Analysis of an isotropic elastic matrix with two elliptical voids or rigid inclusions under anti-plane loading
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 geometrie...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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The Japan Society of Mechanical Engineers
2018-12-01
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| Series: | Mechanical Engineering Journal |
| Subjects: | |
| Online Access: | https://www.jstage.jst.go.jp/article/mej/5/6/5_18-00333/_pdf/-char/en |
| _version_ | 1818982985815293952 |
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| author | Mutsumi MIYAGAWA Takuo SUZUKI Toru SASAKI Takeshi TANE |
| author_facet | Mutsumi MIYAGAWA Takuo SUZUKI Toru SASAKI Takeshi TANE |
| author_sort | Mutsumi MIYAGAWA |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-20T17:55:55Z |
| format | Article |
| id | doaj.art-e708a83a27d64e99951a972d44198ee5 |
| institution | Directory Open Access Journal |
| issn | 2187-9745 |
| language | English |
| last_indexed | 2024-12-20T17:55:55Z |
| publishDate | 2018-12-01 |
| publisher | The Japan Society of Mechanical Engineers |
| record_format | Article |
| series | Mechanical Engineering Journal |
| spelling | doaj.art-e708a83a27d64e99951a972d44198ee52022-12-21T19:30:46ZengThe Japan Society of Mechanical EngineersMechanical Engineering Journal2187-97452018-12-015618-0033318-0033310.1299/mej.18-00333mejAnalysis of an isotropic elastic matrix with two elliptical voids or rigid inclusions under anti-plane loadingMutsumi MIYAGAWA0Takuo SUZUKI1Toru SASAKI2Takeshi TANE3Tokyo Metropolitan College of Industrial TechnologyTokyo Metropolitan College of Industrial TechnologyNational Institute of Technology, Nagaoka CollegeNational Institute of Technology, Kitakyushu CollegeThis 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.https://www.jstage.jst.go.jp/article/mej/5/6/5_18-00333/_pdf/-char/enisotropic elasticityanti-plane problemtwo elliptical voidstwo elliptical rigid inclusionsuniform shear stressconcentrated forcescrew dislocation |
| spellingShingle | Mutsumi MIYAGAWA Takuo SUZUKI Toru SASAKI Takeshi TANE Analysis of an isotropic elastic matrix with two elliptical voids or rigid inclusions under anti-plane loading Mechanical Engineering Journal isotropic elasticity anti-plane problem two elliptical voids two elliptical rigid inclusions uniform shear stress concentrated force screw dislocation |
| title | Analysis of an isotropic elastic matrix with two elliptical voids or rigid inclusions under anti-plane loading |
| title_full | Analysis of an isotropic elastic matrix with two elliptical voids or rigid inclusions under anti-plane loading |
| title_fullStr | Analysis of an isotropic elastic matrix with two elliptical voids or rigid inclusions under anti-plane loading |
| title_full_unstemmed | Analysis of an isotropic elastic matrix with two elliptical voids or rigid inclusions under anti-plane loading |
| title_short | Analysis of an isotropic elastic matrix with two elliptical voids or rigid inclusions under anti-plane loading |
| title_sort | analysis of an isotropic elastic matrix with two elliptical voids or rigid inclusions under anti plane loading |
| topic | isotropic elasticity anti-plane problem two elliptical voids two elliptical rigid inclusions uniform shear stress concentrated force screw dislocation |
| url | https://www.jstage.jst.go.jp/article/mej/5/6/5_18-00333/_pdf/-char/en |
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