Kinds of Periodic Contact Problems of 1D Hexagonal Quasicrystals

MA Xiao-dan; LI Xing

doi:10.21656/1000-0887.370029

Volume 37 Issue 7

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Article Navigation > Applied Mathematics and Mechanics > 2016 > 37(7): 699-709

MA Xiao-dan, LI Xing. Kinds of Periodic Contact Problems of 1D Hexagonal Quasicrystals[J]. Applied Mathematics and Mechanics, 2016, 37(7): 699-709. doi: 10.21656/1000-0887.370029

Citation:

MA Xiao-dan, LI Xing. Kinds of Periodic Contact Problems of 1D Hexagonal Quasicrystals[J]. Applied Mathematics and Mechanics, 2016, 37(7): 699-709. doi: 10.21656/1000-0887.370029

Citation:

MA Xiao-dan, LI Xing. Kinds of Periodic Contact Problems of 1D Hexagonal Quasicrystals[J]. Applied Mathematics and Mechanics, 2016, 37(7): 699-709. doi: 10.21656/1000-0887.370029

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Kinds of Periodic Contact Problems of 1D Hexagonal Quasicrystals

doi: 10.21656/1000-0887.370029

School of Mathematics and Computer Science, Ningxia University,Yinchuan 750021, P.R.China

Funds: The National Natural Science Foundation of China(11362018; 11261045; 11261041)

Received Date: 2016-01-20
Rev Recd Date: 2016-04-13
Publish Date: 2016-07-15

Abstract

Abstract

With the complex variable method, 2 kinds of periodic contact problems (the frictionless and the adhesive periodic contact problems) of 1D hexagonal quasicrystals in the aperiodic plane were discussed. Based on the Hilbert kernel integral formula, the closed-form solutions were obtained to the 2 kinds of periodic contact problems. In the frictionless case, the explicit solutions of contact stresses were given under the actions of 3 common basal punches (the straight horizontal, the straight inclined and the circular basal punches). In the adhesive case, the analytic solutions of contact stresses were given with the wedge-shaped periodic displacement at the contact boundary. If the effect of the phason field is neglected, the obtained results will match well with the corresponding solutions to the periodic contact problems of orthogonal anisotropic materials.
- 1D hexagonal quasicrystal,
- aperiodic plane,
- periodic contact problem,
- complex variable method,
- Hilbert kernel integral formula

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References

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