Symplectic superposition solution for the buckling problem of orthotropic rectangular plates with four clamped edges

The main objective of this study is to uniformly solve the buckling problem of fully clamped (CCCC) orthotropic/isotropic rectangular plates with different thicknesses. The analysis uses the symplectic superposition method. This method describes the buckling problem of orthotropic rectangular moderately thick plates (RMTPs) in the Hamiltonian system for treatment in the symplectic space. First, the governing equations of RMTPs are represented by Hamiltonian canonical equations. Then, the original buckling problem of a CCCC rectangular moderately thick plate (RMTP) is divided into two sub-buckling problems. The variable separation method in the Hamiltonian system is used to calculate the general solutions of these two sub-buckling problems. The symplectic superposition solution of the original buckling problem is obtained by superimposing the general solutions of the two sub-buckling problems. Finally, the analysis results of the buckling load and modal shape of orthotropic rectangular plates under various thicknesses and aspect ratios are presented in numerical examples.