Elastoplastic buckling of thick rectangular plates: Hamiltonian system-based new analytical solutions

Investigating the elastoplastic buckling of thick plates is of great significance as the elastic buckling solutions usually consider an upper bound in design codes and tend to overestimate the critical load. However, due to the difficulty of solving high-order partial differential equations with nonlinear constitutive relations coupled with complex boundary conditions (BCs), the current analytical elastoplastic buckling solutions are specifically limited to the plates under Levy-type BCs. In this paper, the governing elastoplastic buckling equations of thick plates based on Mindlin's first-order shear deformation theory are formulated within the Hamiltonian system. Both the incremental theory (IT) and the deformation theory (DT) are utilized to account for plastic behaviors. Employing the symplectic eigen expansion method, we first obtain the elastoplastic buckling solutions under typical Levy-type BCs and verify their accuracy against existing literature. Further, new analytical solutions for the plates under five typical non-Levy-type BCs are presented by exploring the symplectic superposition method, demonstrating a high degree of agreement with the numerical solutions from the differential quadrature method. The mode shape solutions indicate that the half-wave numbers based on the elastic theory, the IT, and the DT are not identical. Based on the analytical solutions, we further examine the relationships between critical buckling stress factors and key parameters, including aspect ratio, thickness-to-width ratio, ratio of Young's modulus to nominal yield stress, and load ratio. The influence of shear deformation on critical buckling stresses is also investigated. The findings are helpful for the design of plates in engineering applications and the parameter selection in experiments.