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四边固支正交各向异性矩形薄板弯曲问题的辛叠加方法

额布日力吐 冯璐 阿拉坦仓

额布日力吐, 冯璐, 阿拉坦仓. 四边固支正交各向异性矩形薄板弯曲问题的辛叠加方法[J]. 应用数学和力学, 2018, 39(3): 311-323. doi: 10.21656/1000-0887.380092
引用本文: 额布日力吐, 冯璐, 阿拉坦仓. 四边固支正交各向异性矩形薄板弯曲问题的辛叠加方法[J]. 应用数学和力学, 2018, 39(3): 311-323. doi: 10.21656/1000-0887.380092
EBURILITU, FENG Lu, ALATANCANG. Analytical Bending Solutions of Clamped Orthotropic Rectangular Thin Plates With the Symplectic Superposition Method[J]. Applied Mathematics and Mechanics, 2018, 39(3): 311-323. doi: 10.21656/1000-0887.380092
Citation: EBURILITU, FENG Lu, ALATANCANG. Analytical Bending Solutions of Clamped Orthotropic Rectangular Thin Plates With the Symplectic Superposition Method[J]. Applied Mathematics and Mechanics, 2018, 39(3): 311-323. doi: 10.21656/1000-0887.380092

四边固支正交各向异性矩形薄板弯曲问题的辛叠加方法

doi: 10.21656/1000-0887.380092
基金项目: 国家自然科学基金(11362011;11371185;11761029); 内蒙古自然科学基金(2013MS0103)
详细信息
    作者简介:

    额布日力吐(1972—), 男, 蒙古族, 教授, 博士, 硕士生导师(通讯作者. E-mail: eburilitu@aliyun.com);冯璐(1993—), 女, 硕士生 (E-mail: 1657917548@qq.com);阿拉坦仓(1963—), 男, 蒙古族, 教授, 博士, 博士生导师(E-mail: alatanca@imu.edu.cn).

  • 中图分类号: O357.41

Analytical Bending Solutions of Clamped Orthotropic Rectangular Thin Plates With the Symplectic Superposition Method

Funds: The National Natural Science Foundation of China(11362011;11371185;11761029)
  • 摘要: 将正交各向异性矩形薄板方程化为Hamilton系统,利用分离变量法给出相应的无穷维Hamilton算子,进而计算出该无穷维Hamilton算子的本征值及对应的本征函数系, 并分别证明了本征函数系的辛正交性及完备性.之后利用辛叠加方法,求出正交各向异性矩形薄板弯曲问题的解析解.最后通过算例验证了所得解析解的正确性.
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出版历程
  • 收稿日期:  2017-04-10
  • 修回日期:  2017-05-04
  • 刊出日期:  2018-03-15

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