 | | 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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| D.A. Pozharskii, "Contact Problem for an Orthotropic Half-Space," Mech. Solids. 52 (3), 315-322 (2017) |
| Year |
2017 |
Volume |
52 |
Number |
3 |
Pages |
315-322 |
| DOI |
10.3103/S0025654417030086 |
| Title |
Contact Problem for an Orthotropic Half-Space |
| Author(s) |
D.A. Pozharskii (Don State Technical University, pl. Gagarina 1, Rostov-on-Don, 344000 Russia, pozharda@rambler.ru) |
| Abstract |
Numerical and analytical solutions of the 3D contact problem f elasticity on the penetration of a rigid punch into an orthotropic half-space are obtained disregarding the friction forces. A numerical method of Hammerstein-type nonlinear boundary integral equations was used in the case of unknown contact region, which permits determining the contact region and the pressure in this region. The exact solution of the contact problem for a punch shaped as an elliptic paraboloid was used to debug the program of the numerical method. The structure of the exact solution of the problem of indentation of an elliptic punch with polynomial base was determined. The computations were performed for various materials in the case of the penetration of an elliptic or conical punch. |
| Keywords |
contact problem, half-space, anisotropy, orthotropic material |
| References |
| 1. | A. O. Vatul'yan,
"On the Rigid Punch Action on an Anisotropic Half-Space,"
in Static and Dynamical Mixed Problems of Elasticity
(Izdat. RGU, Rostov-on-Don, 1983),
pp. 112-115. |
| 2. | B. A. Galanov,
"The Method of Boundary Equations of the Hammerstein-Type for Contact Problems
of the Theory of Elasticity when the Regions of Contact are not Known,"
Prikl. Mat. Mekh.
49 (5), 827-835 (1985)
[J. Appl. Math. Mech. (Engl. Transl.)
49 (5), 634-640 (1985)]. |
| 3. | B. A. Galanov,
"Nonlinear Boundary Equations for Contact Problems of Elasticity,"
Dokl. Akad. Nauk SSSR
296 (4), 812-815 (1987)
[Sov. Phys. Dokl. (Engl. Transl.)
32 (7), 857-859 (1987)]. |
| 4. | V. A. Sveklo,
"The Action of a Stamp on an Elastic Anisotropic Half-Space,"
Prikl. Mat. Mekh.
34 (1), 172-178 (1970)
[J. Appl. Math. Mech. (Engl. Transl.)
34 (1), 165-171 (1970)]. |
| 5. | A. O. Vatul'yan,
"On the Rigid Punch Action on an Orthotropic Layer,"
Izv. Akad. Nauk Armyan. SSR. Mekh.
31 (4), 31-42 (1978). |
| 6. | A. O. Vatul'yan and V. V. Krasnikov,
"Vibrations of an Orthotropic Half-Plane with a Curvilinear Crack,"
Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 83-90 (2002)
[Mech. Solids (Engl. Transl.)
37 (5), 68-74 (2002)]. |
| 7. | A. O. Vatul'yan and E. M. Chebakova,
"Fundamental Solutions for Stationary Vibrations of an Orthotropic Elastic Medium,"
Zh. Prikl. Mekh. Tekhn. Fiz.
45 (5), 131-139 (2004)
[J. Appl. Mech. Tech. Phys. (Engl. Transl.)
45 (5), 724-731 (2004)]. |
| 8. | A. O. Vatul'yan and O. A. Belyak,
"Various Methods of Reconstruction of a Cavity in an Orthotropic Layer,"
Zh. Prikl. Mekh. Tekhn. Fiz.
50 (3), 181-189 (2009)
[J. Appl. Mech. Tech. Phys. (Engl. Transl.)
50 (3), 512-518 (2009)]. |
| 9. | H. Ding, W. Chen, and L. Zhang,
Elasticity of Transversely Isotropic Materials
(Springer, Dordrecht, 2006). |
| 10. | D. B. Davtyan and D. A. Pozharskii,
"The Action of a Strip Punch on a Transversely Isotropic Half-Space,"
Prikl. Mat. Mekh.
76 (5), 783-794 (2012)
[J. Appl. Math. Mech. (Engl. Transl.)
76 (5), 558-566 (2012)]. |
| 11. | K. S. Aleksandrov and G. T. Prodaivoda,
Anisotropy of Elastic Properties of Minerals and Rocks
(SO RAN, Moscow, 2000)
[in Russian]. |
| 12. | H. Huntington,
"The Elastic Constants of Crystals. II,"
Usp. Fiz Nauk
74 (3), 461-520 (1961). |
| 13. | Wood handbook: Wood as an Engineering Material
(Forest Products Laboratory, Madison, 1999). |
| 14. | V. I. Fabrikant,
"Nontraditional Contact Problem for Transversely Isotropic Half-Space,"
Quart. J. Mech. Appl.
64 (2), 151-170 (2011). |
| 15. | D. B. Davtyan and D. A. Pozharskii,
"Action of an Elliptic Punch on a Transversally Isotropic Half-Space,"
Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 115-124 (2014)
[Mech. Solids (Engl. Transl.)
49 (5), 578-586 (2014)] |
| 16. | L. A. Galin,
Contact Problems of Elasticity
(Gostekhizdat, Moscow, 1953)
[in Russian]. |
|
| Received |
19 January 2015 |
| Link to Fulltext |
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