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Mathematical and Numerical Simulation of Equilibrium of an Elastic Body Reinforced by a Thin Elastic Inclusion. / Kazarinov, N. A.; Rudoy, E. M.; Slesarenko, V. Yu et al.

In: Computational Mathematics and Mathematical Physics, Vol. 58, No. 5, 01.05.2018, p. 761-774.

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

Harvard

Kazarinov, NA, Rudoy, EM, Slesarenko, VY & Shcherbakov, VV 2018, 'Mathematical and Numerical Simulation of Equilibrium of an Elastic Body Reinforced by a Thin Elastic Inclusion', Computational Mathematics and Mathematical Physics, vol. 58, no. 5, pp. 761-774. https://doi.org/10.1134/S0965542518050111

APA

Kazarinov, N. A., Rudoy, E. M., Slesarenko, V. Y., & Shcherbakov, V. V. (2018). Mathematical and Numerical Simulation of Equilibrium of an Elastic Body Reinforced by a Thin Elastic Inclusion. Computational Mathematics and Mathematical Physics, 58(5), 761-774. https://doi.org/10.1134/S0965542518050111

Vancouver

Kazarinov NA, Rudoy EM, Slesarenko VY, Shcherbakov VV. Mathematical and Numerical Simulation of Equilibrium of an Elastic Body Reinforced by a Thin Elastic Inclusion. Computational Mathematics and Mathematical Physics. 2018 May 1;58(5):761-774. doi: 10.1134/S0965542518050111

Author

Kazarinov, N. A. ; Rudoy, E. M. ; Slesarenko, V. Yu et al. / Mathematical and Numerical Simulation of Equilibrium of an Elastic Body Reinforced by a Thin Elastic Inclusion. In: Computational Mathematics and Mathematical Physics. 2018 ; Vol. 58, No. 5. pp. 761-774.

BibTeX

@article{9796152272c241f1b1985943a09b3e46,
title = "Mathematical and Numerical Simulation of Equilibrium of an Elastic Body Reinforced by a Thin Elastic Inclusion",
abstract = "A boundary value problem describing the equilibrium of a two-dimensional linear elastic body with a thin rectilinear elastic inclusion and possible delamination is considered. The stress and strain state of the inclusion is described using the equations of the Euler–Bernoulli beam theory. Delamination means the existence of a crack between the inclusion and the elastic matrix. Nonlinear boundary conditions preventing crack face interpenetration are imposed on the crack faces. As a result, problem with an unknown contact domain is obtained. The problem is solved numerically by applying an iterative algorithm based on the domain decomposition method and an Uzawa-type algorithm for solving variational inequalities. Numerical results illustrating the efficiency of the proposed algorithm are presented.",
keywords = "delamination crack, domain decomposition method, nonpenetration condition, thin elastic inclusion, Uzawa algorithm, variational inequality",
author = "Kazarinov, {N. A.} and Rudoy, {E. M.} and Slesarenko, {V. Yu} and Shcherbakov, {V. V.}",
note = "Publisher Copyright: {\textcopyright} 2018, Pleiades Publishing, Ltd.",
year = "2018",
month = may,
day = "1",
doi = "10.1134/S0965542518050111",
language = "English",
volume = "58",
pages = "761--774",
journal = "Computational Mathematics and Mathematical Physics",
issn = "0965-5425",
publisher = "PLEIADES PUBLISHING INC",
number = "5",

}

RIS

TY - JOUR

T1 - Mathematical and Numerical Simulation of Equilibrium of an Elastic Body Reinforced by a Thin Elastic Inclusion

AU - Kazarinov, N. A.

AU - Rudoy, E. M.

AU - Slesarenko, V. Yu

AU - Shcherbakov, V. V.

N1 - Publisher Copyright: © 2018, Pleiades Publishing, Ltd.

PY - 2018/5/1

Y1 - 2018/5/1

N2 - A boundary value problem describing the equilibrium of a two-dimensional linear elastic body with a thin rectilinear elastic inclusion and possible delamination is considered. The stress and strain state of the inclusion is described using the equations of the Euler–Bernoulli beam theory. Delamination means the existence of a crack between the inclusion and the elastic matrix. Nonlinear boundary conditions preventing crack face interpenetration are imposed on the crack faces. As a result, problem with an unknown contact domain is obtained. The problem is solved numerically by applying an iterative algorithm based on the domain decomposition method and an Uzawa-type algorithm for solving variational inequalities. Numerical results illustrating the efficiency of the proposed algorithm are presented.

AB - A boundary value problem describing the equilibrium of a two-dimensional linear elastic body with a thin rectilinear elastic inclusion and possible delamination is considered. The stress and strain state of the inclusion is described using the equations of the Euler–Bernoulli beam theory. Delamination means the existence of a crack between the inclusion and the elastic matrix. Nonlinear boundary conditions preventing crack face interpenetration are imposed on the crack faces. As a result, problem with an unknown contact domain is obtained. The problem is solved numerically by applying an iterative algorithm based on the domain decomposition method and an Uzawa-type algorithm for solving variational inequalities. Numerical results illustrating the efficiency of the proposed algorithm are presented.

KW - delamination crack

KW - domain decomposition method

KW - nonpenetration condition

KW - thin elastic inclusion

KW - Uzawa algorithm

KW - variational inequality

UR - http://www.scopus.com/inward/record.url?scp=85048611928&partnerID=8YFLogxK

U2 - 10.1134/S0965542518050111

DO - 10.1134/S0965542518050111

M3 - Article

AN - SCOPUS:85048611928

VL - 58

SP - 761

EP - 774

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 5

ER -

ID: 14047476