Numerical solution for a crack embedded in multiple elliptic layers with different elastic properties

Chen, Y. Z.

doi:10.1007/s00707-015-1351-1

Cited by 3 publications

(1 citation statement)

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“…In [9] the study was done of the stress intensity factor along the crack front of an elliptical crack in a rotating shaft. In [4] considered medium is composed of an elliptic inclusion and many confocal elliptic layers. The crack is embedded in the elliptic inclusion.…”

Section: Introductionmentioning

confidence: 99%

Study of deflected mode of ellipse and ellipse weakened with crack

Zirakashvili

2017

Z Angew Math Mech

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The paper considers the boundary value problems of elasticity for an ellipse and ellipse with a crack when tangential stress is applied to the ellipse boundary. The mathematical models of these problems are obtained by setting the relevant problems for a semi-ellipse: a) the continuity conditions for the problem solution are given at the linear border, b) the continuity conditions for the problem solution are given at the portion of the linear boundary, beyond the focuses, with the tangential stresses given on the section between the focuses. So, a semi-ellipse can be bound as a whole ellipse, with the continuity conditions of the solution on the section between its focuses met in one case (when there is no crack) and not met in another case (when there is a crack, which is affected by the tangential stress). The problem solution for the cracked ellipse is reduced to the solution of the internal and external problems of elasticity, which are solved quite simply by the method of separation of variables.

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Section: Introductionmentioning

confidence: 99%