圆内平面弹性问题的边界积分公式

基金项目: 中国科学院科学基金资助项目(AMIV20032C05)

Boundary Integral Formula of the Elastic Problems in Circle Plane

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

摘要: 根据双解析函数可以得到单位圆内平面弹性问题应力函数的边界积分公式，但式中包含强奇异积分，不能用于直接计算．将边界上的应力函数展开为Fourier级数，再利用广义函数论中的几个公式进行卷积计算，可以得到不含强奇异积分核的边界积分公式，通过边界的应力函数值和法向导数的积分，直接得到圆内应力函数值，并给出几个算例，表明该结果用于求解单位圆内平面弹性问题十分方便．
- 圆内平面 /
- 弹性问题 /
- 双调和方程 /
- 应力函数 /
- 边界积分公式
Abstract: By bianalytic functions, the boundary integral formula of the stress function for the elastic problem in a circle plane is developed. But this integral formula includes a strongly singular integral and can not be directly calculated. After the stress function is expounded to Fourier series, making use of some formulas in generalized functions to the convolutions, the boundary integral formula which doesn't include strongly singular integral is derived further. Then the stress function can be got simply by the integration of the values of the stress function and its derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function for the elastic problem is convenient.
- elastic problem in circle plane /
- bi-harmonic equation /
- stress function /
- boundary integral formula /

[1]	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.
[2]	余德浩.自然边界元法的数学理论[M].北京：科学出版社，1993，184—186.
[3]	徐芝纶.弹性力学[M].北京：高等教育出版社，1990，124—126.
[4]	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.

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