The discontinuous solutions of Lame�s equations for a conical defect
In this article the discontinuous solutions of� Lame�s equations are constructed for the case of a conical defect. Under a defect one considers a part of a surface (mathematical cut on the surface) when passing through which function and its normal derivative have discontinuities of continuity of th...
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Gruppo Italiano Frattura
2018-07-01
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| Series: | Fracture and Structural Integrity |
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| Online Access: | http://www.gruppofrattura.it/pdf/rivista/numero45/numero_45_art_16.pdf |
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| author | O. Reut N. Vaysfeld |
| author_facet | O. Reut N. Vaysfeld |
| author_sort | O. Reut |
| collection | DOAJ |
| description | In this article the discontinuous solutions of� Lame�s equations are constructed for the case of a conical defect. Under a defect one considers a part of a surface (mathematical cut on the surface) when passing through which function and its normal derivative have discontinuities of continuity of the first kind. A discontinuous solution of a certain differential equation in the partial derivatives is a solution that satisfies this equation throughout the region of determining an unknown function, with the exception of the defect points. To construct such a solution the method of integral transformations is used with a generalized scheme. Here this approach is applied to construct the discontinuous solution of Helmholtz�s equation for a conical defect. On the base of it the discontinuous solutions of Lame�s equations are derived for a case of steady state loading of a medium. |
| format | Article |
| id | doaj-art-b0717d161ca14876a822d27c942a558c |
| institution | Kabale University |
| issn | 1971-8993 |
| language | English |
| publishDate | 2018-07-01 |
| publisher | Gruppo Italiano Frattura |
| record_format | Article |
| series | Fracture and Structural Integrity |
| spelling | doaj-art-b0717d161ca14876a822d27c942a558c2025-01-03T01:50:54ZengGruppo Italiano FratturaFracture and Structural Integrity1971-89932018-07-01124518319010.3221/IGF-ESIS.45.1610.3221/IGF-ESIS.45.16The discontinuous solutions of Lame�s equations for a conical defectO. ReutN. VaysfeldIn this article the discontinuous solutions of� Lame�s equations are constructed for the case of a conical defect. Under a defect one considers a part of a surface (mathematical cut on the surface) when passing through which function and its normal derivative have discontinuities of continuity of the first kind. A discontinuous solution of a certain differential equation in the partial derivatives is a solution that satisfies this equation throughout the region of determining an unknown function, with the exception of the defect points. To construct such a solution the method of integral transformations is used with a generalized scheme. Here this approach is applied to construct the discontinuous solution of Helmholtz�s equation for a conical defect. On the base of it the discontinuous solutions of Lame�s equations are derived for a case of steady state loading of a medium.http://www.gruppofrattura.it/pdf/rivista/numero45/numero_45_art_16.pdfConical defectHelmholtz�s equationWave potentialIntegral TransformationLame�s equations |
| spellingShingle | O. Reut N. Vaysfeld The discontinuous solutions of Lame�s equations for a conical defect Fracture and Structural Integrity Conical defect Helmholtz�s equation Wave potential Integral Transformation Lame�s equations |
| title | The discontinuous solutions of Lame�s equations for a conical defect |
| title_full | The discontinuous solutions of Lame�s equations for a conical defect |
| title_fullStr | The discontinuous solutions of Lame�s equations for a conical defect |
| title_full_unstemmed | The discontinuous solutions of Lame�s equations for a conical defect |
| title_short | The discontinuous solutions of Lame�s equations for a conical defect |
| title_sort | discontinuous solutions of lame�s equations for a conical defect |
| topic | Conical defect Helmholtz�s equation Wave potential Integral Transformation Lame�s equations |
| url | http://www.gruppofrattura.it/pdf/rivista/numero45/numero_45_art_16.pdf |
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