Abstract

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.

Details

Title
The discontinuous solutions of Lame’s equations for a conical defect
Author
Vaysfel'd, Natalya D; Reut, O
Pages
183-190
Section
Articles
Publication year
2018
Publication date
Jul 2018
Publisher
Gruppo Italiano Frattura
e-ISSN
19718993
Source type
Scholarly Journal
Language of publication
English; Italian
ProQuest document ID
2149957068
Copyright
© 2018. This article is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.