On the stress concentration factor of circular/elliptic hole and rigid inclusion under the remote anti-plane shear by using degenerate kernels

Chen, Jeng‐Tzong; Kao, Jui-Hsiang; Huang, Yu‐Te; Kao, Shing‐Kai

doi:10.1007/s00419-020-01814-z

Cited by 14 publications

(11 citation statements)

References 20 publications

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“…where l denotes a magnified or a reduced factor. As ln t À t o j j in o xy = ln t À t o j j in o x d y d + ln l, substituting this relation into (11) yields…”

Section: Discussionmentioning

confidence: 99%

“…In computation N = 120 is used. The observation points t o in (11), (13), or (15) are assumed at the middle point of divisions, and are denoted by q 1 , q 2 ,.q N . Simply because of singular behavior for the function p(t(s)) at the rigid line tip, on the first division we can assume The similar expression is used for the last division p N p N + 1 .…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Similar to the single rigid curve case (see (11)), we can formulate the degenerate scale problem for the two rigid curves case, which is governed by the following BIE (Figure 5(a) and (b)):…”

Section: Formulation For the Degenerate Scale Problem For The Case Of Multiple Rigid Curvesmentioning

confidence: 99%

“…The stress concentration factor (SCF) along the boundary of a hole and a rigid inclusion in an infinite isotropic solid under the antiplane shear was studied by using the degenerate kernels in [11]. The crack and the rigid-line inclusion problems under the antiplane shear were solved in [12].…”

Section: Introductionmentioning

confidence: 99%

“…Figure 3. Discretization in the numerical solution of integral equation for the rigid curve with q j (j = 1,2,.,N) being the point t o in(11),(13), and(15).…”

mentioning

confidence: 99%

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Solution for the degenerate scale for a rigid curve in antiplane elasticity by using a weakly singular integral equation

2021

Mathematics and Mechanics of Solids

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This paper provides a numerical solution for the degenerate scale for a rigid curve in antiplane elasticity. The degenerate scale problem for the rigid curve is formulated on the usage of the logarithmic potential. After assuming the displacement to be a vanishing value along the rigid curve, the boundary integral equation (BIE) is formulated. The problem can be first formulated in the degenerate scale. After making a coordinate transform, we can obtain the relevant BIE in the ordinary scale. Finally, a numerical solution is achieved. Several numerical examples are provided. In addition, the degenerate scale problem for the multiple rigid curves is also solved.

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“…where l denotes a magnified or a reduced factor. As ln t À t o j j in o xy = ln t À t o j j in o x d y d + ln l, substituting this relation into (11) yields…”

Section: Discussionmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

Section: Formulation For the Degenerate Scale Problem For The Case Of Multiple Rigid Curvesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Figure 3. Discretization in the numerical solution of integral equation for the rigid curve with q j (j = 1,2,.,N) being the point t o in(11),(13), and(15).…”

mentioning

confidence: 99%

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Solution for the degenerate scale for a rigid curve in antiplane elasticity by using a weakly singular integral equation

2021

Mathematics and Mechanics of Solids

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Interaction between a screw dislocation and an elliptical hole or rigid inclusion by using the angular basis function

et al. 2022

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The complex‐valued fundamental solution ln(z) can be decomposed into the radial basis function (RBF) and the angular basis function (ABF). In this paper, not only the RBF but also the ABF are employed to solve the problem of interaction between a screw dislocation and an elliptical hole or rigid inclusion. The problem is decomposed into a free field with a screw dislocation and a boundary value problem subject to a specific boundary condition. The boundary value problem is solved by using the RBF and the boundary integral equation. Since the geometric shape is an ellipse, the degenerate kernel is expanded to a series form under the elliptic coordinates, while the unknown boundary densities are expanded to Fourier series. By combining the degenerate kernel and the null‐field integral equation, the boundary value problem can be easily solved. Finally, two examples are demonstrated to verify the validity of the present approach.

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Interaction between a screw dislocation and an elastic elliptical inhomogeneity by using the angular basis function

Chen

Lee

Kao

2022

Z. Angew. Math. Phys.

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The behavior of displacement field due to a screw dislocation is similar to the angular basis function (ABF) Arg(z). It is different from the radial basis function (RBF) ln(r) that is used to describe the velocity potential of a sink or source. Nevertheless, the complex-valued fundamental solution ln(z) contains the two parts of RBF ln(r) and ABF Arg(z). In this paper, not only the RBF in the null-field boundary integral equation (BIE) but also the ABF for the screw dislocation are employed to study the interaction between a screw dislocation and an elastic elliptical inhomogeneity. This problem is decomposed into a free field with a screw dislocation and a boundary value problem containing an elliptical inhomogeneity. The boundary value problem is solved by using the RBF and the null-field BIE. Since the geometric shape is an ellipse, the degenerate kernel is expanded to a series form under the elliptical coordinates, while the unknown boundary densities are expanded to eigenfunctions. By combining the degenerate kernel and the null-field BIE, the boundary value problem can be easily solved. The inconsistency between Sendeckyj [1] and Gong & Meguid [2] for the problem was also found by using the present approach. The error in [2] was also printed out. Finally, some examples are demonstrated to verify the validity of the present approach.

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On the stress concentration factor of circular/elliptic hole and rigid inclusion under the remote anti-plane shear by using degenerate kernels

Cited by 14 publications

References 20 publications

Solution for the degenerate scale for a rigid curve in antiplane elasticity by using a weakly singular integral equation

Solution for the degenerate scale for a rigid curve in antiplane elasticity by using a weakly singular integral equation

Interaction between a screw dislocation and an elliptical hole or rigid inclusion by using the angular basis function

Interaction between a screw dislocation and an elastic elliptical inhomogeneity by using the angular basis function

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