Fredholm integral equation for the multiple circular arc crack problem in plane elasticity

Chen, Y. Z.; Hasebe, Norio

doi:10.1007/s004190050129

Cited by 9 publications

(7 citation statements)

References 10 publications

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“…Some known elastic solutions for the arc crack problem can be obtained from [17], and they are stated in the following. In these solutions, the SIFs at crack tips B and A in Figure 2 are expressed by…”

Section: Appendix Amentioning

confidence: 99%

Thermoelastic Problem of Arc Crack With Heat Source or Doublet

Chen¹

2004

Journal of Thermal Stresses

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Section: Appendix Amentioning

confidence: 99%

Thermoelastic Problem of Arc Crack With Heat Source or Doublet

Chen¹

2004

Journal of Thermal Stresses

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“…From the geometry, the coordinates of ^ and ξU can easily be determined to have following expressions, -yjl-c 2 cos 2 Q 0 )e-K + i % -ic (6) in which θ 0 is the angle measured from the reference line introduced to facilitate the transformation. So far, the parameter c does not have any geometrical meaning at all.…”

Section: Domain Mappingmentioning

confidence: 99%

“…Ioakimidis and Theocaris [5] gave the numerical solution of a circular-arc crack in isotropic elastic half-plane. Also, Chen and Hasebe [6] obtained an elementary solution for multiple circular-arc crack problems.…”

Section: Introductionmentioning

confidence: 98%

In-Plane Bending Fracture of a Large Beam Containing a Circular-Arc Crack

et al. 2002

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In this paper, the crack problem of a large beam-like strip weakened by a circular arc crack with in-plane bending moments applied at both ends is approximately solved using the complex variable technique. Complex stress functions corresponding to the applied bending moments are superposed with those due to the disturbance of the crack to satisfy the governing boundary equation. The conformal mapping function devised to transform the contour surface of a circular arc crack to a unit circle is then substituted in the boundary equation to facilitate the evaluation of Cauchy integrals. In this way, the complex stress functions due to the crack disturbance are determined and the stress intensity factors are calculated through a limiting process to give their explicit forms. Eventually, the geometric functions for the variation of the stress intensity factors on account of the crack shape are plotted as a function of the curvature of a circular-arc crack.

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“…Several types of integral equations have been developed to formulate the single crack problem such as singular integral equation [1], Fredholm integral equation [2], hypersingular integral equation [3] and interaction integral equation [4]. Formulation for the multiple cracks problem are also obtained in terms of singular integral equation [5], Fredholm integral equation [6] and hypersingular integral equation [7] for various set of cracks positions.…”

Section: Introductionmentioning

confidence: 99%

Mode Stresses for the Interaction between Straight and Curved Cracks Problem in Plane Elasticity

Aridi¹,

Long²,

Eshkuvatov³

2014

JAMP

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In this paper, the complex variable function method is used to obtain the hypersingular integral equations for the interaction between straight and curved cracks problem in plane elasticity. The curved length coordinate method and suitable quadrature rule are used to solve the integrals for the unknown function, which are later used to evaluate the stress intensity factor, SIF. Three types of stress modes are presented for the numerical results.

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Fredholm integral equation for the multiple circular arc crack problem in plane elasticity

Cited by 9 publications

References 10 publications

Thermoelastic Problem of Arc Crack With Heat Source or Doublet

Thermoelastic Problem of Arc Crack With Heat Source or Doublet

In-Plane Bending Fracture of a Large Beam Containing a Circular-Arc Crack

Mode Stresses for the Interaction between Straight and Curved Cracks Problem in Plane Elasticity

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