Equilibrium of an Elastic Body with Closely Spaced Thin Inclusions

A. M. Khludnev

doi:10.1134/S096554251810007X

Equilibrium of an Elastic Body with Closely Spaced Thin Inclusions

A. M. Khludnev

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

1 Citation (Scopus)

Abstract

Abstract: Problems with unknown boundaries describing an equilibrium of two-dimensional elastic bodies with two thin closely spaced inclusions are considered. The inclusions are in contact with each other, which means that there is a crack between them. On the crack faces, nonlinear boundary conditions of the inequality type that prevent the interpenetration of the faces are set. The unique solvability of the problems is proved. The passages to the limit as the stiffness parameter of thin inclusions tends to infinity are studied, and limiting models are analyzed.

Original language	English
Pages (from-to)	1660-1672
Number of pages	13
Journal	Computational Mathematics and Mathematical Physics
Volume	58
Issue number	10
DOIs	https://doi.org/10.1134/S096554251810007X
Publication status	Published - 1 Oct 2018

Keywords

boundary conditions of mutual nonpenetration
crack
limiting models
stiffness of inclusion
thin inclusion
CONTACT
CRACK
ASYMPTOTIC-BEHAVIOR
SHAPE SENSITIVITY-ANALYSIS
ENERGY INTEGRALS
BODIES
BOUNDARY
NONPENETRATION
PLATE
RIGID INCLUSION

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title = "Equilibrium of an Elastic Body with Closely Spaced Thin Inclusions",

abstract = "Abstract: Problems with unknown boundaries describing an equilibrium of two-dimensional elastic bodies with two thin closely spaced inclusions are considered. The inclusions are in contact with each other, which means that there is a crack between them. On the crack faces, nonlinear boundary conditions of the inequality type that prevent the interpenetration of the faces are set. The unique solvability of the problems is proved. The passages to the limit as the stiffness parameter of thin inclusions tends to infinity are studied, and limiting models are analyzed.",

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author = "Khludnev, {A. M.}",

year = "2018",

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AU - Khludnev, A. M.

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N2 - Abstract: Problems with unknown boundaries describing an equilibrium of two-dimensional elastic bodies with two thin closely spaced inclusions are considered. The inclusions are in contact with each other, which means that there is a crack between them. On the crack faces, nonlinear boundary conditions of the inequality type that prevent the interpenetration of the faces are set. The unique solvability of the problems is proved. The passages to the limit as the stiffness parameter of thin inclusions tends to infinity are studied, and limiting models are analyzed.

AB - Abstract: Problems with unknown boundaries describing an equilibrium of two-dimensional elastic bodies with two thin closely spaced inclusions are considered. The inclusions are in contact with each other, which means that there is a crack between them. On the crack faces, nonlinear boundary conditions of the inequality type that prevent the interpenetration of the faces are set. The unique solvability of the problems is proved. The passages to the limit as the stiffness parameter of thin inclusions tends to infinity are studied, and limiting models are analyzed.

KW - boundary conditions of mutual nonpenetration

KW - crack

KW - limiting models

KW - stiffness of inclusion

KW - thin inclusion

KW - CONTACT

KW - CRACK

KW - ASYMPTOTIC-BEHAVIOR

KW - SHAPE SENSITIVITY-ANALYSIS

KW - ENERGY INTEGRALS

KW - BODIES

KW - BOUNDARY

KW - NONPENETRATION

KW - PLATE

KW - RIGID INCLUSION

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