Transfer function calculation for the Poincaré–Steklov operator in the case of a functionally gradient elastic strip
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2023), pp. 52-60 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A boundary value problem is considered in a functionally graded elastic strip. A three-term asymptotic expansion of a transfer function is obtained for the Poincaré–Steklov operator that maps normal stresses to normal displacements on a part of a strip boundary. Padé approximations are determined for the obtained asymptotic series. An approach to computing the transfer function using the asymptotic series and the Padé approximations is proposed, which reduces computational costs.
@article{VMUMM_2023_5_a7,
     author = {A. A. Bobylev},
     title = {Transfer function calculation for the {Poincar\'e{\textendash}Steklov} operator in the case of a functionally gradient elastic strip},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {52--60},
     year = {2023},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2023_5_a7/}
}
TY  - JOUR
AU  - A. A. Bobylev
TI  - Transfer function calculation for the Poincaré–Steklov operator in the case of a functionally gradient elastic strip
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2023
SP  - 52
EP  - 60
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2023_5_a7/
LA  - ru
ID  - VMUMM_2023_5_a7
ER  - 
%0 Journal Article
%A A. A. Bobylev
%T Transfer function calculation for the Poincaré–Steklov operator in the case of a functionally gradient elastic strip
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2023
%P 52-60
%N 5
%U http://geodesic.mathdoc.fr/item/VMUMM_2023_5_a7/
%G ru
%F VMUMM_2023_5_a7
A. A. Bobylev. Transfer function calculation for the Poincaré–Steklov operator in the case of a functionally gradient elastic strip. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2023), pp. 52-60. http://geodesic.mathdoc.fr/item/VMUMM_2023_5_a7/

[1] Saleh B., Jiang J., Fathi R., Al-hababi T., Xu Q., Wang L., Song Dan., Ma A., “30 Years of functionally graded materials: An overview of manufacturing methods. Applications and Future Challenges”, Composites. Part B: Engineering, 201 (2020), 108376 | DOI

[2] Aleksandrov V.M., Mkhitaryan S.M., Kontaktnye zadachi dlya tel s tonkimi pokrytiyami i prosloikami, Nauka, M., 1963

[3] Barber J.R., Contact Mechanics, Springer, Cham, 2018 | MR | Zbl

[4] Goryacheva I.G., Mekhanika friktsionnogo vzaimodeistviya, Nauka, M., 2001

[5] Torskaya E.V., Modeli friktsionnogo vzaimodeistviya tel s pokrytiyami, In-t kompyuternykh issledovanii, M.–Izhevsk, 2020

[6] Bobylev A.A., “Algoritm resheniya zadach diskretnogo kontakta dlya uprugoi polosy”, Prikl. matem. i mekhan, 86:3 (2022), 404–423 | Zbl

[7] Bobylev A.A., Belashova I.S., “Chislennoe reshenie ploskikh kontaktnykh zadach dlya uprugikh tel s funktsionalno-gradientnymi pokrytiyami”, Nelineinyi mir, 11:10 (2013), 689–695

[8] Vatulyan A.O., Plotnikov D.K., “K issledovaniyu kontaktnoi zadachi dlya neodnorodnoi uprugoi polosy”, Prikl. matem. i mekhan, 85:3 (2021), 283–293

[9] Vorovich I.I., Aleksandrov V.M., Babeshko V.A., Neklassicheskie smeshannye zadachi teorii uprugosti, Nauka, M., 1974

[10] Nikishin V.S., “Staticheskie kontaktnye zadachi dlya mnogosloinykh uprugikh tel”, Mekhanika kontaktnykh vzaimodeistvii, FIZMATLIT, M., 2001, 212–233

[11] Aizikovich S.M., Aleksandrov V.M., Belokon A.V., Krenev L.I., Trubchik I.S., Kontaktnye zadachi teorii uprugosti dlya neodnorodnykh sred, FIZMATLIT, M., 2006

[12] Babeshko V.A., Glushkov E.V., Glushkova N.V., “Metody postroeniya matrits Grina dlya stratifitsirovannogo uprugogo poluprostranstva”, Zhurn. vychisl. matem. i matem. fiz, 27:1 (1987), 93–101 | MR | Zbl

[13] Bobylev A.A., “Chislennoe postroenie transformanty yadra integralnogo predstavleniya operatora Puankare–Steklova dlya uprugoi polosy”, Differents. uravneniya, 59:1 (2023), 115–129 | MR | Zbl

[14] Vishik M.I., Lyusternik L.A., “Regulyarnoe vyrozhdenie i pogranichnyi sloi dlya lineinykh differentsialnykh uravnenii s malym parametrom”, Uspekhi matem. nauk, 12:5 (1957), 3–122 | Zbl

[15] Beiker Dzh., ml., Greivs-Morris P., Approksimatsiya Pade, Mir, M., 1986 | MR