TY - JOUR
AU - Vaysfel'd, Natalya D.
AU - Reut, O.
PY - 2018/07/03
Y2 - 2022/09/28
TI - The discontinuous solutions of Lame’s equations for a conical defect
JF - Frattura ed Integrità Strutturale
JA - Fra&IntStrut
VL - 12
IS - 45
SE - Miscellanea
DO - 10.3221/IGF-ESIS.45.16
UR - https://www.fracturae.com/index.php/fis/article/view/2137
SP - 183-190
AB - <p>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.</p>
ER -