Eigenfunction expansion method of upper triangular operator matrixand application to two-dimensional elasticity problems based onstress formulation  

作　　者：额布日力吐 阿拉坦仓 

机构地区：[1]School of Mathematical Sciences,Inner Mongolia University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2012年第2期223-232,共10页应用数学和力学（英文版）

基　　金：supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20070126002);the National Natural Science Foundation of China (No. 10962004)

摘　　要：This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.

关 键 词：eigenfunction expansion method two-dimensional （2D） elasticity problem upper triangular operator matrix general solution 

分 类 号：O175[理学—数学] O343[理学—基础数学]