Geodesic
Stress concentration in a layered plane with an elliptical cutout
Čebyševskij sbornik, Tome 24 (2023) no. 1, pp. 253-263.

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

The article deals with the problem of stress concentration in an elastic layered plane with an elliptical cutout. The phenomenon is investigated using the concept of stress concentration tensor. Two levels of concentration are studied: because of the layering and because of the cutout. Formulas for the stress concentration tensor components are given separately in the case of an infinite layered plane (first level), as well as in the case of a homogeneous anisotropic plane with an elliptical cutout (second level). Stress concentration tensor in a layered plane with It is represented as a product of concentration tensors at the first and second levels. Approximate formulas for the components of the concentration tensor are given. The case of the coincidence of the orientation of the layers and the main axes of the elliptical hole is considered in detail. In this case, the concentration coefficients at characteristic points are calculated, graphs of the dependence of these coefficients on the ratio of the elastic modulus of the layers are given. In addition, a numerical solution of the problem was carried out using a finite element analysis package. The obtained analytical and numerical results are consistent with good accuracy.
Keywords: mechanics of deformable solids, layered composite, stress concentration. 
@article{CHEB_2023_24_1_a19,
     author = {V. I. Gorbachev and V. V. Nekrasov},
     title = {Stress concentration in a layered plane with an elliptical cutout},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {253--263},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2023_24_1_a19/}
}
TY  - JOUR
AU  - V. I. Gorbachev
AU  - V. V. Nekrasov
TI  - Stress concentration in a layered plane with an elliptical cutout
JO  - Čebyševskij sbornik
PY  - 2023
SP  - 253
EP  - 263
VL  - 24
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2023_24_1_a19/
LA  - ru
ID  - CHEB_2023_24_1_a19
ER  - 
%0 Journal Article
%A V. I. Gorbachev
%A V. V. Nekrasov
%T Stress concentration in a layered plane with an elliptical cutout
%J Čebyševskij sbornik
%D 2023
%P 253-263
%V 24
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2023_24_1_a19/
%G ru
%F CHEB_2023_24_1_a19
V. I. Gorbachev; V. V. Nekrasov. Stress concentration in a layered plane with an elliptical cutout. Čebyševskij sbornik, Tome 24 (2023) no. 1, pp. 253-263. http://geodesic.mathdoc.fr/item/CHEB_2023_24_1_a19/

[1] Feodos'ev V. I., Soprotivlenie materialov, Nauka, M., 1979, 560 pp.

[2] Kirsch E. G., “Die theorie der elastizitat und die bedurfnisse der festigkeitslehre”, Zeitschrift des Vereines Deutscher Ingenieure, 42 (1898), 797–807

[3] Lekhnickij S. G., “Koncentraciya napryazhenij vblizi ellipticheskogo i krugovogo otverstiya v rastyagivaemoj anizotropnoj plastinke”, Vestn. inzh. i tekhn., no. 5

[4] Rabotnov YU. N., Vvedenie v mekhaniku razrusheniya, Nauka, M., 1987

[5] Nejber G., Koncentraciya napryazhenij, OGIZ, M.-L., 1947

[6] Muskhelishvili N.I., Nekotorye osnovnye zadachi matematicheskoj teorii uprugosti, Nauka, M., 1966, 708 pp. | MR

[7] Savin G.N., Raspredelenie napryazhenij okolo otverstij, Naukova dumka, Kiev, 1968, 888 pp. | MR

[8] Savin G.N., Tul'chij V.I., Spravochnik po koncentracii napryazhenij, Vishcha shkola, Kiev, 1976, 412 pp.

[9] Kosmodamianskij A.S., Napryazhennoe sostoyanie anizotropnyh sred s otverstiyami i polostyami, Vishcha shkola, Kiev–Doneck, 1976, 200 pp.

[10] Kishkin B.P., Konstrukcionnaya prochnost' materialov, Izd-vo Mosk. un-ta, M., 1976, 184 pp.

[11] Aleksandrov V.M., Smetanin B.I., Sobol' B.V., Tonkie koncentratory napryazhenij v uprugih telah, Nauka, M., 1993, 224 pp.

[12] Mavlyutov R.R., Koncentraciya napryazhenij v elementah konstrukcij, Nauka, M., 1996, 240 pp.

[13] Lomakin V.A., Teoriya uprugosti neodnorodnyh tel, Izd-vo MGU, M., 1976

[14] Gorbachev V.I., Pobedrya B.E., “Ob uprugom ravnovesii neodnorodnyh polos”, Izvestiya AN SSSR, MTT, 1979, no. 5 | Zbl

[15] Gorbachev V.I., “Operatory koncentracii napryazhenij i deformacij v uprugih telah”, Raschety na prochnost', 30, Mashinostroenie, M., 1989

[16] Gorbachev V. I., Gadelev R. R., “Koncentraciya napryazhenij v uprugih telah s mnozhestvennymi koncentratorami”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 2014, no. 6, 45–50 | Zbl

[17] Gorbachev V.I., Variant metoda osredneniya dlya resheniya kraevyh zadach neodnorodnoj uprugosti, dis. doktora fiziko-matematicheskih nauk: 01.02.04, MGU im. M. V. Lomonosova, M., 1991