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| 圆内平面弹性问题的边界积分公式 | |
| 引用本文： | 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. |
| 作者姓名： | 董正筑 李顺才 余德浩 |
| 作者单位： | 1. 中国矿业大学,理学院,江苏,徐州,221008;中国科学院,计算数学与科学工程计算研究所,北京,100080 2. 中国矿业大学,理学院,江苏,徐州,221008;徐州师范大学,工学院,江苏,徐州,221011 3. 中国科学院,计算数学与科学工程计算研究所,北京,100080 |
| 基金项目： | 中国科学院科学基金资助项目(AMIV20032C05) |
| 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· |
| 关 键 词： | 圆内平面 弹性问题 双调和方程 应力函数 边界积分公式 |
| 文章编号： | 1000-0887(2005)05-0556-05 |
| 修稿时间： | 2003年9月30日 |
Boundary Integral Formula of the Elastic Problems in Circle Plane |
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| DONG Zheng-zhu,LI Shun-cai,YU De-hao.Boundary Integral Formula of the Elastic Problems in Circle Plane[J].Applied Mathematics and Mechanics,2005,26(5):556-560. | |
| Authors: | DONG Zheng-zhu LI Shun-cai YU De-hao |
| Institution: | DONG Zheng_zhu~ |
| 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. |
| Keywords: | elastic problem in circle plane bi_harmonic equation stress function boundary integral formula |
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