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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

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Abstract

The stress concentration factor (SCF) along the boundary of a hole and a rigid inclusion in an infinite isotropic solid under the anti-plane shear is revisited by using degenerate kernels in the boundary integral equation (BIE) although this result was obtained by invoking the extended circle theorem of Milne-Thomson as well as the complex variable approach. The degenerate kernel of series form for the closed-form fundamental solution is used for the circle and the ellipse in terms of polar and elliptic coordinates, respectively. The slender ratio of the ellipse and the orientation are two parameters for our study. The strain energy density along the boundary is increased or decreased due to the different types of loading and various aspect ratios of the ellipse. An analytical solution for the SCF is then derived for any orientation of the ellipse relative to the applied load. The reciprocal relation for the SCF between a hole and a rigid inclusion with respect to different loading is also addressed. Besides, this analytical derivation can clearly show the appearing mechanism why the BEM/BIEM suffers the degenerate scale in the rigid inclusion.

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Acknowledgements

Financial support from the Ministry of Science and Technology, Taiwan, under the Grant No. MOST106-2221-E-019-009-MY3 for the National Taiwan Ocean University is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, 20224, Taiwan

    Jeng-Tzong Chen, Jeng-Hong Kao, Yi-Ling Huang & Shing-Kai Kao

  2. Department of Mechanical and Mechatronic Engineering, National Taiwan Ocean University, Keelung, 20224, Taiwan

    Jeng-Tzong Chen

  3. Department of Civil Engineering, National Cheng Kung University, Tainan, 70101, Taiwan

    Jeng-Tzong Chen

  4. Bachelor Degree Program in Ocean Engineering and Technology, National Taiwan Ocean University, Keelung, 20224, Taiwan

    Jeng-Tzong Chen

  5. Center of Excellence for Ocean Engineering, National Taiwan Ocean University, Keelung, 20224, Taiwan

    Jeng-Tzong Chen

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  1. Jeng-Tzong Chen
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Chen, JT., Kao, JH., Huang, YL. et al. On the stress concentration factor of circular/elliptic hole and rigid inclusion under the remote anti-plane shear by using degenerate kernels. Arch Appl Mech 91, 1133–1155 (2021). https://doi.org/10.1007/s00419-020-01814-z

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  • DOI: https://doi.org/10.1007/s00419-020-01814-z

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