New Buckling Analysis of Non-Lévy-Type Rectangular Plates with Point Supports: Analytical Solutions

This paper focuses on the buckling behavior of non-Lévy-type rectangular thin plates with point supports, which are widely used in engineering but were rarely studied by analytical methods. The governing equations based on the Hamiltonian system are presented to facilitate the application of the mathematical techniques within the symplectic space. Specifically, the separation of variables, symplectic eigenvalue solutions, and superposition are employed. The analytical solutions of the non-Lévy-type plates are derived from a set of equations equivalent to the superposition of three subproblems. The buckling loads and buckling modes for the non-Lévy-type plates involving clamped/simply supported edges with point supports have been obtained as benchmarks. The strong agreement with the finite element analysis provides validation for both the effectiveness and accuracy of the analytical solutions. The new buckling solutions and a parametric analysis result in some novel conclusions. The present solution framework can be further expanded to address more complex problems which are beyond the capabilities of conventional analytical approaches.