New Analytical Solutions for Elastoplastic Buckling of Non-Lévy‐Type Rectangular Plates

Abstract

Analytical solutions for elastoplastic buckling of plates play a crucial role in providing benchmark results and facilitating fast structural analyses for preliminary designs. However, the analytical solutions for elastoplastic buckling of plates remain incomplete due to the inherent mathematical difficulties associated with higher-order partial differential equations and material nonlinearity. Consequently, the existing analytical solutions for rectangular plates are only applicable to those with Lévy‐type boundary conditions. To address the limitation, this study extends a novel symplectic superposition method to obtain new analytical elastoplastic buckling solutions of non-Lévy‐type rectangular plates, where both the incremental theory (IT) and deformation theory (DT) are adopted. Comprehensive benchmark elastoplastic buckling loads are presented and validated by the modified differential quadrature method. The plastic buckling paradox is explicitly observed, which highlights a significant disparity between the IT and DT in predicting buckling loads for relatively thick plates. Furthermore, our analysis reveals that the DT provides an optimal load ratio for buckling resistance, while no such finding is observed with the IT. The stability criterion curves are plotted using the elastic theory and plastic theories (IT and DT) to further reveal the importance of incorporating the effect of plasticity as well as to provide a useful guideline for the relevant analyses and designs.