Application of the Complex Variable Function Method to SH-Wave Scattering Around a Circular Nanoinclusion
This paper focuses on analyzing SH-wave scattering around a circular nanoinclusion using the complex variable function method. The surface elasticity theory is employed in the analysis to account for the interface effect at the nanoscale. Considering the interface effect, the boundary condition is g...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2019/7203408 |
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| _version_ | 1850166556120580096 |
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| author | Hongmei Wu |
| author_facet | Hongmei Wu |
| author_sort | Hongmei Wu |
| collection | DOAJ |
| description | This paper focuses on analyzing SH-wave scattering around a circular nanoinclusion using the complex variable function method. The surface elasticity theory is employed in the analysis to account for the interface effect at the nanoscale. Considering the interface effect, the boundary condition is given, and the infinite algebraic equations are established to solve the unknown coefficients of the scattered and refracted wave solutions. The analytic solutions of the stress field are obtained by using the orthogonality of trigonometric function. Finally, the dynamic stress concentration factor and the radial stress of a circular nanoinclusion are analyzed with some numerical results. The numerical results show that the interface effect weakens the dynamic stress concentration but enhances the radial stress around the nanoinclusion; further, we prove that the analytic solutions are correct. |
| format | Article |
| id | doaj-art-d7e871ca733245b488180442813888fe |
| institution | OA Journals |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-d7e871ca733245b488180442813888fe2025-08-20T02:21:25ZengWileyAdvances in Mathematical Physics1687-91201687-91392019-01-01201910.1155/2019/72034087203408Application of the Complex Variable Function Method to SH-Wave Scattering Around a Circular NanoinclusionHongmei Wu0School of Mechanical and Electronical Engineering, Lanzhou University of Technology, Lanzhou, Gansu, ChinaThis paper focuses on analyzing SH-wave scattering around a circular nanoinclusion using the complex variable function method. The surface elasticity theory is employed in the analysis to account for the interface effect at the nanoscale. Considering the interface effect, the boundary condition is given, and the infinite algebraic equations are established to solve the unknown coefficients of the scattered and refracted wave solutions. The analytic solutions of the stress field are obtained by using the orthogonality of trigonometric function. Finally, the dynamic stress concentration factor and the radial stress of a circular nanoinclusion are analyzed with some numerical results. The numerical results show that the interface effect weakens the dynamic stress concentration but enhances the radial stress around the nanoinclusion; further, we prove that the analytic solutions are correct.http://dx.doi.org/10.1155/2019/7203408 |
| spellingShingle | Hongmei Wu Application of the Complex Variable Function Method to SH-Wave Scattering Around a Circular Nanoinclusion Advances in Mathematical Physics |
| title | Application of the Complex Variable Function Method to SH-Wave Scattering Around a Circular Nanoinclusion |
| title_full | Application of the Complex Variable Function Method to SH-Wave Scattering Around a Circular Nanoinclusion |
| title_fullStr | Application of the Complex Variable Function Method to SH-Wave Scattering Around a Circular Nanoinclusion |
| title_full_unstemmed | Application of the Complex Variable Function Method to SH-Wave Scattering Around a Circular Nanoinclusion |
| title_short | Application of the Complex Variable Function Method to SH-Wave Scattering Around a Circular Nanoinclusion |
| title_sort | application of the complex variable function method to sh wave scattering around a circular nanoinclusion |
| url | http://dx.doi.org/10.1155/2019/7203408 |
| work_keys_str_mv | AT hongmeiwu applicationofthecomplexvariablefunctionmethodtoshwavescatteringaroundacircularnanoinclusion |