Bending analysis of FG plates using trigonometric and Viola-Tornabene four parameters and different homogenization models

This study investigates the bending deflection and normal stress behavior of functionally graded (FG) plates under sinusoidal and uniform mechanical loading conditions. Three macroscopic volume fraction models are analyzed: the power law, trigonometric, and a newly developed four-parameter Viola-Tornabene formulation. Additionally, the effects of various micromechanical models, including the mixture law (Voigt model), Reuss model, Tamura model, and Mori-Tanaka model, on the composite behavior are examined. The governing equations are derived using higher-order shear and normal deformation plate theory, coupled with Navier's solution approach. The predictions of the macroscopic and micromechanical models are benchmarked against published numerical results, revealing the improved accuracy of the Viola-Tornabene model and the Mori Tanaka homogenization approach for certain plate configurations and loading cases. Comprehensive parametric studies elucidate the combined effects of ceramic content, plate geometry, loading profiles, and micromechanical considerations on the mechanics of FG plates. The findings highlight the potential of the Viola-Tornabene model and the Mori-Tanaka homogenization technique as efficient analytical tools for the design and analysis of FG plates.