Mathematical Approach for Verifying Buckling in Steel Plates.

A mathematical study was conducted to investigate the buckling of isotropic steel plates using instability theories. The First-Order Shear Deformation Theory (FSDT) and Higher-Order Shear Deformation Theory (HSDT) were employed to account for shear effects. These latter theories were adopted because they consider shear deformation with high precision, unlike classical theories that neglect this important action. The equilibrium equations, derived from Hamilton's principle, were used, and Navier-type solutions were preferred to calculate buckling loads under uniaxial or biaxial loading. Parametric variations and different buckling modes were investigated, and the results showed excellent agreement with existing references. The main objective of this study in civil engineering is to continuously find mathematical formulations to solve plate buckling problems with extreme accuracy and to predict buckling behavior in simulations, mimicking what happens to metallic structures. Keywords: Plate Buckling-Elastic Instability-Isotropic Metal Plate-First-Order Shear Deformation Theory (FSDT)-Higher-Order Shear Deformation Theory (HSDT).