Eburilitu, Alatancang. Eigenfunction Expansion Method of Upper Triangular Operator Matrix and Application to Two-Dimensional Elasticity Problems Based on Stress Formulation[J]. Applied Mathematics and Mechanics, 2012, 33(2): 221-230. doi: 10.3879/j.issn.1000-0887.2012.02.007
Citation: Eburilitu, Alatancang. Eigenfunction Expansion Method of Upper Triangular Operator Matrix and Application to Two-Dimensional Elasticity Problems Based on Stress Formulation[J]. Applied Mathematics and Mechanics, 2012, 33(2): 221-230. doi: 10.3879/j.issn.1000-0887.2012.02.007

Eigenfunction Expansion Method of Upper Triangular Operator Matrix and Application to Two-Dimensional Elasticity Problems Based on Stress Formulation

doi: 10.3879/j.issn.1000-0887.2012.02.007
  • Received Date: 2011-02-25
  • Rev Recd Date: 2011-12-01
  • Publish Date: 2012-02-15
  • The eigenfunction expansion method to solve twodimensional (2D) elasticity problems based on stress formulation was studied. The fundamental system of partial differential equations 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.
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