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Natalya D. Vaysfel'd O. Reut

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.

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    How to Cite

    Vaysfel’d, N. D. and Reut, O. (2018) “The discontinuous solutions of Lame’s equations for a conical defect”, Frattura ed Integrità Strutturale, 12(45), pp. 183-190. doi: 10.3221/IGF-ESIS.45.16.