Analysis of Antiplane Problems with Singular Disturbances for Isotropic Elastic Medium Having Many Circular Elastic Inclusions.

Hirashima, Ken-ichi; Miyagawa, Mutsumi; Nakane, Shigerou

doi:10.1299/kikaia.64.1895

Cited by 7 publications

(7 citation statements)

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“…In the above solutions, we confirmed that the calculus results were in complete agreement with the results reported by Moriguchi (1956) for the single void problem and Hirashima (1994Hirashima ( ,1998 for the two-circular-voids problem.…”

Section: Solution To the Anti-plane Problem In The Presence Of A Singsupporting

confidence: 91%

“…In a multi-void problem, Honein (1992) and Hirashima (1994) found a general solution that a matrix with two circular inclusions is loaded under the anti-plane problem. We then expand to multi-inclusions for quasi-three-dimensional problems (Miyagawa ,1998(Miyagawa , ,2011(Miyagawa , ,2012(Miyagawa , ,2013a(Miyagawa , ,2013b. However, those problems are only multi-circular inclusions.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of an isotropic elastic matrix with two elliptical voids or rigid inclusions under anti-plane loading

Miyagawa

Suzuki

Sasaki

et al. 2018

Mechanical Engineering Journal

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This paper presents theoretical solutions for cases of a two-dimensional isotropic elastic matrix containing two elliptical voids or rigid inclusions under anti-plane loading. These two ellipses have different long-axial radii, short-axial radii, inclining angles, and central points. Their geometries are arbitrary. The matrix is assumed to be subjected to arbitrary loading by, for example, uniform shear stresses, as well as to a concentrated force and screw dislocation at an arbitrary point. The solutions are obtained through iterations of the Möbius transformation as a series with an explicit general term involving the complex potential functions of the corresponding homogeneous problem. This procedure is referred to as heterogenization. Using these solutions, several numerical examples are presented graphically.

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Section: Solution To the Anti-plane Problem In The Presence Of A Singsupporting

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Analysis of an isotropic elastic matrix with two elliptical voids or rigid inclusions under anti-plane loading

Miyagawa

Suzuki

Sasaki

et al. 2018

Mechanical Engineering Journal

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“…The purpose of the present study is to apply the reflection principle of Moriguchi (1) , who investigated a single hole in in-plane problems, and the techniques of Honein (2) and Hirashima (4)∼ (6) to consider anti-plane multi-hole problems. We obtained general solutions (7) (8) for up to two circular inclusions.…”

Section: Introductionmentioning

confidence: 99%

Analysis of In-Plane Problems for an Isotropic Elastic Medium with Many Circular Holes or Rigid Inclusions

Miyagawa¹,

Shimura²,

Suzuki³

et al. 2013

JMMP

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“…The purpose of the present study is to apply the reflection principle of Moriguchi (1) , who investigated a single hole, and Sendeckyj (3) and Dunders (2) , who each produced a general solution of a single elastic inclusion in in-plane problems. We use the techniques of Honein (4) and Hirashima (5)∼ (7) to consider anti-plane problems. Using these techniques, in our most recent paper (8) we expanded this single-hole problem to a problem involving two circular holes or rigid inclusions.…”

Section: Introductionmentioning

confidence: 99%

Analysis of In-Plane Problems for an Isotropic Elastic Medium with Two Circular Inclusions

Miyagawa¹,

Tamiya²,

Shimura³

et al. 2012

JMMP

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In the present paper, we derive a solution for two circular elastic inclusions that are perfectly bonded to an elastic medium (matrix) of infinite extent under in-plane deformation. These two inclusions have different radii, central points, and elasticities. The matrix is subjected to arbitrary loading by, for example, uniform stresses, as well as to a concentrated force at an arbitrary point. In this paper, we present a solution under uniform stresses at infinity as an example. The solution is obtained through iterations of the Möbius transformation as a series with an explicit general term involving the complex potential of the corresponding homogeneous problem. This procedure is referred to as heterogenization. Using these solutions, several numerical examples are presented graphically.

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Analysis of Antiplane Problems with Singular Disturbances for Isotropic Elastic Medium Having Many Circular Elastic Inclusions.

Cited by 7 publications

References 0 publications

Analysis of an isotropic elastic matrix with two elliptical voids or rigid inclusions under anti-plane loading

Analysis of an isotropic elastic matrix with two elliptical voids or rigid inclusions under anti-plane loading

Analysis of In-Plane Problems for an Isotropic Elastic Medium with Many Circular Holes or Rigid Inclusions

Analysis of In-Plane Problems for an Isotropic Elastic Medium with Two Circular Inclusions

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