Equilibrium problems for elastic body with a crack and thin conjugated inclusions
Dalʹnevostočnyj matematičeskij žurnal, Tome 24 (2024) no. 1, pp. 73-95.

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

An equilibrium problem for an elastic body is considered. It is assumed that the body has crack which junction the thin inclusion at a given point. We analyze a conjugate conditions parts of thin inclusion. Inequality type boundary conditions are considered at the crack faces to prevent a mutual penetration between the faces. Existence of solutions is proved. Equivalent problem formulations are discussed. The passage to the limit under stiffness parameter of thin inclusions to infinity.
@article{DVMG_2024_24_1_a7,
     author = {N. A. Nikolaeva},
     title = {Equilibrium problems for elastic body with a crack and thin conjugated inclusions},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {73--95},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2024_24_1_a7/}
}
TY  - JOUR
AU  - N. A. Nikolaeva
TI  - Equilibrium problems for elastic body with a crack and thin conjugated inclusions
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2024
SP  - 73
EP  - 95
VL  - 24
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2024_24_1_a7/
LA  - ru
ID  - DVMG_2024_24_1_a7
ER  - 
%0 Journal Article
%A N. A. Nikolaeva
%T Equilibrium problems for elastic body with a crack and thin conjugated inclusions
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2024
%P 73-95
%V 24
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2024_24_1_a7/
%G ru
%F DVMG_2024_24_1_a7
N. A. Nikolaeva. Equilibrium problems for elastic body with a crack and thin conjugated inclusions. Dalʹnevostočnyj matematičeskij žurnal, Tome 24 (2024) no. 1, pp. 73-95. http://geodesic.mathdoc.fr/item/DVMG_2024_24_1_a7/

[1] Mettyuz F., Rolings R., Kompozitnye materialy. Mekhanika i tekhnologiya, Tekhnosfera, M., 2004

[2] Solomonov Yu. S., Georgievskii V. P., Nedbai A. Ya., Andryushin V. A., Prikladnye zadachi mekhaniki kompozitnykh tsilindricheskikh obolochek, Fizmatlit, M., 2014

[3] Khludnev A. M., Kovtunenko V. A., Analysis of Cracks in Solids, WIT Press, Southampton-Boston, 2000

[4] Khludnev A. M., Zadachi teorii uprugosti v negladkikh oblastyakh., Fizmatlit, M., 2010

[5] Khludnev A. M., Leugering G., “On elastic bodies with thin rigid inclusions and cracks”, Math. Meth. Appl. Sci., 33:16 (2010), 1955–1967 | MR | Zbl

[6] Lazarev N. P., “Zadacha o ravnovesii plastiny Timoshenko, soderzhaschei treschinu vdol tonkogo zhestkogo vklyucheniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki., 1 (2014), 32–45 | Zbl

[7] Fankina I. V., “Kontaktnaya zadacha dlya uprugoi plastiny s tonkim zhestkim vklyucheniem”, Sib. zhurn. industr. matem., 19:3 (2016), 90–98 | MR | Zbl

[8] Scherbakov V. V., “Ob odnoi zadache upravleniya formoi tonkikh vklyuchenii v uprugikh telakh”, Sib. zhurn. industr. matem., 16:1 (2013), 138–147

[9] Furtsev A. I., “O kontakte tonkogo prepyatstviya i plastiny, soderzhaschei tonkoe vklyuchenie”, Sib. zhurn. chist. i prikl. matem., 17:4 (2017), 94–111 | MR | Zbl

[10] Namm R. V., Tsoy G. I., “Solution of a contact elasticity problem with a rigid inclusion”, Computational Mathematics and Mathematical Physics, 59:4 (2019), 659–666 | DOI | MR | Zbl

[11] Popova T. S., “Zadachi o tonkikh vklyucheniyakh v dvumernom vyazkouprugom tele”, Sib. zhurn. industr. matem., 21:2 (2018), 66–78 | Zbl

[12] Nikolaeva N. A., “O ravnovesii uprugikh tel s treschinami, peresekayuschimi tonkie vklyucheniya”, Sib. zhurn. industr. matem., 22:4 (2019), 68–80

[13] Nikolaeva N., “The conjugation thin inclusions problem in elastic bodies with crack”, Journal of Physics: Conference Series, 1666:1 (2020), 012038 | DOI

[14] Khludnev A. M., “Equilibrium of an elastic body with closely spaced thin inclusions”, Comp. Math. Math. Phys., 58 (2018), 1660–1672 | DOI | MR | Zbl

[15] Faella L., Khludnev A. M., “Junction problem for elastic and rigid inclusions in elastic bodies”, Mathematical Methods in the Applied Sciences, 39:12 (2016) | DOI | MR | Zbl

[16] Nikolaeva N. A., “Plastina Kirkhgofa–Lyava s ploskim zhestkim vklyucheniem”, Chelyab. fiz.-matem. zhurn., 8:1 (2023), 29–46 | Zbl

[17] Khludnev A. M., Leugering G., “Delaminated thin elastic inclusion inside elastic bodies”, Math. Mech. Complex Systems., 2:1 (2014), 1–21 | DOI | MR | Zbl

[18] Khludnev A. M., “On modeling thin inclusions in elastic bodies with a damage parameter”, Math. Mech. Solids \ | DOI | MR

[19] Khludnev A. M., Popova T. S., “Ob ierarkhii tonkikh vklyuchenii v uprugikh telakh”, Matematicheskie zametki SVFU, 23:1 (2016), 87–107 | Zbl

[20] Khludnev A. M., Popova T. S., “Junction problem for Euler–Bernoulli and Timoshenko elastic inclusions in elastic bodies”, Quart. Appl. Math., 74 (2016), 705–718 | DOI | MR | Zbl

[21] Khludnev A. M., Popova T. S., “Zadacha sopryazheniya uprugogo vklyucheniya Timoshenko i poluzhestkogo vklyucheniya”, Matematicheskie zametki SVFU, 25:1 (2018), 73–89 | Zbl

[22] Khludnev A. M., Faella L., Popova T. S., “Junction problem for rigid and Timoshenko elastic inclusions in elastic bodies”, Mathematics and Mechanics of Solids, 22:4 (2017), 1–14 | DOI | MR

[23] Rudoy E. M., Lazarev N. P., “Domain decomposition technique for a model of an elastic body reinforced by a Timoshenko’s beam”, Journal of Computational and Applied Mathematics, 334 (2018), 18–26 | DOI | MR | Zbl

[24] Morozov N. F., Matematicheskie voprosy teorii treschin, Nauka, M., 1984

[25] Samarskii A. A., Andreev V. B., Raznostnye metody dlya ellipticheskikh uravnenii, Nauka, M., 1976 | MR

[26] Boerquin F., Ciarlet P. G., “Modeling and justification of eigenvalue problems for junctions between elastic structures”, J. Functional Analysis, 87 (1989), 392–427 | DOI | MR

[27] Gaudiello A., Monneau R., Mossino J., al. et., “Junctions of elastic plates and beams”, J. Control Optimisation and Calculus of Variations, 13:3 (2007), 419–457 | DOI | MR | Zbl

[28] Dret H. Le, “Modeling of the junction between two rods”, J. Math. Pures Appl., 68:3 (1989), 365–397 | MR | Zbl

[29] Bogan Yu. A., “Ob usloviyakh sopryazheniya A. A. Samarskogo i V. B. Andreeva v teorii uprugikh balok”, Matem. zametki, 92:5 (2012), 662–669 | DOI | MR | Zbl

[30] Berezhnitskii L. T., Panasyuk V. V., Staschuk N. G., “Vzaimodeistvie zhestkikh lineinykh vklyuchenii i treschin v deformiruemom tele”, Raznostnye metody dlya ellipticheskikh uravnenii, Nauk. dumka, Kiev, 1983

[31] Mochalov E. V., Silvestrov V. V., “Zadacha vzaimodeistviya tonkikh zhestkikh ostrokonechnykh vklyuchenii, raspolozhennykh mezhdu raznymi uprugimi materialami”, Izv. RAN. MTT, 5 (2011), 99–117

[32] Mkhitaryan S. M., “O napryazhennom sostoyanii uprugoi beskonechnoi plastiny s konechnoi treschinoi, vzaimodeistvuyuschei s absolyutno zhestkim tonkim vklyucheniem”, Doklady NAN RA, 118:1 (2018), 39–48 | MR

[33] Bogan Yu. A., “Osrednenie neodnorodnoi uprugoi balki pri sopryazhenii elementov sharnirom konechnoi zhestkosti”, Sib. zhurn. industr. matem., 1:2 (1998), 67–72 | MR | Zbl

[34] Durante T., Nazarov S. A., Kardone Dzh., “Modelirovanie sochlenenii plastin i sterzhnei posredstvom samosopryazhennykh rasshirenii”, Vestnik SPbGU, 1:2 (2009), 3–14

[35] Zhiltsov A. V., Namm R. V., “Ustoichivyi algoritm resheniya polukoertsitivnoi zadachi kontakta dvukh tel s treniem na granitse”, Dalnevost. matem. zhurn., 19:2 (2019), 173–-184 | MR | Zbl

[36] Khludnev A. M., Popova T. S., “Semirigid inclusions in elastic bodies: Mechanical interplay and optimal control”, Comp. Math. Appl., 77 (2019), 253–262 | DOI | MR | Zbl