A refined adaptive logistic-trigonometric shear deformation theory for the precise bending analysis of functionally graded plates

Abstract

This study presents a refined Logistic-Trigonometric Shear Deformation Theory (LTHT) for the bending and interlaminar stress analysis of functionally graded (FG) plates. The proposed theory utilizes a hybrid shape function that incorporates a logistic (sigmoid) component and a trigonometric distribution to represent transverse shear strain through the thickness. Unlike conventional higher-order theories with fixed kinematic assumptions, the LTHT introduces an adaptive parameter that is optimized to account for the asymmetric material distribution and the shifting neutral axis inherent in FG systems. The governing equations are derived using the principle of virtual work. Numerical results are obtained through an optimization framework that minimizes the variance between the proposed theory and reference solutions across a broad range of power-law indices and geometric aspect ratios. Benchmarking against 3D elasticity solutions demonstrates that the LTHT provides highly accurate predictions of displacements and continuous stress distributions. The results suggest that the adaptive nature of the logistic-trigonometric function offers a robust and computationally efficient paradigm for the structural analysis of advanced composite plates with high material gradients.