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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Gruppo Italiano Frattura
2018-07-01
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| Series: | Fracture and Structural Integrity |
| Subjects: | |
| Online Access: | http://www.gruppofrattura.it/pdf/rivista/numero45/numero_45_art_16.pdf |
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| Summary: | 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. |
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| ISSN: | 1971-8993 |