Analysis of functionally graded plates

TLDR

The plates are assumed to have isotropic, two‑constituent material distribution through the thickness, with the modulus of elasticity varying according to a power‑law distribution of the constituents' volume fractions. The study presents a theoretical formulation, Navier solutions for rectangular plates, and finite element models based on third‑order shear deformation theory to analyze through‑thickness functionally graded plates. The authors develop a third‑order shear deformation plate model that incorporates Navier solutions, finite element implementation, thermomechanical coupling, time dependence, and von Kármán geometric non‑linearity. Numerical simulations show that the power‑law material distribution affects deflections and stresses in both linear third‑order and nonlinear first‑order plate theories. © 2000 John Wiley & Sons, Ltd.

Abstract

Theoretical formulation, Navier's solutions of rectangular plates, and finite element models based on the third-order shear deformation plate theory are presented for the analysis of through-thickness functionally graded plates. The plates are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity of the plate is assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. The formulation accounts for the thermomechanical coupling, time dependency, and the von Kármán-type geometric non-linearity. Numerical results of the linear third-order theory and non-linear first-order theory are presented to show the effect of the material distribution on the deflections and stresses. Copyright © 2000 John Wiley & Sons, Ltd.