On new buckling solutions of moderately thick rectangular plates by the symplectic superposition method within the Hamiltonian-system framework

摘要

This paper presents a first attempt to explore the symplectic superposition method for analytic buckling solutions of non-Levy-type moderately thick rectangular plates, which were hard to tackle by classical semi-inverse methods. In contrast with the conventional Lagrangian-system-based expression that is solved in the Euclidean space, this study describes the issue in the Hamiltonian system for treatment in the symplectic space. The follow-up solution procedure involves the conversion of an original problem into sub-problems with symplectic solutions and superposition for final analytic buckling solutions, where the constitution of symplectic eigenvalue problem and symplectic eigen expansion are crucial. Comprehensive buckling load and mode shape results for representative plates are tabulated or plotted, which are all well validated by satisfactory agreement with other solution methods. With the present solutions, parametric analysis has been investigated. Due to the advantages on strictness and accuracy, the developed method provides a solid approach for exploring new analytic solutions of similar problems.