再论各向异性平面弹性中的一个周期接触问题——纪念李国平院士吴新谋教授诞辰100周年

数学物理学报 ›› 2010, Vol. 30 ›› Issue (5): 1194-1197.

再论各向异性平面弹性中的一个周期接触问题——纪念李国平院士吴新谋教授诞辰100周年

路见可|蔡海涛

武汉大学数学与统计学院武汉 430072；中南大学数学学院长沙 410083

收稿日期:2009-12-08 出版日期:2010-10-25 发布日期:2010-10-25

Reconsideration on a Periodic Contact Problem in Anisotropic Plane Elasticity

LU Jian-Ke, CAI Hai-Tao

School of Mathematics and Statistics, Wuhan University, Wuhan 430072； School of Mathematics, Central South University, Changsha 410083

Received:2009-12-08 Online:2010-10-25 Published:2010-10-25

摘要/Abstract

摘要：

该文对下面的一个弹性接触问题进行了再讨论.一列周期排列刚性压头压入一个各向异性弹性半平面的边界上,并有摩擦力存在, 求应力平衡.此问题在文献[1, 2]中曾讨论过并求出其解.但解法似不完全确切.该文将它进行修正从而获得精确解的封闭形式.

关键词: 周期各向异性问题, 摩擦, Riemann-Hilbert 边值问题, 接触

Abstract:

The following elastic contact problem is reconsidered. A series of periodic rigid stamps is pressed to the boundary of an anisotropic half-plane with friction. Find the stresses in equilibrium. The problem was considered and solved in [1, 2]. However, the method of solution is not exact.
In this note, it is modified so that the exact solution is obtained in closed form.

Key words: Periodic anisotroptic problem, Friction, Riemann-Hilbert boundary value problem, Contact

中图分类号:

74B05

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——纪念李国平院士吴新谋教授诞辰100周年[J]. 数学物理学报, 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.