| 矩形悬臂厚板的解析解 |
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| 引用本文： | 钟阳,张永山.矩形悬臂厚板的解析解[J].工程力学,2006,23(2):52-55,46. |
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| 作者姓名： | 钟阳 张永山 |
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| 作者单位： | 1. 大连理工大学,土木学院,大连,116012
2. 广州大学,土木学院,广州,510405 |
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| 摘 要： | 首先把胡海昌提出的弹性厚板弯曲问题的简化方程表示成为Hamilton正则方程,然后利用辛几何方法对全状态相变量进行分离变量,求出其本征值后,再按本征函数展开的方法求出矩形悬臂厚板的解析解。由于在求解过程中不需要事先人为地选取挠度函数,而是从厚板弯曲的基本方程出发,直接利用数学的方法求出可以满足其边界条件的这类问题的解析解,使得问题的求解更加合理论化。最后还给出了计算实例来验证所采用的方法以及所推导出的公式的正确性。
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| 关 键 词： | 矩形悬臂厚板 Hamilton正则方程 辛几何 分离变量 解析解 |
| 文章编号： | 1000-4750（2006）02-0052-04 |
| 收稿时间： | 2004-03-25 |
| 修稿时间： | 2004-03-252005-03-17 |
THEORETIC SOLUTION FOR RECTANGULAR CANTILEVER THICK PLATES BY SYMPLECTIC GEOMETRY METHOD |
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| ZHONG Yang,ZHANG Yong-shan.THEORETIC SOLUTION FOR RECTANGULAR CANTILEVER THICK PLATES BY SYMPLECTIC GEOMETRY METHOD[J].Engineering Mechanics,2006,23(2):52-55,46. |
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| Authors: | ZHONG Yang ZHANG Yong-shan |
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| Affiliation: | 1. Dalian University of Tech., Dalian 116024, China; 2. Guangzhuo University, Guangzhuo 510405, China |
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| Abstract: | A theoretic solution for rectangular cantilever thick plate is derived by symplectic geometry method. The simplified equations for elastic thick plate given by Hu are transferred into Hamilton canonical equations. The symplectic geometry method is used to separate the whole variables and the eigenvalues are obtained. With the method of eigen-function expansion, the explicit solution for rectangular cantilever thick plate is presented. Since the basic elasticity equations of thick plate is used only, the prior selection of the deformation function is rendered unnecessary. Therefore, the solution in the paper is more reasonable. A numerical example is presented to verify the present solution. |
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| Keywords: | rectangular cantilever thick plate Hamilton canonical equation symplectic geometry method variable separation theoretic solution |
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