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On modeling elastic bodies with defects. / Khludnev, Alexandr Mikhailovich.

In: Сибирские электронные математические известия, Vol. 15, 01.01.2018, p. 153-166.

Research output: Contribution to journal › Article › peer-review

Harvard

Khludnev, AM 2018, 'On modeling elastic bodies with defects', Сибирские электронные математические известия, vol. 15, pp. 153-166. https://doi.org/10.17377/semi.2018.15.015

APA

Khludnev, A. M. (2018). On modeling elastic bodies with defects. Сибирские электронные математические известия, 15, 153-166. https://doi.org/10.17377/semi.2018.15.015

Vancouver

Khludnev AM. On modeling elastic bodies with defects. Сибирские электронные математические известия. 2018 Jan 1;15:153-166. doi: 10.17377/semi.2018.15.015

Author

Khludnev, Alexandr Mikhailovich. / On modeling elastic bodies with defects. In: Сибирские электронные математические известия. 2018 ; Vol. 15. pp. 153-166.

BibTeX

@article{61a0d0a970324877a030f6eb4d0620eb,
title = "On modeling elastic bodies with defects",
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 = "Damage parameter, Defect, Derivative of energy functional, Non-penetration boundary conditions, Optimal control, Variational inequality",
author = "Khludnev, {Alexandr Mikhailovich}",
year = "2018",
month = jan,
day = "1",
doi = "10.17377/semi.2018.15.015",
language = "English",
volume = "15",
pages = "153--166",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",

}

RIS

TY - JOUR

T1 - On modeling elastic bodies with defects

AU - Khludnev, Alexandr Mikhailovich

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - Damage parameter

KW - Defect

KW - Derivative of energy functional

KW - Non-penetration boundary conditions

KW - Optimal control

KW - Variational inequality

UR - http://www.scopus.com/inward/record.url?scp=85045711912&partnerID=8YFLogxK

U2 - 10.17377/semi.2018.15.015

DO - 10.17377/semi.2018.15.015

M3 - Article

AN - SCOPUS:85045711912

VL - 15

SP - 153

EP - 166

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -

ID: 12690618