Geodesic
A certain approach to solving of some one-dimensional contact problems
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 1, pp. 77-84 
M. A. Osipenko; Yu. I. Nyashin. A certain approach to solving of some one-dimensional contact problems. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 1, pp. 77-84. http://geodesic.mathdoc.fr/item/ISU_2011_11_1_a9/
@article{ISU_2011_11_1_a9,
     author = {M. A. Osipenko and Yu. I. Nyashin},
     title = {A certain approach to solving of some one-dimensional contact problems},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {77--84},
     year = {2011},
     volume = {11},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2011_11_1_a9/}
}
TY  - JOUR
AU  - M. A. Osipenko
AU  - Yu. I. Nyashin
TI  - A certain approach to solving of some one-dimensional contact problems
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2011
SP  - 77
EP  - 84
VL  - 11
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ISU_2011_11_1_a9/
LA  - ru
ID  - ISU_2011_11_1_a9
ER  - 
%0 Journal Article
%A M. A. Osipenko
%A Yu. I. Nyashin
%T A certain approach to solving of some one-dimensional contact problems
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2011
%P 77-84
%V 11
%N 1
%U http://geodesic.mathdoc.fr/item/ISU_2011_11_1_a9/
%G ru
%F ISU_2011_11_1_a9

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper deals with the problems of the unbonded contact of beams, strings, circular membranes and plates. A new approach to solving of such problems is suggested. This approach includes the rigorous problem statement, the elementary proof of the uniqueness of solution and the analytical solution construction method. The method is based on the iterative correction of the contact region. A number of examples of this method application are given.

[1] Rabotnov Yu. N., Mekhanika deformiruemogo tverdogo tela, Nauka, M., 1988, 711 pp. | Zbl

[2] Dyuvo Zh., Lions Zh.-L., Neravenstva v mekhanike i fizike, Nauka, M., 1980, 383 pp. | MR

[3] Kravchuk A. S., Variatsionnye i kvazivariatsionnye neravenstva v mekhanike, Izd-vo MGAPI, M., 1997, 340 pp.

[4] Feodosev V. I., Izbrannye zadachi i voprosy po soprotivleniyu materialov, Nauka, M., 1973, 400 pp.

[5] Grigolyuk E. I., Tolkachev V. M., Kontaktnye zadachi teorii plastin i obolochek, Mashinostroenie, M., 1980, 415 pp.

[6] Nyashin Yu. I., Osipenko M. A., Rudakov R. N., “K teorii izgiba listovoi ressory”, Izv. RAN. MTT, 2002, no. 6, 134–143

[7] Osipenko M. A., “Ob odnoi kontaktnoi zadache dlya sistemy strun”, Vest. PGTU. Ser. Prikladnaya matematika i mekhanika, 2005, no. 1, 82–86

[8] Li H., Dempsey J. P., “Unbonded Contact of Finite Timoshenko Beam on Elastic Layer”, J. of Engineering Mechanics, 114:7 (1988), 1265–1284

[9] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Izd-vo MGU, M., 1999, 798 pp. | MR