| Winkler弹性地基上梁的精化理论 |
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| 引用本文： | 赵宝生,王敏中,于新.Winkler弹性地基上梁的精化理论[J].应用力学学报,2005,22(4):602-605. |
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| 作者姓名： | 赵宝生 王敏中 于新 |
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| 作者单位： | 1. 鞍山科技大学,鞍山,114044
2. 北京大学,北京,100871 |
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| 基金项目： | 国家自然科学基金(10372003)，辽宁省教育厅科学研究计划(2004F051)，鞍山科技大学董事会青年基金(004598) |
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| 摘 要： | 将Cheng精化理论推广到winkler弹性地基上梁的研究当中,对winkler弹性地基上的梁进行了精确的分析,给出其精化理论。首先将板内的位移利用中面上位移及其沿梁厚方向的梯度表示出来,并获得梁内应力张量。再利用winkler弹性地基条件和Lur'e算子方法,获得弹性地基上梁的控制方程。若略去控制方程中的高阶项,与弹性地基上欧拉-伯努利梁的挠度控制方程一致。
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| 关 键 词： | 精化理论 弹性地基 梁 Papkovich-Neuber通解 |
| 文章编号： | 1000-4939（2005）04-0602-04 |
| 收稿时间： | 2004-11-16 |
| 修稿时间： | 2004-11-162005-04-19 |
Refined Theory of Beam on Winkler Foundation |
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| Zhao Baosheng,Wang Minzhong,Yu Xin.Refined Theory of Beam on Winkler Foundation[J].Chinese Journal of Applied Mechanics,2005,22(4):602-605. |
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| Authors: | Zhao Baosheng Wang Minzhong Yu Xin |
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| Institution: | Zhao Baosheng~1 Wang Minzhong~2 Yu Xin~1 |
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| Abstract: | Cheng's refined theory is extended to investigate the beam on the elastic foundation,and an exact analysis for the beam on the elastic foundation is carried out.The expressions of the displacements and stress components are obtained in term of the midsurface displacement and the derivatives.With Lur'e method,the refined theory of the beam on the elastic foundation is aquired from the Winkler Foundation boundary conditions.If the higher-order terms are omitted,the deflection equation of the refined theory is degenerated into the classic governing equation of beam on the elastic foundation. |
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| Keywords: | refined theory the elastic foundation beam Papkovich-Neuber general solution |
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