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An arbitrarily shaped inclusion with uniform eigencurvatures in an infinite plate, semi-infinite plate, two bonded semi-infinite plates or a circular plate

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Abstract

Within the framework of the Kirchhoff–Love isotropic and homogeneous plate theory, we obtain, in a unified manner, the analytic solutions to the Eshelby’s problem of an inclusion of arbitrary shape with uniform eigencurvatures in an infinite plate, a semi-infinite plate, one of two bonded semi-infinite plates or a circular plate by means of conformal mapping and analytical continuation. The edge of the semi-infinite plate can be rigidly clamped, free or simply supported, while that of the circular plate can be rigidly clamped, free or perfectly bonded to the surrounding infinite plate. Several examples of practical and theoretical interests are presented to demonstrate the general method. In particular, the elementary expressions of the internal elastic fields of bending moments and deflections within an (n + 1)-fold rotational symmetric inclusion described by a five-term mapping function, a symmetric airfoil cusp inclusion, a symmetric lip cusp inclusion and an inclusion described by a rational mapping function in an infinite plate are derived.

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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

  2. School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore

    Kun Zhou

Authors
  1. Xu Wang
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  2. Kun Zhou
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Correspondence to Xu Wang.

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Wang, X., Zhou, K. An arbitrarily shaped inclusion with uniform eigencurvatures in an infinite plate, semi-infinite plate, two bonded semi-infinite plates or a circular plate. Z. Angew. Math. Phys. 66, 433–454 (2015). https://doi.org/10.1007/s00033-014-0408-7

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  • DOI: https://doi.org/10.1007/s00033-014-0408-7

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