一维六方准晶的两类周期接触问题

马小丹; 李星

doi:10.21656/1000-0887.370029

一维六方准晶的两类周期接触问题

doi: 10.21656/1000-0887.370029

马小丹,
李星

宁夏大学数学计算机学院, 银川 750021

基金项目: 国家自然科学基金(11362018; 11261045; 11261041)；高等学校博士学科点专项科研基金(20116401110002)

详细信息

作者简介:
马小丹(1992—)，女，回族，硕士生(E-mail: 958262794@qq.com)；李星(1964—)，男，教授，博士，博士生导师(通讯作者. E-mail: li_x@nxu.edu.cn).

中图分类号: O343
计量
- 文章访问数: 1138
- HTML全文浏览量: 155
- PDF下载量: 575
- 被引次数: 0
出版历程
- 收稿日期: 2016-01-20
- 修回日期: 2016-04-13
- 刊出日期: 2016-07-15

Kinds of Periodic Contact Problems of 1D Hexagonal Quasicrystals

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

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

摘要

摘要: 利用复变函数方法讨论了一维六方准晶非周期平面的两类周期接触问题，即无摩擦周期接触以及半平面粘结周期接触问题.利用Hilbert核积分公式，得到了两类周期接触问题封闭形式的解.对于无摩擦周期接触问题，给出了3种常见压头（周期直水平基底、周期直倾斜基底、周期圆基底）作用下接触应力的显式表达式；对于半平面粘结周期接触问题，给出了实际工程中常见的边界上有尖劈形周期位移情况下应力的解析表达式.当忽略相位子场的贡献时，结果与正交各向异性材料周期接触问题的相应结果一致.
- 一维六方准晶 /
- 非周期平面 /
- 周期接触问题 /
- 复变函数方法 /
- Hilbert核积分公式
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

HTML全文

参考文献(13)

[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))