Complex potentials and integral equations for curved crack and curved rigid line problems in plane elasticity

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

doi:10.1007/s00707-005-0305-4

Cited by 14 publications

(17 citation statements)

References 32 publications

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“…In the following, the perturbation field for the curved crack is studied (Figure 2b). It was proved that the complex potentials for this field could be expressed as [Savruk 1981;Chen and Lin 2006] …”

Section: Evaluation For the T-stress In A Curved Crack Using The Cracmentioning

confidence: 99%

“…For the curved crack problem, a singular integral equation was suggested previously [Savruk 1981;Chen and Lin 2006]:…”

Section: Evaluation For the T-stress In A Curved Crack Using The Cracmentioning

confidence: 99%

“…In addition, the dislocation distribution g (t) should satisfy the following single-valued condition of displacements [Savruk 1981;Chen and Lin 2006],…”

Section: Evaluation For the T-stress In A Curved Crack Using The Cracmentioning

confidence: 99%

“…Once the solution for the function g (t) is obtained, the SIFs (stress intensity factors) at the right crack tip A and the left crack tip B can be evaluated by [Savruk 1981;Chen and Lin 2006] …”

Section: Evaluation For the T-stress In A Curved Crack Using The Cracmentioning

confidence: 99%

“…It is known that in most cases the complex potentials in the plane elasticity crack problem can be formulated successfully [Savruk 1981;Chen and Lin 2006]. In addition, the stress components can be expressed by the complex potentials explicitly.…”

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confidence: 99%

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Crack front position and crack back position techniques for evaluating theT-stress at crack tip using functions of a complex variable

Chen

Wang

Lin

2008

JOMMS

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In this paper, the crack front position and the crack back position techniques for evaluating the T-stress using complex variables are suggested. In the crack front technique, an expression for stress components in the crack front position is expressed through a complex variable. The limit value of the expression from the crack front position will give the T-stress. In the crack back technique, the other expression of stress components in the crack back position is expressed through the complex variable. The limit value of the expression from the crack back position will give the T-stress. The suggested techniques are used to evaluate T-stress in the arc crack and the curved crack problems. It is found from a detailed derivation that both techniques give the same result in the crack problem. Numerical examples are carried out for two problems: an elliptic crack with a central crack and a curved crack with parabolic configuration.

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Section: Evaluation For the T-stress In A Curved Crack Using The Cracmentioning

confidence: 99%

“…For the curved crack problem, a singular integral equation was suggested previously [Savruk 1981;Chen and Lin 2006]:…”

Section: Evaluation For the T-stress In A Curved Crack Using The Cracmentioning

confidence: 99%

“…In addition, the dislocation distribution g (t) should satisfy the following single-valued condition of displacements [Savruk 1981;Chen and Lin 2006],…”

Section: Evaluation For the T-stress In A Curved Crack Using The Cracmentioning

confidence: 99%

Section: Evaluation For the T-stress In A Curved Crack Using The Cracmentioning

confidence: 99%

mentioning

confidence: 99%

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Crack front position and crack back position techniques for evaluating theT-stress at crack tip using functions of a complex variable

Chen

Wang

Lin

2008

JOMMS

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Degenerate scale problem arising from curved rigid line inclusion

Chen

Lin

Wang

2008

Numer Methods Biomed Eng

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SUMMARYThis paper investigates the degenerate scale problem arising from the curved rigid line inclusion. The problem is modeled by a continuous distribution of the body force along the prospective site of the curve. In the first step, the problem is formulated on the configuration of the degenerate scale, and an integral equation is suggested. Later, after using a modification for the coordinates, the problem is solved in a modified scale or in the normal scale. From the solution of the integral equation in the normal scale, the degenerate scale will be obtained immediately. Finally, several numerical examples are given. From computed results it is proved that the degenerate scale depends only on the configuration of the curve and does not depend on the initial normal scale used.

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Noether’s Approach to Elasticity

Kobelev

2024

Mathematical Engineering

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Complex potentials and integral equations for curved crack and curved rigid line problems in plane elasticity

Cited by 14 publications

References 32 publications

Crack front position and crack back position techniques for evaluating theT-stress at crack tip using functions of a complex variable

Crack front position and crack back position techniques for evaluating theT-stress at crack tip using functions of a complex variable

Degenerate scale problem arising from curved rigid line inclusion

Noether’s Approach to Elasticity

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