Eigenfunction expansion method and its application to two-dimensional elasticity problems based on stress formulation  

作　　者：黄俊杰 阿拉坦仓 王华 

机构地区：[1]School of Mathematical Sciences, Inner Mongolia University [2]College of Sciences, Inner Mongolia University of Technology

出　　处：《Applied Mathematics and Mechanics(English Edition)》2010年第8期1039-1048,共10页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (No. 10962004);the Special-ized Research Fund for the Doctoral Program of Higher Education of China (No. 20070126002);the Chunhui Program of Ministry of Education of China (No. Z2009-1-01010);the Natural Science Foundation of Inner Mongolia (No. 2009BS0101)

摘　　要：This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.

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

分 类 号：O343[理学—固体力学]