Joint deformation of a circular inclusion and a matrix

Research output

5 Citations (Scopus)

Abstract

An elastic infinite plane with a circular inclusion at specified tractions and displacements jumps along the interface and under nonzero conditions at infinity is considered. Explicit expressions are derived for Goursat-Kolosov's complex potentials of this problem. The solution constructed can be used for the cases of different circular interfacial defects including interfacial cracks and rigid parts of the interface. It is pointed out that the problem is a base of a superposition method applied to solving a lot of problems in which a circular region is an element of polyphase elastic medium. In such a case, a correctness of the problem statement related with an actual dependance of traction jumps upon displacements jumps and vice versa entirely follows from the superposition method. The technique of the application of this method is demonstrated in this paper by the example of solving singular problems on action of a point force and an edge dislocation located in the inclusion or in the matrix. Computational
Original languageEnglish
Pages (from-to)114-121
JournalVestnik St. Petersburg University: Mathematics
Volume43
Issue number2
DOIs
Publication statusPublished - 2010

Fingerprint

Inclusion
Jump
Superposition
Interfacial Crack
Complex Potential
Singular Problems
Dislocation
Correctness
Defects
Infinity

Cite this

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title = "Joint deformation of a circular inclusion and a matrix",
abstract = "An elastic infinite plane with a circular inclusion at specified tractions and displacements jumps along the interface and under nonzero conditions at infinity is considered. Explicit expressions are derived for Goursat-Kolosov's complex potentials of this problem. The solution constructed can be used for the cases of different circular interfacial defects including interfacial cracks and rigid parts of the interface. It is pointed out that the problem is a base of a superposition method applied to solving a lot of problems in which a circular region is an element of polyphase elastic medium. In such a case, a correctness of the problem statement related with an actual dependance of traction jumps upon displacements jumps and vice versa entirely follows from the superposition method. The technique of the application of this method is demonstrated in this paper by the example of solving singular problems on action of a point force and an edge dislocation located in the inclusion or in the matrix. Computational",
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journal = "Vestnik St. Petersburg University: Mathematics",
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TY - JOUR

T1 - Joint deformation of a circular inclusion and a matrix

AU - Grekov, M.A.

PY - 2010

Y1 - 2010

N2 - An elastic infinite plane with a circular inclusion at specified tractions and displacements jumps along the interface and under nonzero conditions at infinity is considered. Explicit expressions are derived for Goursat-Kolosov's complex potentials of this problem. The solution constructed can be used for the cases of different circular interfacial defects including interfacial cracks and rigid parts of the interface. It is pointed out that the problem is a base of a superposition method applied to solving a lot of problems in which a circular region is an element of polyphase elastic medium. In such a case, a correctness of the problem statement related with an actual dependance of traction jumps upon displacements jumps and vice versa entirely follows from the superposition method. The technique of the application of this method is demonstrated in this paper by the example of solving singular problems on action of a point force and an edge dislocation located in the inclusion or in the matrix. Computational

AB - An elastic infinite plane with a circular inclusion at specified tractions and displacements jumps along the interface and under nonzero conditions at infinity is considered. Explicit expressions are derived for Goursat-Kolosov's complex potentials of this problem. The solution constructed can be used for the cases of different circular interfacial defects including interfacial cracks and rigid parts of the interface. It is pointed out that the problem is a base of a superposition method applied to solving a lot of problems in which a circular region is an element of polyphase elastic medium. In such a case, a correctness of the problem statement related with an actual dependance of traction jumps upon displacements jumps and vice versa entirely follows from the superposition method. The technique of the application of this method is demonstrated in this paper by the example of solving singular problems on action of a point force and an edge dislocation located in the inclusion or in the matrix. Computational

KW - circular inclusion

KW - interface

KW - singular problems

KW - point force

KW - edge dislocation

U2 - 10.3103/S1063454110020081

DO - 10.3103/S1063454110020081

M3 - Article

VL - 43

SP - 114

EP - 121

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -