E. M. Rudoǐ, “Invariant integrals in the plane elasticity problem for bodies with rigid inclusions and cracks”, Sib. Zh. Ind. Mat., 15:1 (2012), 99–109; J. Appl. Industr. Math., 6:3 (2012), 371

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Sibirskii Zhurnal Industrial'noi Matematiki, 2012, Volume 15, Number 1, Pages 99–109 (Mi sjim714)

This article is cited in 11 scientific papers (total in 11 papers)

Invariant integrals in the plane elasticity problem for bodies with rigid inclusions and cracks

E. M. Rudoĭ^ab

^a Lavrent'ev Institute of Hydrodynamics SB RAS, Novosibirsk, RUSSIA
^b Novosibirsk State University, Novosibirsk, RUSSIA

Full-text PDF (266 kB) Citations (11)

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Abstract: We consider the plane elasticity problem for a body with a rigid inclusion and a crack along the boundary between the elastic matrix and rigid inclusion. We show that this problem possesses $J$- and $M$-invariant integrals. In particular, we construct an invariant integral of Cherepanov–Rice type for straight cracks.

Keywords: invariant integrals, rigid inclusion, crack, derivative of the energy functional, Cherepanov–Rice integral.

Received: 21.01.2011

English version:
Journal of Applied and Industrial Mathematics, 2012, Volume 6, Issue 3, Pages 371–380
DOI: https://doi.org/10.1134/S199047891203012X

Bibliographic databases:

Document Type: Article

UDC: 539.375

Language: Russian

Citation: E. M. Rudoǐ, “Invariant integrals in the plane elasticity problem for bodies with rigid inclusions and cracks”, Sib. Zh. Ind. Mat., 15:1 (2012), 99–109; J. Appl. Industr. Math., 6:3 (2012), 371–380

Citation in format AMSBIB

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\pages 99--109

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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3112337}

\transl

\jour J. Appl. Industr. Math.

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\vol 6

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\pages 371--380

\crossref{https://doi.org/10.1134/S199047891203012X}

Linking options:

https://www.mathnet.ru/eng/sjim714

https://www.mathnet.ru/eng/sjim/v15/i1/p99

This publication is cited in the following 11 articles:

Zhiming Hu, Xin Feng, Xiang Mu, Gan Song, Liangliang Zhang, Yang Gao, “Eshelby tensors and effective stiffness of one-dimensional orthorhombic quasicrystal composite materials containing ellipsoidal particles”, Arch Appl Mech, 93:8 (2023), 3275
Furtsev A., Itou H., Rudoy E., “Modeling of Bonded Elastic Structures By a Variational Method: Theoretical Analysis and Numerical Simulation”, Int. J. Solids Struct., 182 (2020), 100–111
V. A. Puris, “The conjugation problem for thin elastic and rigid inclusions in an elastic body”, J. Appl. Industr. Math., 11:3 (2017), 444–452
E. Rudoy, “On numerical solving a rigid inclusions problem in 2D elasticity”, ZAMM Z. Angew. Math. Phys., 68:1 (2017), 19
E. M. Rudoy, “Numerical solution of an equilibrium problem for an elastic body with a delaminated thin rigid inclusion”, J. Appl. Industr. Math., 10:2 (2016), 264–276
E. M. Rudoy, “First-order and second-order sensitivity analyses for a body with a thin rigid inclusion”, Math. Meth. Appl. Sci., 39:17 (2016), 4994–5006
V. V. Shcherbakov, “The Griffith formula and $J$-integral for elastic bodies with Timoshenko inclusions”, ZAMM Z. Angew. Math. Mech., 96:11 (2016), 1306–1317
E. M. Rudoy, V. V. Shcherbakov, “Domain decomposition method for a membrane with a delaminated thin rigid inclusion”, Sib. Electron. Math. Rep., 13 (2016), 395–410
V. V. Shcherbakov, “Existence of an optimal shape for thin rigid inclusions in the Kirchhoff–Love plate”, J. Appl. Industr. Math., 8:1 (2014), 97–105
Lazarev N.P., “Equilibrium Problem for a Timoshenko Plate with an Oblique Crack”, J. Appl. Mech. Tech. Phys., 54:4 (2013), 662–671
N. P. Lazarev, “Invariantnye integraly v zadache o ravnovesii plastiny Timoshenko s usloviyami tipa Sinorini na treschine”, Vestn. SamGU. Estestvennonauchn. ser., 2013, no. 6(107), 100–115

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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