| 应用虚拟功的互等定理求解均载悬臂厚矩形板的弯曲 |
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| 引用本文： | 常锦才,马醒花,李向东,杨爱民.应用虚拟功的互等定理求解均载悬臂厚矩形板的弯曲[J].数学的实践与认识,2006,36(8):160-167. |
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| 作者姓名： | 常锦才 马醒花 李向东 杨爱民 |
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| 作者单位： | 河北理工大学理学院,河北,唐山,063009 |
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| 摘 要： | 悬臂矩形板的弯曲问题一直是平板经典理论中的著名难题,利用中厚板虚拟功的互等定理,借助付宝连提出的角点静力边界条件,得到了均布载荷作用下悬臂厚矩形板弯曲的封闭解析解,并采用现代数值方法和计算软件对所得解析解进行了数值计算.结果表明功的互等法是求解中厚板弯曲问题的一个简明有效的方法.
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| 关 键 词： | 功的互等法 虚拟功的互等定理 中厚板弯曲 迭代改善法 |
| 修稿时间： | 2005年10月20 |
The Calculation of Thick Cantilever Rectangular Plate By Virtual Reciprocal Theorem |
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| CHANG Jin-cai,MA Xing-hua,LI Xiang-dong,YANG Ai-min.The Calculation of Thick Cantilever Rectangular Plate By Virtual Reciprocal Theorem[J].Mathematics in Practice and Theory,2006,36(8):160-167. |
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| Authors: | CHANG Jin-cai MA Xing-hua LI Xiang-dong YANG Ai-min |
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| Abstract: | The bending of cantilever rectangular plate used to be a difficult problem in the classical theories of plates.This paper obtains the closed analytical solutions to the bending of cantilever thick rectangular plate under uniform pressure by virtual reciprocal theorem,with the help of the exact static conditions at corner points which was found by Fu Baolian.Serials of numerical values are given by applying modern computational methods and software.Analysis and calculation show that reciprocal theorem method is simple and effective for the problems of the bending of thick plate. |
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| Keywords: | reciprocal theorem method virtual reciprocal theorem bending of thick plate ill-conditioned problems modified iteration method |
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