对边简支矩形薄板方程的算子半群方法

刘杰; 黄俊杰; 阿拉坦仓

doi:10.3879/j.issn.1000-0887.2015.07.006

对边简支矩形薄板方程的算子半群方法

doi: 10.3879/j.issn.1000-0887.2015.07.006

¹内蒙古大学数学科学学院, 呼和浩特 010021;²内蒙古大学满洲里学院, 内蒙古满洲里 021400

基金项目: 国家自然科学基金(11305097)；陕西省教育厅科研计划项目(2013JK0616)

详细信息

作者简介:
刘杰（1980—），男，蒙古族，讲师，博士生(E-mail: ljdzxx@sina.cn);黄俊杰（1979—），男，蒙古族，教授，博士生导师（通讯作者. E-mail: huangjunjie@imu.edu.cn);阿拉坦仓（1963—），男，蒙古族，教授，博士生导师.

中图分类号: O175.3
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出版历程
- 收稿日期: 2014-09-30
- 修回日期: 2015-05-09
- 刊出日期: 2015-07-15

An Operator Semigroup Method for Rectangular Plates With 2 Opposite Sides Simply Supported

¹School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P.R.China;²School of Manzhouli, Inner Mongolia University, Manzhouli, Neimenggu 021400, P.R.China

Funds: The National Natural Science Foundation of China(11305097)

摘要

摘要: 考虑弹性理论中对边简支矩形薄板方程，用算子半群方法求解问题.首先,将方程转换成抽象Cauchy问题.其次,构造空间框架并证明对应的算子矩阵生成压缩半群.最后,经Fourier变换,采用一致连续半群做逼近,进而给出对边简支矩形薄板方程的解析解.该方法自然蕴含着解的存在唯一性.
- 矩形板 /
- 抽象Cauchy问题 /
- C₀半群 /
- 解析解
Abstract: The problem of solving a rectangular thin plate with 2 opposite sides simply supported in elasticity theory by means of the operator semigroup method was addressed. First, the plate equations were transformed into the abstract Cauchy problem. Then, the Hilbert space was defined and it was proved that the corresponding operator matrix generates contraction semigroups. Finally, the uniformly continuous semigroup approximation was applied through the Fourier transform, and the analytical solutions to the equations were given. The method naturally implies the existence and uniqueness of the solution.
- rectangular plate /
- abstract Cauchy problem /
- C₀ semigroup /
- analytical solution

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参考文献(15)

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[2]	钟万勰. 弹性力学求解新体系[M]. 大连: 大连理工大学出版社, 1995.(ZHONG Wan-xie. A New Systematic Methodology for Theory of Elasticity [M]. Dalian: Dalian University of Technology Press, 1995.(in Chinese))
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[4]	LI Rui, ZHONG Yang, LI Ming. Analytic bending solutions of free rectangular thin plates resting on elastic foundations by a new symplectic superposition method[J]. Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences,2013,469(2153): 20120681.
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对边简支矩形薄板方程的算子半群方法

doi: 10.3879/j.issn.1000-0887.2015.07.006

作者简介:
刘杰（1980—），男，蒙古族，讲师，博士生(E-mail: ljdzxx@sina.cn);黄俊杰（1979—），男，蒙古族，教授，博士生导师（通讯作者. E-mail: huangjunjie@imu.edu.cn);阿拉坦仓（1963—），男，蒙古族，教授，博士生导师.

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An Operator Semigroup Method for Rectangular Plates With 2 Opposite Sides Simply Supported

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目录

留言板

对边简支矩形薄板方程的算子半群方法

doi: 10.3879/j.issn.1000-0887.2015.07.006

作者简介: 刘杰（1980—），男，蒙古族，讲师，博士生(E-mail: ljdzxx@sina.cn);黄俊杰（1979—），男，蒙古族，教授，博士生导师（通讯作者. E-mail: huangjunjie@imu.edu.cn);阿拉坦仓（1963—），男，蒙古族，教授，博士生导师.

计量

出版历程

An Operator Semigroup Method for Rectangular Plates With 2 Opposite Sides Simply Supported

计量

出版历程

目录

作者简介:
刘杰（1980—），男，蒙古族，讲师，博士生(E-mail: ljdzxx@sina.cn);黄俊杰（1979—），男，蒙古族，教授，博士生导师（通讯作者. E-mail: huangjunjie@imu.edu.cn);阿拉坦仓（1963—），男，蒙古族，教授，博士生导师.