The Solution of Mitchell's Problem for the Elastic Infinite Cone with a Spherical Crack
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-20, 20 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-06-22
Country of Publication
Egypt
No. of Pages
20
Main Subjects
Abstract EN
The new problem about the stress concentration around a spherical crack inside of an elastic cone is solved for the point tensile force enclosed to a cone's edge.
The constructed discontinuous solutions of the equilibrium equations have allowed to express the displacements and stress in a cone through their jumps and the jumps of their normal derivatives across the crack's surface.
The application of the integral transformation method under the generalized scheme has reduced the problem solving to the solving of the integrodifferential equation system with regard to the displacements' jumps.
This system was solved approximately by the orthogonal polynomial method.
The use of this method has allowed to take into consideration the order of the solution's singularities at the ends of an integral interval.
The correlation between the crack's geometrical parameters, its distance from an edge, and the SIF values is established after the numerical analysis.
The limit of the proposed method applicability is specified.
American Psychological Association (APA)
Popov, G. Ya.& Vaysfel'd, N. D.. 2010. The Solution of Mitchell's Problem for the Elastic Infinite Cone with a Spherical Crack. Mathematical Problems in Engineering،Vol. 2010, no. 2010, pp.1-20.
https://search.emarefa.net/detail/BIM-473344
Modern Language Association (MLA)
Popov, G. Ya.& Vaysfel'd, N. D.. The Solution of Mitchell's Problem for the Elastic Infinite Cone with a Spherical Crack. Mathematical Problems in Engineering No. 2010 (2010), pp.1-20.
https://search.emarefa.net/detail/BIM-473344
American Medical Association (AMA)
Popov, G. Ya.& Vaysfel'd, N. D.. The Solution of Mitchell's Problem for the Elastic Infinite Cone with a Spherical Crack. Mathematical Problems in Engineering. 2010. Vol. 2010, no. 2010, pp.1-20.
https://search.emarefa.net/detail/BIM-473344
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-473344