A. M. Khludnev, “On modeling elastic bodies with defects”, Sib. Èlektron. Mat. Izv., 15 (2018), 153

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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2018, Volume 15, Pages 153–166
DOI: https://doi.org/10.17377/semi.2018.15.015 (Mi semr906)

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

Differentical equations, dynamical systems and optimal control

On modeling elastic bodies with defects

A. M. Khludnev^ab

^a Lavrentyev Institute of Hydrodynamics of SB RAS pr. Lavrentieva, 15, 630090, Novosibirsk, Russia
^b Novosibirsk State University, Pirogova str., 1, 630090, Novosibirsk, Russia

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DOI: https://doi.org/10.17377/semi.2018.15.015

Abstract: The paper concerns a mathematical analysis of equilibrium problems for 2D elastic bodies with thin defects. The defects are characterized with a damage parameter. A presence of defects implies that the problems are formulated in a nonsmooth domain with a cut. Nonlinear boundary conditions at the cut faces are considered to prevent a mutual penetration between the faces. Weak and strong formulations of the problems are analyzed. The paper provides an asymptotic analysis with respect to the damage parameter. We obtain invariant integrals over curves surrounding the defect tip. An optimal control problem is investigated with a cost functional equal to the derivative of the energy functional with respect to the defect length, and the damage parameter being a control function.

Keywords: defect, damage parameter, non-penetration boundary conditions, variational inequality, optimal control, derivative of energy functional.

Received December 29, 2017, published February 15, 2018

Bibliographic databases:

Document Type: Article

UDC: 517.958,539.3

MSC: 35Q74,35Q93

Language: English

Citation: A. M. Khludnev, “On modeling elastic bodies with defects”, Sib. Èlektron. Mat. Izv., 15 (2018), 153–166

Citation in format AMSBIB

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\paper On modeling elastic bodies with defects

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\pages 153--166

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Linking options:

https://www.mathnet.ru/eng/semr906

https://www.mathnet.ru/eng/semr/v15/p153

This publication is cited in the following 11 articles:

E. V. Pyatkina, “Ravnovesie trekhsloinoi plastiny s treschinoi”, Sib. zhurn. industr. matem., 25:1 (2022), 105–120
E. M. Rudoy, “Asymptotic modelling of bonded plates by a soft thin adhesive layer”, Sib. elektron. matem. izv., 17 (2020), 615–625
E. V. Pyatkina, “A contact of two elastic plates connected along a thin rigid inclusion”, Sib. elektron. matem. izv., 17 (2020), 1797–1815
A. M. Khludnev, “Inverse problem for elastic body with thin elastic inclusion”, J. Inverse Ill-Posed Probl., 28:2 (2020), 195–209
I. V. Frankina, “on the Equilibrium Problem For a Two-Layer Structure With the Upper Layer Covering a Defect Tip”, Sib. Electron. Math. Rep., 17 (2020), 141–160
A. Furtsev, H. Itou, E. Rudoy, “Modeling of bonded elastic structures by a variational method: theoretical analysis and numerical simulation”, Int. J. Solids Struct., 182 (2020), 100–111
I. V. Fankina, “O ravnovesii dvusloinoi konstruktsii pri nalichii defekta”, Sib. elektron. matem. izv., 16 (2019), 959–974
E. V. Pyatkina, “Zadacha o skleike dvukh plastin Kirkhgofa–Lyava”, Sib. elektron. matem. izv., 16 (2019), 1351–1374
A. I. Furtsev, “A contact problem for a plate and a beam in presence of adhesion”, J. Appl. Industr. Math., 13:2 (2019), 208–218
A. Khludnev, “On thin timoshenko inclusions in elastic bodies with defects”, Arch. Appl. Mech., 89:8 (2019), 1691–1704
A. M. Khludnev, “On thin inclusions in elastic bodies with defects”, Z. Angew. Math. Phys., 70:2 (2019), 45

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

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