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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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(13)

References

[1]	FAN Tian-you. Mathematical Theory of Elasticity of Quasicrystals and Its Applications[M]. Beijing: Science Press, 2010.
[2]	郭俊宏, 刘官厅. 一维六方准晶中带双裂纹的椭圆孔口问题的解析解[J]. 应用数学和力学, 2008,29(4): 439-446.(GUO Jun-hong, LIU Guan-ting. Analytic solutions of problem about an elliptic hole with two straight cracks in one-dimensional hexagonal quasicrystals[J]. Applied Mathematics and Mechanics,2008,29(4): 439-446.(in Chinese))
[3]	LI Xian-fang, SUN Ying-fei, FAN Tian-you. Elastic field of a straight dislocation in one-dimensional hexagonal quasicrystals[J]. Journal of Beijing Institute of Technology,1999,8(1): 65-70.
[4]	赵雪芬, 李星. SH波对一维六方准晶中直裂纹的散射[J]. 计算力学学报, 2015,32(5): 693-698.(ZHAO Xue-fen, LI Xing. The scattering of SH wave on a linear crack in one-dimensional hexagonal quasicrystal[J]. Chinese Journal of Computational Mechanics,2015,32(5): 693-698.(in Chinese))
[5]	Peng Y Z, Fan T Y. Crack and indentation problems for one-dimensional hexagonal quasicrystals[J]. The European Physical Journal B,2001,21(1): 39-44.
[6]	尹姝媛, 周旺民, 范天佑. 八次对称二维准晶材料接触问题[J]. 力学季刊, 2002,23(2): 255-259.(YIN Shu-yuan, ZHOU Wang-ming, FAN Tian-you. Contact problem in octagonal two-dimensional quasicrystalline material[J]. Chinese Quarterly of Mechanics,2002,23(2): 255-259.(in Chinese))
[7]	ZHOU Wang-ming, FAN Tian-you. Contact problem in decagonal two-dimensional quasicrystal[J]. Journal of Beijing Institute of Technology,2001,10(1): 51-55.
[8]	ZHOU Wang-min, FAN Tian-you, YIN Shu-yuan. Axisymmetric contact problem of cubic quasicrystalline materials[J]. Acta Mechanica Solida Sinica,2002,15(1): 68-74.
[9]	GAO Yang, Ricoeur A. Three-dimensional Green’s function for two-dimensional quasi-crystal bimaterials[J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences,2011,467(2133): 2622-2642.
[10]	王旭, 张俊乾, 郭兴明. 点群10 mm十次对称二维准晶中的两类接触问题[J]. 力学学报, 2005,37(2): 169-174.(WANG Xu, ZHANG Jun-qian, GUO Xing-ming. Two kinds of contact problems in decagonal quasicrystalline materials of point group 10 mm[J]. Acta Mechanica Sinica,2005,37(2): 169-174.(in Chinese))
[11]	刘士强. 复合材料弹性平面的周期接触问题[J]. 应用数学学报, 1992,15(3): 289-296.(LIU Shi-qiang. Problem of the periodic contact of bonded plane materials[J]. Acta Mathematicae Applicatae Sinica,1992,15(3): 289-296.(in Chinese))
[12]	路见可, 蔡海涛. 再论各向异性平面弹性中的一个周期接触问题[J]. 数学物理学报(A辑), 2010,30(5): 1194-1197.(LU Jian-ke, CAI Hai-tao. Reconsideration on a periodic contact problem in anisotropic plane elasticity[J]. Acta Mathematica Scientia(Series A),2010,30(5): 1194-1197.(in Chinese))
[13]	刘官厅, 何青龙, 郭瑞平. 一维六方准晶非周期平面内的平面应变理论[J]. 物理学报, 2009,58(S1): 118-123.(LIU Guan-ting, HE Qing-long, GUO Rui-ping. The plane strain theory for one-dimensional hexagonal quasicrystals in aperiodical plane[J]. Acta Physica Sinica,2009,58(S1): 118-123.(in Chinese))