| The bending problem of orthotropic rectangular thin plate under a uniform load with two adjacent free edges and the others clamped are solved by the symplectic superposition method.First,the eigenvalues and eigenfunction system of Hamiltonian operator with one side simply supported and the opposite side slidingly supported are calculated,and the symplectic orthogonality of the eigenfunction system and its completeness in the sense of Cauchy's principal value are verified.According to the completeness of the eigenfunction system,the general solution of the corresponding Hamiltonian canonical equation is obtained.Then,the analytical solution of the bending equation of orthotropic rectangular thin plate under a uniform load with two adjacent free edges and the others clamped is derived by the symplectic superposition method.Finally,the validity of the obtained analytical solution is verified by two specific examples. |
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