Study on the stress intensity factor and the double-degeneracy mechanism in the BEM/BIEM for anti-plane shear problems

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

doi:10.1016/j.tafmec.2020.102830

Cited by 13 publications

(3 citation statements)

References 38 publications

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“…In the literature [7], an analytical solution of the circular case was derived by Smith as shown in Eqs. (19) and (20). The screw dislocation is located at (1.2, 0) d = s…”

Section: The Present Methods -Degenerate Kernel Of the Angular Basis ...mentioning

confidence: 99%

“…Zheng et al [15] proposed a meshless local RBF collocation method to calculate the band structures of 2D anti-plane transverse elastic waves in photonic crystals. The RBF was used to interpolate the data as well as to solve the PDE in recent decades [16][17][18][19][20]. Since the conventional fundamental solution is also one kernel of the RBF, e.g.…”

Section: Introductionmentioning

confidence: 99%

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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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“…In the literature [7], an analytical solution of the circular case was derived by Smith as shown in Eqs. (19) and (20). The screw dislocation is located at (1.2, 0) d = s…”

Section: The Present Methods -Degenerate Kernel Of the Angular Basis ...mentioning

confidence: 99%

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 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]. In the study, the kernel can be expanded into the degenerate form by separating the source point and field point in the elliptic coordinates.…”

Section: Introductionmentioning

confidence: 99%

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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Weakly singular BIE-based procedure for T-stress analysis of cracks in 3D anisotropic linear elastic finite media

Sukulthanasorn

Watanavit

et al. 2022

Int J Fract

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Study on the stress intensity factor and the double-degeneracy mechanism in the BEM/BIEM for anti-plane shear problems

Cited by 13 publications

References 38 publications

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

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

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

Weakly singular BIE-based procedure for T-stress analysis of cracks in 3D anisotropic linear elastic finite media

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