Exact bending solutions of circular sandwich plates with functionally graded material-undercoated layer subjected to axisymmetric distributed loads

Abstract

In this study, the closed-form bending solutions of simply supported circular sandwich plates subjected to linearly or power-law, or partial uniform distributed loads are derived. The circular sandwich plate contains two homogeneous substrates and a functionally graded material-undercoated layer added between two homogeneous substrates. The Poisson’s ratio of the circular sandwich plates is assumed to be uniform. The Young’s moduli in the undercoated functionally graded material layer vary continuously throughout the thickness according to the volume fraction of constituents based on power-law, sigmoid, or exponential function. To solve the problem, first, the in-plane and bending problems of circular sandwich plate are uncoupled by properly choosing the origin of the z-axis such that the parameter [Formula: see text]. Then the fundamental bending solution of a simply supported circular sandwich plate under axisymmetric ring load is found based on the classical plate theory. Finally, by superposing the fundamental solutions, the closed-form bending solutions of circular sandwich plates under arbitrarily axisymmetric transverse loads are determined. Results reveal that the closed-form solutions agree very well with the finite element calculation and, when degenerated, coincide with the available solutions for isotropic homogenous plates in the literature. Moreover, the exact solutions of the circular sandwich plates subjected to axisymmetric transverse loads exhibit the relation of [Formula: see text] for the stresses [Formula: see text] and bending moments [Formula: see text]. The effects of the material gradient, the material distribution, and the thickness of the undercoated-functionally graded material layer on the mechanical behaviors of the circular sandwich plates are under investigation in detail.