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Uniform fields inside two interacting non-parabolic and non-elliptical inhomogeneities

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Abstract

With the aid of conformal mapping for a doubly connected domain, we prove the existence of internal uniform stress fields inside two interacting elastic inhomogeneities: one of non-parabolic open shape and the other of non-elliptical closed shape, when the matrix is subjected to uniform remote anti-plane and in-plane stresses. The uniformity property is unconditional for anti-plane elasticity but conditional for plane elasticity. The internal uniform stress fields are independent of the specific open and closed shapes of the two inhomogeneities. Typical numerical examples are presented to demonstrate the feasibility and effectiveness of the proposed theory.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 11272121) and through a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada (Grant No: RGPIN – 2017 - 03716115112).

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Authors and Affiliations

  1. School of Mechanical and Power Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai, 200237, China

    Xu Wang & Ping Yang

  2. Department of Mechanical Engineering, University of Alberta, 10-203 Donadeo Innovation Centre for Engineering, Edmonton, AB, T6G 1H9, Canada

    Peter Schiavone

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  1. Xu Wang
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  2. Ping Yang
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  3. Peter Schiavone
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Correspondence to Xu Wang or Peter Schiavone.

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Wang, X., Yang, P. & Schiavone, P. Uniform fields inside two interacting non-parabolic and non-elliptical inhomogeneities. Z. Angew. Math. Phys. 71, 25 (2020). https://doi.org/10.1007/s00033-019-1245-5

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  • DOI: https://doi.org/10.1007/s00033-019-1245-5

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