Fracture and Structural Integrity e-ISSN 1971-8993 Open access
Miscellanea Vol. 12, No. 45 (2018)

The discontinuous solutions of Lame’s equations for a conical defect

Author and affiliation details
  • Natalya D. Vaysfel'd Corresponding author Odessa National Mechnikov University, Ukraine vaysfeld@onu.edu.ua
  • O. Reut Odessa Mechnikov University, Institute of Mathematics, Economics and Mechanics, Ukraine
DOI
10.3221/IGF-ESIS.45.16
Pages
183-190
Published
Published inVol. 12, No. 45 (2018)Go to the issue

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.

Keywords

Article history

  1. ReceivedUntil the next stage: 0 days
  2. AcceptedUntil the next stage: 9 days
  3. Published

How to cite

APA

Vaysfel'd, N. D., & Reut, O. (2018). The discontinuous solutions of Lame’s equations for a conical defect. Fracture and Structural Integrity, 12(45), 183–190. https://doi.org/10.3221/IGF-ESIS.45.16

IEEE

N. D. Vaysfel'd and O. Reut, “The discontinuous solutions of Lame’s equations for a conical defect,” Fracture and Structural Integrity, vol. 12, no. 45, pp. 183–190, 2018, doi: 10.3221/IGF-ESIS.45.16.

MLA

Vaysfel'd, Natalya D., and O. Reut. “The discontinuous solutions of Lame’s equations for a conical defect.” Fracture and Structural Integrity, vol. 12, no. 45, 2018, pp. 183–190. https://doi.org/10.3221/IGF-ESIS.45.16.

Chicago

Vaysfel'd, Natalya D., and O. Reut. 2018. “The discontinuous solutions of Lame’s equations for a conical defect.” Fracture and Structural Integrity 12 (45): 183–190. https://doi.org/10.3221/IGF-ESIS.45.16.

Harvard

Vaysfel'd, N.D. and Reut, O. (2018) ‘The discontinuous solutions of Lame’s equations for a conical defect’, Fracture and Structural Integrity, 12(45), pp. 183–190. doi: 10.3221/IGF-ESIS.45.16.

Vancouver

Vaysfel'd ND, Reut O. The discontinuous solutions of Lame’s equations for a conical defect. Fracture and Structural Integrity. 2018;12(45):183-190. doi:10.3221/IGF-ESIS.45.16

BibTeX

@article{vaysfeld2018, author = {Vaysfel'd, Natalya D. and Reut, O.}, title = {The discontinuous solutions of Lame’s equations for a conical defect}, journal = {Fracture and Structural Integrity}, year = {2018}, volume = {12}, number = {45}, pages = {183--190}, doi = {10.3221/IGF-ESIS.45.16}, url = {https://doi.org/10.3221/IGF-ESIS.45.16}, issn = {1971-8993} }

RIS

TY - JOUR AU - Vaysfel'd, Natalya D. AU - Reut, O. TI - The discontinuous solutions of Lame’s equations for a conical defect JO - Fracture and Structural Integrity T2 - Fracture and Structural Integrity PY - 2018 DA - 2018/07/03 VL - 12 IS - 45 SP - 183 EP - 190 DO - 10.3221/IGF-ESIS.45.16 UR - https://doi.org/10.3221/IGF-ESIS.45.16 SN - 1971-8993 ER -

Licence

Copyright © 2018 Natalya D. Vaysfel'd, O. Reut.

Copyright 
Authors are allowed to retain both the copyright and the publishing rights of their articles without restrictions.  

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