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

Chen, Y. Z.; Lin, X. Y.

doi:10.1007/s10704-005-0990-y

Cited by 3 publications

(4 citation statements)

References 23 publications

(47 reference statements)

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“…For convenience of reading this paper, a compact description for the derivation of the equation is carried out below, and the detail can be referred to [Chen (2003); Chen and Lin (2005)]. The complex variable function method plays an important role in plane elasticity [Muskhelishvili (1953)].…”

Section: Hypersingular Integral Equation Methods For the Contact Problmentioning

confidence: 99%

“…Second, J 1 value depends not only on the position of a point "z", but also on the direction of the segment "dz/dz". An appropriate complex potential for the problem is [Chen (2003); Chen and Lin (2005)] as follows:…”

Section: Hypersingular Integral Equation Methods For the Contact Problmentioning

confidence: 99%

“…(20) later. In addition, it is found that a suggested quadrature rule in conjunction with the curve length method provides a very effective way to solve the HSIE [Mayrhofer and Fischer (1992); Chen (2003); Chen and Lin (2005)].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Solution of Contact Problem for an Arc Crack Using Hypersingular Integral Equation

Chen

Lin

Wang

et al. 2008

Int. J. Comput. Methods

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This paper investigates the contact problem for an arc crack, for example, under a remote compression. A hypersingular integral equation (HSIE) for curved cracks in plane elasticity is suggested. It is found that the direct usage of HSIE cannot solve the mentioned contact problem. For the contact problem, one must take necessary modifications for solving the HSIE. The main modified points are as follows. First, one should assume some portion along the crack under contact. The margin or the end of the contacted portion is determined by the vanishing normal contact stress at the margin point. In addition, it is found that a suggested quadrature rule in conjunction with the curve length method provides a very effective way to solve the HSIE. Finally, several numerical examples are given.

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Section: Hypersingular Integral Equation Methods For the Contact Problmentioning

confidence: 99%

Section: Hypersingular Integral Equation Methods For the Contact Problmentioning

confidence: 99%

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Solution of Contact Problem for an Arc Crack Using Hypersingular Integral Equation

Chen

Lin

Wang

et al. 2008

Int. J. Comput. Methods

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“… used hypersingular integral equation to formulate and solve the micromechanical models. In addition, there are more cracks problems that were solved using the hypersingular integral equations .…”

Section: Introductionmentioning

confidence: 99%

Stress intensity factor for multiple inclined or curved cracks problem in circular positions in plane elasticity

et al. 2017

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The problems of multiple inclined or curved cracks in circular positions is treated by using the hypersingular integral equation method. The cracks center are placed at the edge of a virtual circle with radius R. The first crack is fixed on the x-axis while the second crack is located on the boundary of a circle with the varying angle, θ. A system of hypersingular integral equations is formulated and solved numerically for the stress intensity factor (SIF). Numerical examples demonstrate the effect of interaction between two cracks in circular positions are given. It is found that, the severity at the second crack tips are significant when the ratio length of the second to the first crack is small and it is placed at a small angle of θ .

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Integral Equation Methods for Multiple Crack Problems and Related Topics

Chen

2007

Applied Mechanics Reviews

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The content of this review consists of recent developments covering an advanced treatment of multiple crack problems in plane elasticity. Several elementary solutions are highlighted, which are the fundamentals for the formulation of the integral equations. The elementary solutions include those initiated by point sources or by a distributed traction along the crack face. Two kinds of singular integral equations, three kinds of Fredholm integral equations, and one kind of hypersingular integral equation are suggested for the multiple crack problems in plane elasticity. Regularization procedures are also investigated. For the solution of the integral equations, the relevant quadrature rules are addressed. A variety of methods for solving the multiple crack problems is introduced. Applications for the solution of the multiple crack problems are also addressed. The concept of the modified complex potential (MCP) is emphasized, which will extend the solution range, for example, from the multiple crack problem in an infinite plate to that in a circular plate. Many multiple crack problems are addressed. Those problems include: (i) multiple semi-infinite crack problem, (ii) multiple crack problem with a general loading, (iii) multiple crack problem for the bonded half-planes, (iv) multiple crack problem for a finite region, (v) multiple crack problem for a circular region, (vi) multiple crack problem in antiplane elasticity, (vii) T-stress in the multiple crack problem, and (viii) periodic crack problem and many others. This review article cites 187 references.

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

Cited by 3 publications

References 23 publications

Solution of Contact Problem for an Arc Crack Using Hypersingular Integral Equation

Solution of Contact Problem for an Arc Crack Using Hypersingular Integral Equation

Stress intensity factor for multiple inclined or curved cracks problem in circular positions in plane elasticity

Integral Equation Methods for Multiple Crack Problems and Related Topics

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