Three-dimensional elasticity solution for bending of transversely isotropic functionally graded plates

Abstract

This paper presents a three-dimensional elasticity solution for a simply supported, transversely isotropic functionally graded plate subjected to transverse loading, with Young's moduli and the shear modulus varying exponentially through the thickness and Poisson's ratios being constant. The approach makes use of the recently developed displacement functions for inhomogeneous transversely isotropic media. Dependence of stress and displacement fields in the plate on the inhomogeneity ratio, geometry and degree of anisotropy is examined and discussed. The developed three-dimensional solution for transversely isotropic functionally graded plate is validated through comparison with the available three-dimensional solutions for isotropic functionally graded plates, as well as the classical and higher-order plate theories.

General thermo-elastic solution of radially heterogeneous, spherically isotropic rotating sphere

“…(27) are the system of non-homogeneous Euler differential equations with general and particular solutions. Hence, the general solutions can be written as follows: In which B and C are unknown constants determined by applying the given boundary condition.…”

“…Moreover, c ij 0 are the five independent constants of elasticity for the inner surface of transversely isotropic material. These parameters can be represented in terms of the engineering constants as [27], ( ) ( ) ( ) shear modulus in the plane of isotropy (i.e., any plane normal to the r-direction) at the inner surface. Also, 0 E and 0 G represent Young's modulus and shear modulus in any plane normal to the plane of isotropy at the inner surface.…”

A review of theories for the modeling and analysis of functionally graded plates and shells

“…The exact solutions for the 3D static bending analysis of FG plates were derived by Kashtalyan [353] and Woodward and Kashtalyan [354]. Exact solutions for the stresses and displacements of simply supported plates under transverse pressure were obtained using Plevako displacement functions.…”

A sampling surfaces method and its implementation for 3D thermal stress analysis of functionally graded plates

“…3-5 list the implementation of the numerical algorithm developed for a homogeneous isotropic plate by means of three MATLAB modules. The first module serves for the computation of Lagrange polynomials (8) and their derivatives (11). The second module provides the calculation of displacements and strains of sampling surfaces (17), (18), (19) and (21).…”

“…Another popular approach to 3D exact solutions, namely, asymptotic approach was applied efficiently to FG plates subjected to thermomechanical loading [8,9]. A new approach to closed-form elasticity solutions for FG isotropic and transversely isotropic plates is considered in papers [10,11]. These solutions are based on the general solution of the equilibrium equations of inhomogeneous elastic media [12].…”