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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Gruppo Italiano Frattura
2018-07-01
|
| Series: | Fracture and Structural Integrity |
| Subjects: | |
| Online Access: | https://www.fracturae.com/index.php/fis/article/view/2137 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1841564274852364288 |
|---|---|
| author | Natalya D. Vaysfel'd O. Reut |
| author_facet | Natalya D. Vaysfel'd O. Reut |
| author_sort | Natalya D. Vaysfel'd |
| 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-d4cdbbac0bfc4ca0b04e0dd3587ed281 |
| 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-d4cdbbac0bfc4ca0b04e0dd3587ed2812025-01-02T23:01:28ZengGruppo Italiano FratturaFracture and Structural Integrity1971-89932018-07-011245The discontinuous solutions of Lame’s equations for a conical defectNatalya D. Vaysfel'd0O. Reut1Odessa National Mechnikov University, UkraineOdessa Mechnikov University, Institute of Mathematics, Economics and Mechanics, UkraineIn 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.https://www.fracturae.com/index.php/fis/article/view/2137Conical defectHelmholtz’s equationWave potentialIntegral TransformationLame’s equations |
| spellingShingle | Natalya D. Vaysfel'd O. Reut 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 | https://www.fracturae.com/index.php/fis/article/view/2137 |
| work_keys_str_mv | AT natalyadvaysfeld thediscontinuoussolutionsoflamesequationsforaconicaldefect AT oreut thediscontinuoussolutionsoflamesequationsforaconicaldefect AT natalyadvaysfeld discontinuoussolutionsoflamesequationsforaconicaldefect AT oreut discontinuoussolutionsoflamesequationsforaconicaldefect |