An enhanced finite element model for static bending analysis of functionally graded plates with power-law, exponential, and sigmoid material gradients

Abstract

This study presents a finite element model formulated to analyze accurately the bending behavior of functionally graded (FG) plates, employing an improved first-order shear deformation theory (FSDT). In contrast to the conventional Mindlin–Reissner theory, our enhanced FSDT incorporates a parabolic shear strain distribution, providing a more realistic depiction of shear strain throughout the plate’s thickness. Material properties of the FG plates are modeled to undergo continuous variation through the thickness, utilizing power law, exponential, and sigmoid distributions. The investigation focuses on assessing the impact of material composition and geometric parameters under both sinusoidal and uniformly distributed loads, considering various boundary conditions. Comparative analyses with previously published literature underscore the precision and simplicity of our model. The obtained results demonstrate strong agreement with solutions derived from other high-order theories, affirming the accuracy of our proposed model. This research contributes valuable insights into the bending behavior of FG plates and reinforces the reliability of the developed finite element model.