上三角算子矩阵的本征函数展开法在应力形式的二维弹性问题中的应用

额布日力吐; 阿拉坦仓

doi:10.3879/j.issn.1000-0887.2012.02.007

上三角算子矩阵的本征函数展开法在应力形式的二维弹性问题中的应用

doi: 10.3879/j.issn.1000-0887.2012.02.007

内蒙古大学数学科学学院, 呼和浩特 010021

基金项目: 高等学校博士学科点专项科研基金资助项目（20070126002）;国家自然科学基金资助项目(10962004)

详细信息

通讯作者:
额布日力吐(1972—), 男, 内蒙古人, 副教授, 博士生(E-mail:nmgbeb@sohu.com);阿拉坦仓(1963—), 男, 内蒙古人, 教授, 博士, 博士生导师(联系人.E-mail:alatanca@imu.edu.cn).

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出版历程
- 收稿日期: 2011-02-25
- 修回日期: 2011-12-01
- 刊出日期: 2012-02-15

Eigenfunction Expansion Method of Upper Triangular Operator Matrix and Application to Two-Dimensional Elasticity Problems Based on Stress Formulation

School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P.R.China

摘要

摘要: 深入研究了求解基于应力形式的二维弹性问题的本征函数展开法．根据已有的研究结果,将基于应力形式的二维弹性问题的基本偏微分方程组等价地转化为上三角微分系统,并导出了相应的上三角算子矩阵．通过深入研究,分别获得了该算子矩阵的两个对角块算子更为简洁的正交本征函数系,并证明了它们在相应空间中的完备性,进而应用本征函数展开法给出了该二维弹性问题的更为简洁实用的一般解．此外,对该二维弹性问题,还指出了什么样的边界条件可以应用此方法求解．最后应用具体的算例验证了所得结论的合理性．
- 本征函数展开法 /
- 二维弹性问题 /
- 上三角算子矩阵 /
- 一般解
Abstract: The eigenfunction expansion method to solve twodimensional (2D) elasticity problems based on stress formulation was studied. The fundamental system of partial differential equations of the 2D problems was rewritten as an upper triangular differential system based on the known results, and then the associated upper triangular operator matrix was obtained. By further researching, the two simpler complete orthogonal systems of eigenfunctions in some space were obtained, which belong to the two block operators arising in the operator matrix. Then a more simple and convenient general solution for the 2D problem was given by the eigenfunction expansion method. Furthermore, it was indicated what boundary conditions for the 2D problem can be solved by this method. Finally, the validity of the obtained results was verified by a specific example.
- eigenfunction expansion method /
- two-dimensional (2D) elasticity problem /
- upper triangular operator matrix /
- general solution

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参考文献(14)

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上三角算子矩阵的本征函数展开法在应力形式的二维弹性问题中的应用

doi: 10.3879/j.issn.1000-0887.2012.02.007

通讯作者:
额布日力吐(1972—), 男, 内蒙古人, 副教授, 博士生(E-mail:nmgbeb@sohu.com);阿拉坦仓(1963—), 男, 内蒙古人, 教授, 博士, 博士生导师(联系人.E-mail:alatanca@imu.edu.cn).

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Eigenfunction Expansion Method of Upper Triangular Operator Matrix and Application to Two-Dimensional Elasticity Problems Based on Stress Formulation

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上三角算子矩阵的本征函数展开法在应力形式的二维弹性问题中的应用

doi: 10.3879/j.issn.1000-0887.2012.02.007

通讯作者: 额布日力吐(1972—), 男, 内蒙古人, 副教授, 博士生(E-mail:nmgbeb@sohu.com);阿拉坦仓(1963—), 男, 内蒙古人, 教授, 博士, 博士生导师(联系人.E-mail:alatanca@imu.edu.cn).

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出版历程

Eigenfunction Expansion Method of Upper Triangular Operator Matrix and Application to Two-Dimensional Elasticity Problems Based on Stress Formulation

计量

出版历程

目录

通讯作者:
额布日力吐(1972—), 男, 内蒙古人, 副教授, 博士生(E-mail:nmgbeb@sohu.com);阿拉坦仓(1963—), 男, 内蒙古人, 教授, 博士, 博士生导师(联系人.E-mail:alatanca@imu.edu.cn).