圆外平面弹性问题的边界积分公式

Boundary Integral Formula for the Elastic Plane Problem of Exterior Circular Domain

College of Science, China University of Mining & Technology, Xuzhou, Jiangsu 221008, P. R. China;

摘要: 将边界上的应力函数及其法向导数展开为罗朗级数，与复应力函数的罗朗级数的表达式对比，可以确定罗朗级数的各系数，再利用傅利叶级数和卷积的几个公式进行计算，得到应力函数边界积分公式．通过边界的应力函数及其法向导数的积分，直接得到圆外应力函数值，并给出几个算例，表明结果用于求解单位圆外平面弹性问题十分方便．
- 圆外平面弹性问题 /
- 双调和方程 /
- 傅利叶级数 /
- 应力函数 /
- 边界积分公式
Abstract: After the stress function and its normal derivative on the boundary for the plane problem of exterior circular domain are expanded into Laurent series, comparing them with the Laurent series of the complex stress function and making use of some formulas in Fourier series and in the convolutions, the boundary integral formula of the stress function is derived further. Then the stress function can be obtained directly by the integration of the stress function and its normal derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function is convenient to be used for solving the elastic plane problem of exterior circular domain.
- elastic plane problem of exterior circular domain /
- bi-harmonic equation /
- Fourier series /
- stress function /
- boundary integral formula

[1]	徐芝纶.弹性力学[M].北京：高等教育出版社，1990，101，118—133，213.
[2]	武际可，王敏中，王炜.弹性力学引论[M].北京：北京大学出版社，2000，167—168.
[3]	唐寿高，曹志远.半无限及含孔无限平面在各种边界条件下的复位势基本解[J].应用数学和力学，1998,19(4)：311—319.
[4]	余德浩.自然边界元法的数学理论[M].北京：科学出版社，1993，93，202.
[5]	郑神州，郑学良.双解析函数、双调和函数和平面弹性问题[J].应用数学和力学，2000,21(8)：797—802.
[6]	董正筑，李顺才，余德浩.圆内平面弹性问题的边界积分公式[J].应用数学和力学,2005,26(5)：556—560.

点击查看大图