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Stress concentration of an ellipsoidal inclusion of revolution in a semi-infinite body under biaxial tension

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Summary

This paper deals with the stress concentration problem of an ellipsoidal inclusion of revolution in a semi-infinite body under biaxial tension. The problem is formulated as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where unknowns are densities of body forces distributed in ther- andz-directions in semi-infinite bodies having the same elastic constants as the ones of the matrix and inclusion. In order to satisfy the boundary conditions along the ellipsoidal boundary, four fundamental density functions proposed in [24, 25] are used. The body-force densities are approximated by a linear combination of fundamental density functions and polynomials. The present method is found to yield rapidly converging numerical results for stress distributiion along the boundaries even when the inclusion is very close to the free boundary. The effect of the free surface on the stress concentration factor is discussed with varying the distance from the surface, the shape ratio and the elastic modulus ratio. The present results are compared with the ones of an ellipsoidal cavity in a semi-infinite body.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Kyushu Institute of Technology, 804-8550, Kitakyushu, Japan

    Nao-Aki Noda & Yasuhiro Moriyama

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  1. Nao-Aki Noda
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  2. Yasuhiro Moriyama
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Correspondence to Nao-Aki Noda.

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Noda, NA., Moriyama, Y. Stress concentration of an ellipsoidal inclusion of revolution in a semi-infinite body under biaxial tension. Arch. Appl. Mech. 74, 29–44 (2004). https://doi.org/10.1007/BF02637207

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  • DOI: https://doi.org/10.1007/BF02637207

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