Angular basis functions formulation for 2D potential flows with non-smooth boundaries

Young, D. L.; Huang, Y.J.; Wu, Chi‐Shin; Sládek, V.; Sládek, J.

doi:10.1016/j.enganabound.2015.06.011

Cited by 8 publications

(7 citation statements)

References 17 publications

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“…Many researchers paid attention to the angle-type fundamental solution. In 2015, Young et al [12] used the ABF to solve potential flow problems. However, a branch-cut problem may result in the difficulty in choosing the location of screw dislocation.…”

Section: Introductionmentioning

confidence: 99%

“…However, a branch-cut problem may result in the difficulty in choosing the location of screw dislocation. Until 2018, Li et al [13] proposed a new approach (method of transformed ABF, MTABF) that can directly adopt source point distributions used in the traditional method of fundamental solutions to improve the method of ABF (MABF) proposed by Young et al [12]. In the same year, Alves et al [14] proposed a remedy which used a pair of two points to restrict the discontinuity appearing only along the line segment between two points, and they named this kind of singularity as cracklets.…”

Section: Introductionmentioning

confidence: 99%

“…[13] proposed a new approach (method of transformed ABF, MTABF) that can directly adopt source point distributions used in the traditional method of fundamental solutions to improve the method of ABF (MABF) proposed by Young et al. [12]. In the same year, Alves et al.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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show abstract

“…After that, many researchers paid attention to the angle-type fundamental solution. In 2015, Young et al [23] used the ABF to solve potential flow problems. However, a branch-cut problem may result in the difficulty in choosing the location of screw dislocation.…”

Section: Introductionmentioning

confidence: 99%

“…However, a branch-cut problem may result in the difficulty in choosing the location of screw dislocation. Until 2018, Li et al [24] proposed a new approach (MTABF) that can directly adopt source point distributions used in the traditional MFS to improve the method of angular basis function (MABF) proposed by Young et al [23]. In the same year, Alves et al [25] proposed a remedy which used a pair of two points to restrict the discontinuity appearing only along the line segment between two points, and they named this kind of singularity as cracklets.…”

Section: Introductionmentioning

confidence: 99%

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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Why dual boundary element method is necessary?

Chen

Yueh

Chang

et al. 2017

Engineering Analysis with Boundary Elements

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Angular basis functions formulation for 2D potential flows with non-smooth boundaries

Cited by 8 publications

References 17 publications

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 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

Why dual boundary element method is necessary?

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