摘要
给出求解基于应力形式的二维弹性问题的本征函数展开方法.通过引入适当的状态函数,将该问题的基本偏微分方程等价地转化为上三角微分系统,导出相应的上三角算子矩阵.证明了该矩阵的两个对角块算子均具有规范的正交本征函数系,并得到它们在相应空间中的完备性.此外,基于本征函数系的完备性,应用本征函数展开法给出了二维弹性问题的一般解.
Eigenfunction expansion method of solving two-dimensional elasticity problems was proposed based on stress formulation. By introducing appropriate state functions,the fundamental system of partial differential equations of the above two-dimensional problems was rewritten as an upper triangular differential system. For the associated operator matrix,the existence and completeness of two normed orthogonal eigenfunction systems in some space are obtained,which belong to the two block operators arising in the operator. Moreover,the general solution of the proceeding two-dimensional problem is given by the eigenfunction expansion method.
出处
《应用数学和力学》
CSCD
北大核心
2010年第8期992-1000,共9页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目(10962004)
高等学校博士学科点专项科研基金资助项目(20070126002)
教育部留学回国人员科研启动基金资助项目
教育部‘春晖计划’资助项目(Z2009-1-01010)
内蒙古自治区自然科学基金资助项目(2009BS0101)
内蒙古大学‘211工程’创新人才培养基金资助
关键词
本征函数展开法
二维弹性问题
上三角微分系统
一般解
eigenfunction expansion method
two-dimensional elasticity problem
upper triangular differential system
general solution
