A robust five-unknowns higher-order deformation theory optimized via machine learning for functionally graded plates

Abstract

This article presents a new kind of higher-order deformation theory, called Parametric Higher-order Deformation Theory (PHDT), for the static analysis of functionally graded plates (FGPs). The novelty of the PHDT is the use of strain shape functions that are calibrated by a set of tuning parameters to approximate 3D results along the plate thickness. The tuning parameters are assumed to vary with side-to-thickness ratios and power-law indexes. In contrast to higher-order shear deformation theories (HSDTs), the PHDT is not mathematically constrained to satisfy the traction-free boundary condition on the bottom plate’s surface. The proposed plate model is based on a 5-unknown HSDT previously presented by one of the authors. The governing equations are derived from the principle of virtual works, and Navier-type closed form solutions have been obtained for simply supported FGPs subjected to bisinuisoidal transverse pressure. A general methodology that uses genetic algorithms to determine the optimal tuning parameters of PHDTs for FGPs with various side-to-thickness ratios and power-law indexes is presented. The accuracy of the PHDT is assessed by comparing the results of numerical examples with a 3D elasticity solution, HSDTs reported in the literature, and the well-known Carrera Unified Formulation. The results show that quasi-3D displacement and stress distribution are obtained using a set of tuning parameters to form adaptable strain shape functions that are optimized for the given structural problem.