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| 极坐标平面问题的四阶差分及应用 | |
| 引用本文： | 孟进军,高慧,董正筑.极坐标平面问题的四阶差分及应用[J].力学与实践,2004,26(6):63-65,13. |
| 作者姓名： | 孟进军 高慧 董正筑 |
| 作者单位： | 1. 中国矿业大学理学院,徐州,221008 2. 上海交通大学,上海,200030 3. 中国矿业大学理学院,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 |
| 摘 要： | 推导出了极坐标系下双调和方程的差分公式，用逐次超松弛迭代法求出圆板平面应力问题的差分解，并和解析解作比较，验证了差分公式的正确性，为解决圆域及其类似区域的平面问题提供了新方法． |
| 关 键 词： | 四阶 平面问题 差分解 类似 平面应力问题 双调和方程 阶差 公式 极坐标 推导 |
Fourth order difference of plane problem in polar coordinate system and its application |
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| MENG Jinjun GAO Hui DONG Zhengzhu.Fourth order difference of plane problem in polar coordinate system and its application[J].Mechanics and Engineering,2004,26(6):63-65,13. | |
| Authors: | MENG Jinjun GAO Hui DONG Zhengzhu |
| Abstract: | The difference formula of the bi-harmonic equation is derived in the polar coordinate system. The finite difference solution to the elastic plane problem of a disk is carried out by successive overrelaxation. By comparing with the theoretical solution of the problem, the validity of the difference formula is verified. The result provides a new and convenient way to solve the plane problem of disk and other similar shapes. |
| Keywords: | polar coordinate system elastic plane problem difference method bi-harmonic equation |
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