The Biorthogonal Expansion Theorem For Some Problems Of Elasticity

The rectangular moderately thick plate bending problem is derived to separable Hamilton system by choosing proper dual vectors. Using the structural characteristics of off-diagonal Hamiltonian operator and the typical mechanical boundary conditions, the biorthogonal relationships of the eigenfunctions are presented. Applying the biorthogonal relationships, a complete biorthogonal expansion of the rectangular moderately thick plate bending problems with two opposites simply supported is established. Then, the numerical example shows the correctness of the biorthogonal expansion method. Finally, the general solutions of the rectangular plane elasticity problems with two opposite simply supported are obtained by applying the biorthogonal expansion theorem, and the feasibility of using the biorthogonal expansion method to solve the problem is proven.