The analytical bending solutions of orthotropic rectangular plates with four clamped edges by the symplectic superposition method

摘要

Abstract The bending problems of fully clamped orthotropic/isotropic rectangular plates with different thicknesses are uniformly solved by the symplectic superposition method. Firstly, the equilibrium equations of orthotropic rectangular moderately thick plates (RMTPs) are transformed into a Hamiltonian system. Then, by analyzing the boundary conditions and loads of the plates, the bending problems of the orthotropic RMTPs with four clamped edges are decomposed into two sub-problems under the condition of two opposite edges simply supported. The general solutions of the two subproblems are obtained by using the variable separation method in the Hamiltonian system. Finally by superposing the general solutions of the two subproblems, we get the bending symplectic superposition solutions of the fully clamped orthotropic RMTPs.