Study on hierarchical models for functionally graded plate-like structures by natural element method

Hierarchical models for three-layered metal-ceramic functionally graded (FG) plate-like structures are introduced and numerically implemented by two-dimensional natural element method (NEM). The study was motivated by the report that the classical theories of plate are insufficient to accurately analyze these structures, and the meshfree methods are limited to 2-D problems because of a difficulty in generating 3-D grid. In the hierarchical models, the thickness-wise displacement variation is assumed using monomials, while the in-plane part of displacement field which is defined on the structure mid-surface is interpolated by 2-D NEM. Hierarchical models are distinguished by the highest order of thickness monomials, called by the model order, and the modeling accuracy increases with the model order. The natural element approximation is performed by generating NEM grid on the structure mid-surface, and the mechanical characteristics of metal-ceramic functionally graded plate-like structures are examined to the structure thickness, the model order and the material index of metal volume fraction. From the present study, it was found that hierarchical models show the model accuracy which is consistent with the 3-D elasticity, and the structural behavior is remarkably influenced by the relative thickness of graded layer and the distribution pattern of volume fractions.