Abstract
This chapter focuses on the solution methodology for plate bending classical theory, which is based on the analogy between plate bending and plane elasticity. The Hamiltonian system formulation can be applied to plate bending problems. The new methodology presents the analytical solutions in rectangular plate via the methods of separation of variables and eigenfunction-vector expansion; it breaks through the limitation of traditional semi-inverse solution. The results show that the new methodology will have vast application vistas. The new methodology applies bending moment function vector and differential, presenting a direct solution via the introduction of Hamiltonian system. The analogy between plate bending and plane elasticity can be applied to not only analytical solutions, but also to plate bending finite element; therefore,the plate bending finite element can be improved to the same level as plane elasticity.
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