Polim., No. 4,
674-681 (1972) [Polimer Mech. (Engl. Transl.) 8 (4),
582-588 (1972)]. |
| 2. | V. V. Vasil'ev, "Stress Tensor Symmetry and Singular Solutions in the Theory of Elasticity," Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 2, 62-72 (2010) [Mech. Solids (Engl. Transl.) 45 (2),
205-213 (2010)]. |
| 3. | S. A. Lurie and V. V. Vasiliev,
The Biharmonic Problem in the Theory of Elasticity
(Gordon and Breach, Australia etc., 1995). |
|
| Received |
20 March 2013 |
| Link to Fulltext |
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