Singular integral equation method for the solution of multiple curved crack problems

Chen, Y.Z.

doi:10.1016/j.ijsolstr.2004.02.004

Cited by 22 publications

(13 citation statements)

References 10 publications

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“…The distribution dislocation functions g 1 (t 1 ) and g 2 (t 2 ) respectively for the crack-1 (L 1 ), and for the crack-2 (L 2 ). Let N 1 (t 10 ) + iT 1 (t 10 ) be the tractions applied on the crack-1 at the point t 10 which obtained from g 1 (t 1 ) and g 2 (t 2 ) [11]. We obtain the singular integral equation for crack-1, which is…”

Section: Multiple Cracks Problem In Elastic Half Planementioning

confidence: 99%

“…where the tractions at at t 20 of crack-2 is N 2 (t 20 ) + iT 2 (t 20 ), and the integrals represented as in [11]. The singlevaluedness conditions for crack-1 and crack-2 are respectively, be given by FIGURE 2: Nondimensional SIFs at the crack tips A, B, C, and D for two cracks in series as in Fig.…”

Section: Multiple Cracks Problem In Elastic Half Planementioning

confidence: 99%

“…The first type is SIE with crack opening displacement function (COD) [1], the second type is SIE with the dislocation distribution function [2,3], the third is weakly singular integral equation with logarithmic kernel [4,5], and the fourth type is HSIE [6,7,8,9]. A curve length method was developed to solve the integral equations for the curved crack problems numerically for infinite plate [10,11], and for elastic half plane [7]. This method is useful to transform the integral defined on the curve into the one on the real axis.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stress intensity factor for multiple cracks in half plane elasticity

Elfakhakhre

Long

Eshkuvatov

2017

AIP Conference Proceedings

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Abstract. The multiple cracks problem in an elastic half-plane is formulated into singular integral equation using the modified complex potential with free traction boundary condition. A system of singular integral equations is obtained with the distribution dislocation function as unknown, and the traction applied on the crack faces as the right hand terms. With the help of the curved length coordinate method and Gauss quadrature rule, the resulting system is solved numerically. The stress intensity factor (SIF) can be obtained from the unknown coefficients. Numerical examples exhibit that our results are in good agreement with the previous works, and it is found that the SIF increase as the cracks approaches the boundary of half plane.

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Section: Multiple Cracks Problem In Elastic Half Planementioning

confidence: 99%

Section: Multiple Cracks Problem In Elastic Half Planementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stress intensity factor for multiple cracks in half plane elasticity

Elfakhakhre

Long

Eshkuvatov

2017

AIP Conference Proceedings

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“…Besides many analytical works have been done, the needs for numerical technique for solving such a problem still remains. Examples are, works by Chen et al (2003) and Chen, whom applied complex potential method to formulate the problems of multiple curved cracks into singular integral equations (Chen, 2004(Chen, , 2007 and a curved crack into hypersingular integral equation (Chen, 1993(Chen, , 2003. These equations were then solved numerically.…”

Section: Introductionmentioning

confidence: 99%

Hypersingular integral equation for multiple curved cracks problem in plane elasticity

Long

Eshkuvatov

2009

International Journal of Solids and Structures

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“…The curve length coordinate method is suggested to evaluate the singular or hypersingular integrals (Chen, 2003(Chen, , 2004. In the method, a substitution dt = (dt/ds)/ds is used, where t = x + iy is a complex variable and ds = [(dx) 2 + (dy) 2 ] 1/2 .…”

Section: Introductionmentioning

confidence: 99%

Numerical solutions of hypersingular integral equation for curved cracks in circular regions

Chen

Lin

2005

Int J Fract

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In this paper, numerical solutions of a hypersingular integral equation for curved cracks in circular regions are presented. The boundary of the circular regions is assumed to be traction free or fixed. The suggested complex potential is composed of two parts, the principle part and the complementary part. The principle part can model the property of a curved crack in an infinite plate. For the case of the traction free boundary, the complementary part can compensate the traction on the circular boundary caused by the principle part. Physically, the proposed idea is similar to the image method in electrostatics. By using the crack opening displacement (COD) as the unknown function and traction as right hand term in the equation, a hypersingular integral equation for the curved crack problems in the circular regions is obtained. The equation is solved by using the curve length coordinate method. In order to prove that the suggested method can be used to solve more complicated cases of the curved cracks, several numerical examples are given.Key words: Curve length coordinate method, curved crack problem in circular regions, image method, numerical solution of hypersingular integral equation.

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Singular integral equation method for the solution of multiple curved crack problems

Cited by 22 publications

References 10 publications

Stress intensity factor for multiple cracks in half plane elasticity

Stress intensity factor for multiple cracks in half plane elasticity

Hypersingular integral equation for multiple curved cracks problem in plane elasticity

Numerical solutions of hypersingular integral equation for curved cracks in circular regions

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