Eigenfunction expansion method and its application to two-dimensional elasticity problems based on stress formulation |
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Authors: | Jun-jie Huang Alatancang Hua Wang |
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Affiliation: | 1. School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,P.R.China 2. School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,P.R.China;College of Sciences,Inner Mongolia University of Technology,Hohhot 010051,P.R.China |
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Abstract: | This paper proposes an eigenfunction expansion method to solve two-dimensional(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. |
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Keywords: | eigenfunction expansion method two-dimensional(2D)elasticity problem upper triangular differential system general solution |
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