@article{SVFU_2016_23_1_a8,
author = {A. M. Khludnev and T. S. Popova},
title = {On the hierarchy of thin delaminated inclusions in elastic bodies},
journal = {Matemati\v{c}eskie zametki SVFU},
pages = {87--107},
year = {2016},
volume = {23},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/SVFU_2016_23_1_a8/}
}
A. M. Khludnev; T. S. Popova. On the hierarchy of thin delaminated inclusions in elastic bodies. Matematičeskie zametki SVFU, Tome 23 (2016) no. 1, pp. 87-107. http://geodesic.mathdoc.fr/item/SVFU_2016_23_1_a8/
[1] Khludnev A. M., Kovtunenko V. A., Analysis of cracks in solids, WIT Press, Southampton; Boston, 2000
[2] Khludnev A. M., Problems of Elasticity Theory in Nonsmooth Domains, Fizmatlit, Moscow, 2010
[3] Kovtunenko V. A., “Invariant energy integrals for the nonlinear crack problem with possible contact of coasts”, Appl. Math. Mech., 67:1 (2003), 109–123 | MR | Zbl
[4] Kovtunenko V. A., “Primal-dual methods of shape sensitivity analysis for curvilinear cracks with nonpenetration”, IMA J. Appl. Math., 71:5 (2006), 635–657 | DOI | MR | Zbl
[5] Knees D., Mielke A., “Energy release rate for cracks in finite-strain elasticity”, Math. Methods Appl. Sci., 31:5 (2008), 501–518 | DOI | MR
[6] Knees D., Schroder A., “Global spatial regularity for elasticity models with cracks, contact and other nonsmooth constraints”, Math. Methods Appl. Sci., 35:15 (2012), 1859–1884 | DOI | MR | Zbl
[7] Rudoyi E. M., “The Griffits formula and Cherepanov–Rise integral for plate with a rigid inclision and crack”, Vestn. Novosib. Gos. Univ., Ser. Mat., Mekh., and Inform., 10:2 (2010), 98–117
[8] Rudoyi E. M., “Asymptotics of energy functional for three-dimentional body with a rigid inclusion and crack”, Appl. Mech. and Techn. Phys., 52:2 (2011), 114–127 | MR
[9] Lazarev N. P., “The problem of equilibrium of a shallow Timoshenko shell containing a solid crack”, Sib. J. Industr. Math., 15:3 (2012), 58–69 | Zbl
[10] Lazarev N. P., Rudoy E. M., “Shape sensitivity analysis of Timoshenko's plate with a crack under the nonpenetration condition”, Z. Angew. Math. Mech., 94 (2014), 730–739 | DOI | MR | Zbl
[11] Sokolowski Y. and Khludnev A. M., “On derivative of energy functional on the crack length in problems of theory of elasticity”, Appl. Math. and Mech., 64:3 (2000), 464–475
[12] Khludnev A. M, “A problem on a crack on the boundary of a rigid inclusion in the elastic plate”, Izv. Akad. Nauk, Solid Mechanics, 2010, no. 5, 98–110
[13] Khludnev A. M., Negri M., “Crack on the boundary of a thin elastic inclusion inside an elastic body”, Z. Angew. Math. Mech., 92:5 (2012), 341–354 | DOI | MR | Zbl
[14] Khludnev A. M., “Thin rigid inclusions with delaminations in elastic plates”, Eur. J. Mech., A, Solids., 32 (2012), 69–75 | DOI | MR | Zbl
[15] Itou H., Khludnev A. M., Rudoy E. M., Tani A., “Asymptotic behaviour at a tip of a rigid line inclusion in linearized elasticity”, Z. Angew. Math. Mech., 92:9 (2012), 716–730 | DOI | MR | Zbl
[16] Khludnev A. M., Leugering G., “On elastic bodies with thin rigid inclusions and cracks”, Math. Methods Appl. Sci., 33:16 (2010), 1955–1967 | MR | Zbl
[17] Khludnev A. M., Leugering G. R., “Delaminated thin elastic inclusion inside elastic bodies”, Math. Mech. Complex Systems, 2:1 (2014), 1–21 | DOI | MR | Zbl
[18] Khludnev A.M., Leugering G. R., “On Timoshenko thin elastic inclusions inside elastic bodies”, Math. Mech. Solids, 20:5 (2015), 495–511 | DOI | MR | Zbl
[19] Itou H., Khludnev A. M., “On delaminated thin Timoshenko inclusions inside elastic bodies”, Math. Methods Appl. Sci., 39:17 (2016), 4980–4993 | DOI | MR | Zbl
[20] Shcherbakov V. V., “Excistence of the optimal form of thin rigid inclusions in a Kiekhgoff–Lyav plate”, Sib. J. Industr. Math., 16:4 (2013), 142–151 | MR
[21] Khludnev A. M., “Thin rigid inclusions with delaminations in elastic plates”, Eur. J. Mech., A, Solids, 32 (2012), 69–75 | DOI | MR | Zbl
[22] Khludnev A. M., Leugering G., “Optimal control of cracks in elastic bodies with thin rigid inclusions”, Z. Angew. Math. Mech., 91:2 (2011), 125–137 | DOI | MR | Zbl
[23] Khludnev A. M., “Singular invariant integrals for elastic body with delaminated thin elastic inclusion”, Quart. Appl. Math., 72:4 (2014), 719–730 | DOI | MR | Zbl
[24] Lazarev N. P., “Shape sensitivity analysis of the energy integrals for the Timoshenko-type plate containing a crack on the boundary of a rigid inclusion”, Z. Angew. Math. Phys., 66:4 (2015), 2025–2040 | DOI | MR | Zbl
[25] Khludnev A. M., “Thin inclusions in elastic bodies crossing an external boundary”, Z. Angew. Math. Mech., 95:11 (2015), 1256–1267 | DOI | MR | Zbl
[26] Grisvard P., Singularities in boundary value problems, Springer-Verl., Masson, 1992 | MR | Zbl
[27] Morozov N. F., Mathamatical theory of cracks, Nauka, Moscow, 1984 | MR
[28] Bessoud A.-L., Krasucki F., Serpilli M., “Plate-like and shell-like inclusions with high rigidity”, C. R. Math., 346 (2008), 697–702 | DOI | MR | Zbl
[29] Bessoud A.-L., Krasucki F., Michaille G., “Multi-materials with strong interface: Variational modelings”, Asymptotic Anal., 61:1 (2009), 1–19 | MR | Zbl
[30] Pasternak I. M., “Plane problem of elasticity theory for anisotropic bodies with thin elastic inclusions”, J. Math. Sci., 186:1 (2012), 31–47 | DOI | MR
[31] Kozlov V. A., Maz'ya V. G., Movchan A. B., Asymptotic analysis of fields in a multi-structure, Oxford Math. Monogr., Oxford Univ. Press, New York, 1999 | MR
[32] Vynnytska L., Savula Y., “Mathematical modeling and numerical analysis of elastic body with thin inclusion”, Comput. Mech., 50:5 (2004), 533–542 | DOI | MR
[33] Neustroeva N. V., “A rigid inclusion in the contact problems for elastic plates”, Sib. J. Industr. Math., 12:4 (2009), 92–105 | MR | Zbl
[34] Neustroeva N. V., “Unilateral contact of elastic plates with a rigid indlusion”, Vestn. Novosib. State Univ., Ser. Math., Mech., and Inform., 9:4 (2009), 51–64 | Zbl
[35] Rotanova T. A., ““On statements and the solvability of problems on the contact of two plates containing rigid inclusions”, Sib. J. Industr. Math., 15:2 (2012), 107–118 | MR | Zbl
[36] Vol'mir A. S., Nonlinear dynamics of plates and shells, Nauka, Moscow, 1972 | MR
[37] Khlufnev A. M., “Weakly curved inclusion in an elastic body in the presence of delamination”, Izv. Akad. Nauk, Solid Mechanics, 2015, no. 5, 131–144