Asymptotical Construction of an Efficient High-Fidelity Model for Functionally Graded Plates

Abstract

This paper constructs an e‐cient high-fldelity model for plates made of functionally graded material. By taking advantage of an inherent small parameter, the ratio of the thickness to the characteristic wavelength of the deformation of the reference surface, we apply the variational asymptotic method to rigorously decouple the original threedimensional anisotropic elasticity problem into a one-dimensional through-the-thickness analysis and a two-dimensional plate analysis. The through-the-thickness analysis provides constitutive relations for the plate analysis as well as the recovery information for the three-dimensional flelds, linking the original, complex three-dimensional anisotropic heterogeneous elasticity problem to a simple two-dimensional plate model which achieves the best compromise between e‐ciency and accuracy. Furthermore, the derived models are geometrically exact and valid for large deformations and global rotations with the restriction that strains are small. Excellent accuracy of present model has been validated by comparing the displacement and stress distributions with exact solutions both for the cylindrical bending of an isotropic plate and the behavior of a thick, simply-supported, two-constituent metal-ceramic functionally grated rectangular plate.