A separable Hamiltonian system of Mindlin plate bending problems is obtained. Using the equivalence between the differen form and integral form of the separable Hamiltonian system, the biorthogonal relationships of th...A separable Hamiltonian system of Mindlin plate bending problems is obtained. Using the equivalence between the differen form and integral form of the separable Hamiltonian system, the biorthogonal relationships of the eigenfunctions are presen! Based on the biorthogonal relationships, a novel complete biorthogonal expansion of the Mindlin plate bending problems x~ two opposite sides simply supported is proposed through the products of operator matrices. The exact solutions to deflections bending moments for the Mindlin plate with fully simply supported sides are obtained. A numerical example is illustrated to ve~ the accuracy and validity of the expansion method.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 10962004)the Natural Science Foundation of Inner Mongolia Autonomous Region of China (Grant No. 2012MS0105)
文摘A separable Hamiltonian system of Mindlin plate bending problems is obtained. Using the equivalence between the differen form and integral form of the separable Hamiltonian system, the biorthogonal relationships of the eigenfunctions are presen! Based on the biorthogonal relationships, a novel complete biorthogonal expansion of the Mindlin plate bending problems x~ two opposite sides simply supported is proposed through the products of operator matrices. The exact solutions to deflections bending moments for the Mindlin plate with fully simply supported sides are obtained. A numerical example is illustrated to ve~ the accuracy and validity of the expansion method.
