The Solution of Mitchell's Problem for the Elastic Infinite Cone with a Spherical Crack
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 con...
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2010-01-01
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Series: | Mathematical Problems in Engineering |
Online Access: | http://dx.doi.org/10.1155/2010/460852 |
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doaj-24c39811980745bd9947c04de203ff672020-11-25T00:14:25ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472010-01-01201010.1155/2010/460852460852The Solution of Mitchell's Problem for the Elastic Infinite Cone with a Spherical CrackG. Ya. Popov0N. D. Vaysfel'd1Institute of Mathematics, Economics and Mechanics, Odessa Mechnikov University, Odessa 65044, UkraineInstitute of Mathematics, Economics and Mechanics, Odessa Mechnikov University, Odessa 65044, UkraineThe 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.http://dx.doi.org/10.1155/2010/460852 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
G. Ya. Popov N. D. Vaysfel'd |
spellingShingle |
G. Ya. Popov N. D. Vaysfel'd The Solution of Mitchell's Problem for the Elastic Infinite Cone with a Spherical Crack Mathematical Problems in Engineering |
author_facet |
G. Ya. Popov N. D. Vaysfel'd |
author_sort |
G. Ya. Popov |
title |
The Solution of Mitchell's Problem for the Elastic Infinite Cone with a Spherical Crack |
title_short |
The Solution of Mitchell's Problem for the Elastic Infinite Cone with a Spherical Crack |
title_full |
The Solution of Mitchell's Problem for the Elastic Infinite Cone with a Spherical Crack |
title_fullStr |
The Solution of Mitchell's Problem for the Elastic Infinite Cone with a Spherical Crack |
title_full_unstemmed |
The Solution of Mitchell's Problem for the Elastic Infinite Cone with a Spherical Crack |
title_sort |
solution of mitchell's problem for the elastic infinite cone with a spherical crack |
publisher |
Hindawi Limited |
series |
Mathematical Problems in Engineering |
issn |
1024-123X 1563-5147 |
publishDate |
2010-01-01 |
description |
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. |
url |
http://dx.doi.org/10.1155/2010/460852 |
work_keys_str_mv |
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