Buckling Analysis of Thin Isotropic Rectangular Plate with Large Displacement Subject to Biaxial In-Plane Forces

Thin rectangular plates, due to their small thickness relative to length and width and their high strength-to-weight ratio, are widely used in structural elements such as ship hulls, bridge decks, and aircraft wings. They are prone to nonlinear buckling under compressive forces, especially under biaxial in-plane compressive loading with large displacements, where linear theories often fail and membrane stresses complicate analysis. This study aimed to formulate a general mathematical equation for buckling analysis of thin rectangular isotropic plates with large displacements subject to biaxial in-plane forces using the Ritz potential energy functional method, and incorporates both geometric and material nonlinearities. Based on the formulated general equation, a specific equation for an all-round simply supported (SSSS) plate was developed using polynomial displacement shape function to determine the stiffness characteristics. Numerical values for critical buckling and post-buckling loads under biaxial compression for a square plate case were obtained. To validate these results, a comparison with values in the literature was made and the results show high consistency. The uniaxial buckling deviations ranged 0.047–0.10%, while undeformed biaxial buckling coefficients across varying aspect ratios and loading ratios (n = Ny/Nx) showed near-zero differences. From the two studies used for comparison, the maximum deviation is 24.42% and the minimum deviation is 1.12%. This indicates that the new model is adequate. Also, the adequacy of this new equation can be judged based on the simplicity of the formulation, and the closed agreement of the obtained numerical results with established results in the literature. This research enhances theoretical understanding of nonlinear buckling in thin plates and offers practical insights for improving structural reliability and efficiency in civil, mechanical, aerospace, and marine engineering. Therefore, the conclusion is that the model is suitable for buckling and post-buckling analysis of thin rectangular isotropic plates.