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Mathematical methods for a class of mixed boundary-value problems of planar pentagonal quasicrystal and some solutions

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Abstract

The mathematical theory of elasticity for planar pentagonal quasicrystals is developed and some analytic solutions for a class of mixed boundary-value problems (corresponding to a Griffith crack) of the theory are offered. An alternate procedure and a direct integral approach are proposed. Some analytical solutions are constructed and the stress and displacement fields of a Griffith crack in the quasicrystals are determined. A basis for further studying the mechanical behavior of the material related to planar defects is provided.

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Authors and Affiliations

  1. Research Center of Materials Science, Beijing Institute of Technology, 100081, Beijing, China

    Tianyou Fan & Yucui Guo

Authors
  1. Tianyou Fan
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  2. Yucui Guo
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Project supported by the Foundation of State Education Commission of China for Doctorate Station.

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Fan, T., Guo, Y. Mathematical methods for a class of mixed boundary-value problems of planar pentagonal quasicrystal and some solutions. Sci. China Ser. A-Math. 40, 990–1003 (1997). https://doi.org/10.1007/BF02878680

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  • DOI: https://doi.org/10.1007/BF02878680

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