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

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 differ...

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Bibliographic Details
Published in:Applied mathematics and mechanics 2010-08, Vol.31 (8), p.1039-1048
Main Author: 黄俊杰 阿拉坦仓 王华
Format: Article
Language:English
Subjects:
Applications of Mathematics
Classical Mechanics
Eigenfunctions
Elasticity
Fluid- and Aerodynamics
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Partial Differential Equations
Stresses
Two dimensional
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Summary: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.
ISSN:0253-4827
1573-2754
DOI:10.1007/s10483-010-1340-x