 | | 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 3 / 2013 | Next article >> |
| N.A. Bazarenko, "Interaction of a Rigid Punch and a Circular Plate with a Fixed Side and a Stress-Free Face," Mech. Solids. 48 (3), 301-316 (2013) |
| Year |
2013 |
Volume |
48 |
Number |
3 |
Pages |
301-316 |
| DOI |
10.3103/S0025654413030072 |
| Title |
Interaction of a Rigid Punch and a Circular Plate with a Fixed Side and a Stress-Free Face |
| Author(s) |
N.A. Bazarenko (Rostov State Academy of Agricultural Machinery Industry, pl. Strany Sovetov 1, Rostov-on-Don, 344023 Russia, n_bazarenko@rambler.ru) |
| Abstract |
The axisymmetric contact problem of a rigid punch indentation into an elastic circular plate with a fixed side and a stress-free face is considered. The problem is solved by a method developed for finite bodies which is based on the properties of a biorthogonal system of vector functions. The problem is reduced to a Volterra integral equation (IE) of the first kind for the contract pressure function and to a system of two Volterra IE of the first kind for functions describing the derivative of the displacement of the plate upper surface outside the punch and the normal (or tangential) stress on the plate lower fixed surface. The last two functions are sought as the sum of a trigonometric series and a power-law function with a root singularity. The obtained ill-conditioned systems of linear algebraic equations are regularized by introducing small parameters and have a stable solution. A method for solving the Volterra IE is given. The contact pressure functions, the normal and tangential stresses on the plate fixed surface, and the dimensionless indentation force are found. Several examples of a plane punch computation are given. |
| Keywords |
biorthogonal function system, SLAE regularization, equivalent boundary conditions, series summation |
| References |
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"The Contact Problem for a Rectangle with Stress-Free Side Faces,"
Prikl. Mat. Mekh.
71 (2), 340-351 (2007)
[J. Appl. Math. Mech. (Engl. Transl.)
71 (2), 305-317 (2007)]. |
| 2. | N. A. Bazarenko,
"The Contact Problem for Hollow and Solid Cylinders with Stress-Free Faces,"
Prikl. Mat. Mekh.
72 (2), 328-341 (2008)
[J. Appl. Math. Mech. (Engl. Transl.)
72 (2), 214-225 (2008)]. |
| 3. | N. A. Bazarenko,
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and a Plate with a Cylindrical Cavity with a Rigid Insert,"
Prikl. Mat. Mekh.
74 (3), 441-454 (2010)
[J. Appl. Math. Mech. (Engl. Transl.)
74 (3), 323-333 (2010)]. |
| 4. | N. A. Bazarenko,
"Interaction of a Rigid Punch with a Base-Secured Elastic Rectangle with Stress-Free Sides,"
Prikl. Mat. Mekh.
74 (4), 667-680 (2010)
[J. Appl. Math. Mech. (Engl. Transl.)
74 (4), 475-485 (2010)]. |
| 5. | N. A. Bazarenko,
"The Contact Problem for a Circular Plate with a Stress-Free End Face,"
Prikl. Mat. Mekh.
74 (6), 978-991 (2010)
[J. Appl. Math. Mech. (Engl. Transl.)
74 (6), 699-709 (2010)]. |
| 6. | N. A. Bazarenko,
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|
| Received |
28 November 2011 |
| Link to Fulltext |
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