This study employs an advanced four-variable plate theory to examine the mechanical bending response of simply supported rectangular metal foam plates. With the rise of composite materials in the aerospace, automotive, and transportation sectors, there is a need for analytical techniques to model their performance in various environments. Functionally graded porous plates (FGPs) are composites with gradual variations in porosity. Nevertheless, few studies have systematically investigated the effects of geometric parameters and mechanical loadings on the mechanical properties of metal foam plates using plate theory. The aim of this study is to shed the light on the elastic bending behavior of imperfect plates under sinusoidal loading by applying a refined plate theory that incorporates both bending and shear components of transverse displacement into the kinematic framework. This formulation simplifies structural analysis by reducing the number of governing equations. Specifically, we analyze a simply supported imperfect metal-foam plate with two distinct porosity levels subjected to a sinusoidally distributed load. The results reveal intricate dependencies between plate geometry, thickness, and deflection behavior, including critical transitions at specific thickness ratios. The refined plate theory closely matches higher-order shear deformation theories, thereby justifying its accuracy and reliability. The findings advance the understanding of metal foam plate mechanics and enhance the design of structures particularly in aerospace and automotive engineering where accurate prediction of plate behavior is essential.
