应用数学和力学2012，Vol.33Issue(2)：221-230,10.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
Eigenfunction Expansion Method of Upper Triangular Operator Matrix and Application to Two-Dimensional Elasticity Problems Based on Stress Formulation
摘要
Abstract
The eigenfunction expansion method to solve two-dimensional (2D) elasticity problems based on stress formulation was studied. The fundamental system of partial differential e-quations 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.关键词
本征函数展开法/二维弹性问题/上三角算子矩阵/一般解Key words
eigenfunction expansion method/ two-dimensional (2D) elasticity problem/ upper triangular operator matrix/ general solution分类
数理科学引用本文复制引用
额布日力吐,阿拉坦仓..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[J].应用数学和力学,2012,33(2):221-230,10.基金项目
高等学校博士学科点专项科研基金资助项目(20070126002) （20070126002）
国家自然科学基金资助项目(10962004) （10962004）
